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Unformatted text preview: Business
Valuation
“Nowadays we know the price of
everything and the value of nothing.”
—Oscar Wilde Valuing the M&M Mushroom Company
Melissa and Mark were young and in love. They also shared a passion for
mushrooms. In fact, they were so passionate about mushrooms they liked
to grow them in their basement. They were quite good at it, and often had
more mushrooms than they knew what to do with. Then they had the idea
of selling their mushrooms to friends and neighbors. This endeavor was
successful beyond their wildest dreams and soon they had quite a business
going. The expanded out of their basement into dedicated production
facilities, incorporated under the name “M&M Mushrooms,” and became
quite famous in the local area for having the best tasting mushrooms around.
The M&M Mushroom Company grew steadily for ten years, enlarging
its sales territory to five states and employing 150 people in three plants.
That’s when the trouble began. Melissa wanted to keep expending the
business, but Mark missed the small, informal operation they used to have
years ago. Also, Mark had recently begun taking flying lessons and had
developed a close relationship with his flight instructor. Mark and Melissa
began spending more and more time apart, and began having more and
more disagreements, until it was apparent that everyone would be better
off if they went their separate ways.
The divorce was amicable, as Melissa and Mark had no children and
the only major assets they owned were their common stock shares in the
M&M Mushroom Corporation (Melissa and Mark each owned 50% of the
shares outstanding, 500 shares each). Since Melissa wanted to continue
managing the business and Mark wanted out, he agreed to sell her his
500 shares. However, they could not agree on a price. Melissa was of the
338 © Falko Matte (http://www.fotolia.com/p/5520) opinion that the shares were worth in the neighborhood of $1,000 each,
making the total value of Mark’s 500 shares $500,000. Mark disagreed.
Pointing to their steady growth during the past ten years, and current wide
area of operations, he maintained the shares were worth at least $2,000
each for a total of $1,000,000.
Melissa and Mark could not settle their differences on their own and soon
found themselves facing each other in court. The primary issue before the
court was to establish the “fair market value” of the shares in question. Each
side engaged an expert to provide an opinion on the value of the shares.
Now suppose you were approached by Melissa or Mark’s attorney and
asked if you would write a report containing an estimate of the fair market
value per share of M&M Mushroom company’s stock. How would you go
about this task? The stock is privately held, and not traded on any stock
exchange, so it would appear that you face a formidable task.
The valuation task is formidable, but it is not impossible. Indeed,
professional appraisers do it regularly, not only to support opposing sides
in court cases, but also to establish a value when the business is to be used
for collateral for a loan, an asking price when the sale of the business is
contemplated, or a value for tax purposes when the business is a part of
an estate settlement.
The techniques appraisers use to estimate market value vary from case to
case, but at their heart they generally involve the calculation of the present
value of an assumed set of future cash flows. You are already familiar with
this technique from your studies of the time value of money in Chapter 8. In
this chapter we show you how to adapt those techniques specifically to the
task of valuing stocks, bonds, and complete businesses.
339 Learning Objectives
After reading this chapter,
you should be able to:
1. Explain the importance of
business valuation.
2. Discuss the concept of
business valuation.
3. Compute the market value
and the yield to maturity of
a bond.
4. Calculate the market value
and expected yield of
preferred stock.
5. Compute the market value
per share of common stock.
6. Compute the market value
of total common equity.
7. Compute the yield on
common stock.
8. Compute the value of a
complete business. 340 Part III Capital Budgeting and Business Valuation Chapter Overview
In this chapter we will discuss how to value businesses in a dynamic marketplace. First,
we will investigate the importance of business valuation and introduce a general model
that analysts and investors use to value assets. Then we will show how to adapt the
model to bonds, preferred stock, and common stock. For common stock, we’ll explore
additional valuation techniques. The Importance of Business Valuation
As Chapter 1 explained, the primary financial goal of financial managers is to maximize
the market value of their firm. It follows, then, that financial managers need to assess
the market value of their firms to gauge progress.
Accurate business valuation is also a concern when a corporation contemplates
selling securities to raise longterm funds. Issuers want to raise the most money possible
from selling securities. Issuers lose money if they undervalue their businesses. Likewise,
wouldbe purchasers are concerned about businesses’ value because they don’t want to
pay more than what the businesses are worth. A General Valuation Model
The value of a business depends on its future earning power. To value a business then,
we consider three factors that affect future earnings:
• Size of cash flows • Timing of cash flows
• Risk These three factors also determine the value of individual assets belonging to
a business, or interests in a business, such as those possessed by bondholders and
stockholders.
In Chapter 7 we examined how risk factors affect an investor’s required rate of
return. In Chapter 8 we learned that time value of money calculations can determine
an investment’s value, given the size and timing of the cash flows. In Chapters 9, 10,
and 11 we learned how to evaluate future cash flows.
Financial managers determine the value of a business, a business asset, or an interest
in a business by finding the present value of the future cash flows that the owner of
the business, asset, or interest could expect to receive. For example, we can calculate
a bond’s value by taking the sum of the present values of each of the future cash flows
from the bond’s interest and principal payments. We can calculate a stock’s value by
taking the sum of the present values of future dividend cash flow payments.
Analysts and investors use a general valuation model to calculate the present value
of future cash flows of a business, business asset, or business interest. This model, the
discounted cash flow model (DCF), is a basic valuation model for an asset that is
expected to generate cash payments in the form of cash earnings, interest and principal
payments, or dividends. The DCF equation is shown in Equation 121: Chapter 12 Business Valuation The Discounted Cash Flow Valuation Model
V0 = where: CF1
+
(1 + k )1 CF2
+
(1 + k )2 CF3
+ ... +
(1 + k )3 CFn
(1 + k ) n (121) V0 = Present value of the anticipated cash flows from the asset, its
current value CF1, 2, 3, and n = Cash flows expected to be received one, two, three, and so on
up to n periods in the future
k = Discount rate, the required rate of return per period
The DCF model values an asset by calculating the sum of the present values of all
expected future cash flows.
The discount rate in Equation 121 is the investor’s required rate of return per time
period, which is a function of the risk of the investment. Recall from Chapter 7 that the
riskier the security, the higher the required rate of return.
The discounted cash flow model is easy to use if we know the cash flows and
discount rate. For example, suppose you were considering purchasing a security that
entitled you to receive payments of $100 in one year, another $100 in two years, and
$1,000 in three years. If your required rate of return for securities of this type were 20
percent, then we would calculate the value of the security as follows:
V0 = $100
+
(1 + .20)1 $100
+
(1 + .20)2 $1, 000
(1 + .20)3 = $83.3333 + $69.4444 + $578.7037
= $731.48 The total of the security’s three future cash flows at a 20 percent required rate of
return yields a present value of $731.48.
In the sections that follow, we’ll adapt the discounted cash flow valuation model to
apply to businesses and business components. Applying the General Valuation Model to Businesses
According to the general valuation model, Equation 121, the value of a business asset
is the present value of the anticipated cash flows from the asset. The value of a complete
business, therefore, is the present value of the cash flows expected to be generated by
the business. In order to use the general valuation model to estimate the value of a
complete business, we must forecast the cash flows expected to be generated by the
business and discount them to the present using the required rate of return appropriate
for the business. This sounds relatively simple, but in fact it is an extremely complex
task requiring the cash flow estimation techniques that you learned in Chapter 11 and
the cost of capital estimation techniques that you learned in Chapter 9.
Instead of tackling the value of a complete business all at once, we will begin with
the present values of the components of the business, as illustrated in Figure 121. 341 342 Part III Capital Budgeting and Business Valuation
Total Market Value of a Business
Value of Current Liabilities Figure 121
Total Market Value
of a Business Total Value
of
Business Assets This figure illustrates how the
total market value of a business
is the sum of the present values
of the components of the
business. Value of LongTerm Debt Value of Preferred Stock Value of Common Stockholders’ Equity As Figure 121 shows, the value of all of a businesses assets (that is, the complete
business) equals the sum of the present values of its current liabilities, longterm debt,
preferred stock, and common stock. In the remainder of this chapter, we will apply
this approach, first examining the valuation of current liabilities and longterm debt
(corporate bonds), then preferred stock, and finally common stock. Following those
individual discussions, we will show how the same techniques can be used to estimate
the total value of a business. Valuing Current Liabilities and LongTerm Debt
Current liabilities are shortterm obligations of a company that are fixed by agreement.
Accounts payable, for example, represents amounts that the company has purchased
from its suppliers and has agreed to pay for in a specified amount of time. Because the
time to maturity of these obligations is not lengthy, the market value of current liabilities
is most often taken to be equal to their book value. Therefore, when analysts value the
currentliability component of a complete business, they normally just read the value
of the current liabilities from the firm’s balance sheet.
LongTerm Debt A company’s longterm obligations may be longterm loans from a
commercial bank or a private investor, corporate bonds, or notes issued to the public. In
each case the value of the debt is the present value of the future cash flows that would
accrue to the owner of the debt, as we have explained previously. In this chapter we will
discuss the valuation of longterm debt when it is in the form of bonds. Bond Valuation
Remember from Chapter 2 that a bond’s cash flows are determined by the bond’s coupon
interest payments, face value, and maturity.
Because coupon interest payments occur at regular intervals throughout the life of
the bond, those payments are an annuity. Instead of using several terms representing
the individual cash flows from the future coupon interest payments (CF1, CF2, and so Chapter 12 Business Valuation 343 on), we adapt Equation 121 by using one term to show the annuity. The remaining
term represents the future cash flow of the bond’s face value, or principal, that is paid
at maturity. Equation 122 shows the adapted valuation model:
The Bond Valuation Formula (Algebraic Method)
1
1 −
n (1 + k d )
VB = INT × kd where:
+ M
(1 + k d )n
(122) VB = Current market value of the bond
INT = Dollar amount of each periodic interest payment
n = Number of times the interest payment is received (which is also
the number of periods until maturity)
M = Principal payment received at maturity
kd = Required rate of return per period on the bond debt
instrument The table version of the bond valuation model is shown in Equation 123, as follows:
VB = (INT × PVIFAk, n) + (M × PVIFk, n) (123) where: PVIFAk, n = Present Value Interest Factor for an Annuity from Table IV
PVIFk, n = Present Value Interest Factor for a single amount from Table II
To use a calculator to solve for the value of a bond, enter the dollar value of the interest
payment as [PMT], the face value payment at maturity as [FV], the number of payments
as n, and the required rate of return, kd depicted as [I/Y] on the TI BAII Plus calculator.
Then compute the present value of the bond’s cash flows.
Now let’s apply the bond valuation model. Suppose Microsoft Corporation issues
a 7 percent coupon interest rate bond with a maturity of 20 years. The face value of the
bond, payable at maturity, is $1,000.
First, we calculate the dollar amount of the coupon interest payments. At a 7 percent
coupon interest rate, each payment is .07 × $1,000 = $70.
Next, we need to choose a required rate of return, kd. Remember that kd is the required
rate of return that is appropriate for the bond based on its risk, maturity, marketability,
and tax treatment. Let’s assume that 8 percent is the rate of return the market determines
to be appropriate.
Now we have all the factors we need to solve for the value of Microsoft Corporation’s
bond. We know that kd is 8 percent, n is 20, the coupon interest payment is $70 per year,
and the face value payment at maturity is $1,000. Using Equation 122, we calculate
the bond’s value as follows: Take Note
The determinants of
nominal interest rates, or
required rates of return,
include the real rate of
interest, the inflation
premium, the default risk
premium, the illiquidity
premium, and the
maturity premium. Each
person evaluating a bond
will select an appropriate
required rate of return,
kd, for the bond based on
these determinants. 344 Part III Capital Budgeting and Business Valuation 1
1 −
20 (1 + .08)
VB = $70 × .08 + $1, 000
20
1 + .08)
( $1, 000 = ($70 × 9.8181474) + 4.660957 = $687.270318 + $214.548214
= $901.82 Notice that the value of Microsoft Corporation’s bond is the sum of the present values
of the 20 annual $70 coupon interest payments plus the present value of the one time
$1,000 face value to be paid 20 years from now, given a required rate of return of 8 percent.
To find the Microsoft bond’s value using present value tables, recall that the bond
has a face value of $1,000, a coupon interest payment of $70, a required rate of return
of 8 percent, and an n value of 20. We apply Equation 123 as shown:
VB = ($70 × PVIFA8%, 20 yrs) + ($1,000 × PVIF8%, 20 yrs)
= ($70 × 9.8181) + ($1,000 × .2145)
= $687.267 + $214.500
= $901.77
We see that the sum of the present value of the coupon interest annuity, $687.267,
plus the present value of the principal, $214.500, results in a bond value of $901.77.
There is a fivecent rounding error in this example when the tables are used.
Here’s how to find the bond’s value using the TI BAII PLUS financial calculator.
Enter the $70 coupon interest payment as PMT, the onetime principal payment of
$1,000 as FV, the 20 years until maturity as n (N on the TI BAII PLUS), and the 8
percent required rate of return—depicted as I/Y on the TI BAII Plus. As demonstrated
in Chapter 8 calculator solutions, clear the time value of money TVM registers before
entering the new data. Skip steps 2 and 3 if you know your calculator is set to one
payment per year and is also set for endofperiod payment mode.
TI BAII PLUS Financial Calculator Solution Step 1: Press to clear previous values.
1 Step 2: Press , repeat until END shows in the display to set the annual interest rate mode and to set the annuity payment to end of period mode.
Step 3: Input the values and compute.
1000 8 20 70 Answer: –901.82 Chapter 12 Business Valuation The $901.82 is negative because it is a cash outflow—the amount an investor would
pay to buy the bond today.
We have shown how to value bonds with annual coupon interest payments in this
section. Next, we show how to value bonds with semiannual coupon interest payments. Semiannual Coupon Interest Payments
In the hypothetical bond valuation examples for Microsoft Corporation, we assumed
the coupon interest was paid annually. However, most bonds issued in the United States
pay interest semiannually (twice per year). With semiannual interest payments, we must
adjust the bond valuation model accordingly. If the Microsoft bond paid interest twice
per year, the adjustments would look like this:
Annual
Basis
Coupon Interest Payments Semiannual
Basis $70 ÷ 2 = $35 per sixmonth period 20 yrs Maturity
Required Rate of Return × 2 = 40 sixmonth periods 8% ÷ 2 = 4% semiannual rate These values can now be used in Equation 122, Equation 123, or a financial
calculator, in the normal manner. For example, if Microsoft’s 7 percent coupon, 20year
bond paid interest semiannually, its present value per Equation 122 would be
1
1 −
40 (1 + .04)
VB = $35 × .04 + $1, 000
(1 + .04)40 $1, 000 = ($35 x 19.792774) + 4.801021
= $692.74709 + $208.2890
= $901.04 The value of our Microsoft bond with semiannual interest and a 4 percent per
semiannual period discount rate is $901.04. This compares to a value of $901.82 for the
same bond if it pays annual interest and has an 8 percent annual discount rate. Note that
a required rate of return of 4 percent per semiannual period is not the same as 8 percent
per year. The difference in the frequency of discounting gives a slightly different answer. The Yield to Maturity of a Bond
Most investors want to know how much return they will earn on a bond to gauge
whether the bond meets their expectations. That way, investors can tell whether they
should add the bond to their investment portfolio. As a result, investors often calculate
a bond’s yield to maturity before they buy a bond. Yield to maturity (YTM) represents
the average rate of return on a bond if all promised interest and principal payments
are made on time and if the interest payments are reinvested at the YTM rate given
the price paid for the bond. 345 346 Part III Capital Budgeting and Business Valuation Calculating a Bond’s Yield to Maturity To calculate a bond’s YTM, we apply the
bond valuation model. However, we apply it differently than we did when solving for a
bond’s present value (price) because we solve for kd, the equivalent of YTM.
To compute a bond’s YTM, we must know the values of all variables except kd. We
take the market price of the bond, PB, as the value of a bond, VB, examining financial
sources such as The Wall Street Journal for current bond prices.
Once you have all variables except kd, solving for kd algebraically is exceedingly
difficult because that term appears three times in the valuation equation. Instead, we
use the trialanderror method. In other words, we guess a value for kd and solve for VB
using that value. When we find a kd value that results in a bond value that matches the
published bond price, PB, we know that the kd value is the correct YTM. The YTM is
1
the return that bond investors require to purchase the bond.
Here’s an illustration of the trialanderror method for finding YTM. Suppose
that The Wall Street Journal reported that the Microsoft bond in our earlier example
is currently selling for $1,114.70. What is the bond’s YTM if purchased at this price?
Recall the annual coupon interest payments for the Microsoft bond were $70 each,
and the bond had a 20year maturity and a face value of $1,000. Applying the bond
valuation model, we solve for the kd that produces a bond value of $1,114.70.
1
1 −
20 (1 + k d )
$1,114.70 = $70 × kd + $1, 000
(1 + k d )20 Although we can try any kd value, remember that when k was 8 percent, the bond’s
calculated value, VB, was $901.82. Bond prices and yields vary inversely—the higher
the YTM, the lower the bond price; and the lower the YTM, the higher the bond price.
The bond’s current market price of $1,114.70 is higher than $901.82, so we know the
YTM must be less than 8 percent. If you pay more than $901.82 to buy the bond, your
return will be less than 8 percent.
Because we know that YTM and bond prices are inversely related, let’s try 7 percent
in our bond valuation model, Equation 122. We find that a kd value of 7 percent results
in the following bond value:
1
1 −
20 (1 + .07)
VB = $70 × .07 + $1, 000
(1 + .07)20 $1, 000 = ($70 × 10.59401425) + 3.86968446 = $741.5809975 + $258.4190028
= $1, 000.00 1 In Chapter 9 this required rate of return was called the firm’s cost of debt capital, which we adjust for taxes. In this chapter,
however, our main focus is finding the value of different types of securities, so kd is referred to as the investor’s required rate
of return. Chapter 12 Business Valuation At a kd of 7 percent, the bond’s value is $1,000 instead of $1,114.70. We’ll need
to try again. Our second guess should be lower than 7 percent because at kd = 7% the
bond’s calculated value is lower than the market price. Let’s try 6 percent. At a kd of 6
percent, the bond’s value is as follows:
1
1 −
20 (1 + .06)
VB = $70 × .06 + $1, 000
20
1 + .06)
( $1, 000 = ($70 × 11.46992122) + 3.20713547 = $802.8944853 + $311.8047269
= $1,114.70 With a kd of 6 percent, the bond’s value equals the current market price of $1,114.70.
We conclude that the bond’s YTM is 6 percent.2
To use the table method to find the YTM of Microsoft’s 7 percent coupon rate,
20year bond at a price of $1,114.70, use Equation 123 as follows:
First guess: kd = 7%:
VB = ($70 × PVIFA7%, 20 periods) + ($1,000 × PVIF7%, 20 periods)
= ($70 × 10.5940) + ($1,000 × .2584)
= $741.58 + $258.40
= $999.98
$999.98 is too low. We must guess again. Let’s try kd = 6%, as follows:
VB = ($70 × PVIFA6%, 20 periods) + ($1,000 × PVIF6%, 20 periods)
= ($70 × 11.4699) + ($1,000 × .3118)
= $802.893 + $311.80
= $1,114.69
Close enough (to $1,114.70). The bond’s YTM is about 6 percent.
Finding a bond’s YTM with a financial calculator avoids the trialanderror method.
Simply plug in the values on the calculator and solve for kd, as shown: 2 We were lucky to find the bond’s exact YTM in only two guesses. Often the trialanderror method requires more guesses. In
fact, we almost always use a financial calculator to compute the YTM. 347 348 Part III Capital Budgeting and Business Valuation
TI BAII PLUS Financial Calculator Solution Step 1: Press
Step 2: Press to clear previous values.
1 , repeat until END shows in the display to set the annual interest rate mode and to set the annuity payment to end of period mode.
Step 3: Input the values and compute.
1,114.70 1000 20 70
Answer: 6.00 Using the financial calculator, we find that the YTM of the Microsoft $1,000 face
value 20year bond with a coupon rate of 7 percent and a market price of $1,114.70 is
6 percent. The Relationship between Bond YTM and Price
A bond’s market price depends on its yield to maturity. When a bond has a YTM greater
than its coupon rate, it sells at a discount from its face value. When the YTM is equal
to the coupon rate, the market price equals the face value. When the YTM is less than
the coupon rate, the bond sells at a premium over face value.
For instance, in our initial calculations of the Microsoft bond, we found that the
present value of its future cash flows was $901.82. That price was lower than the bond’s
$1,000 face value. Because its market price was lower than its face value, the bond sold
at a discount (from its face value). A bond will sell at a discount because buyers and
sellers have agreed that the appropriate rate of return for the bond should be higher than
the bond’s coupon interest rate. With the Microsoft bond, investors required an 8 percent
rate of return, but the fixed coupon interest rate was only 7 percent. To compensate for
a coupon interest rate that is lower than the required rate, investors would be unwilling
to pay the $1,000 face value. Instead, they would only be willing to pay $901.82 to
buy the bond.
Now recall the trialanderror calculations for the YTM of the Microsoft 7 percent
coupon rate bond in the previous section. We found that when the YTM was 7 percent,
the bond’s price was $1,000. This was no coincidence. When the YTM is equal to the
coupon interest rate—that is, when the bond is selling at par—the bond’s price is equal to
its face value. We saw that when wouldbe buyers and sellers of Microsoft Corporation’s
bond agree that the appropriate yield to maturity for the bond is 6 percent instead of 7
percent, the price is above $1,000.
The change from a 7 percent to a 6 percent YTM results in a market value of
$1,114.70. That market value for the bond is higher than the $1,000 face value. Because
the market price is higher than the bond’s face value in our case, the bond sells at a
premium. Why? Investors pay more to receive “extra” interest because the coupon rate
paid is higher than the YTM demanded.
In our example, the calculations show that investors were willing to pay $1,114.70
for a bond with a face value of $1,000 because the coupon interest was one percentage
point higher than the required rate of return.
Figure 122 shows the relationship between YTM and the price of a bond. Chapter 12 Business Valuation 349 $3,000.00 $2,500.00 Price of Bond $2,000.00 $2,082.73
$1,595.10 $1,500.00 $1,249.2 4
$1,000.0 0 $1,000.00 $817.43
$681.47
$578.51 $500.00 $0.00 1% 3% 5% 7% 9% 11% 13% Yield to Maturity The inverse relationship between bond price and YTM is important to bond traders.
Why? Because if market YTM interest rates rise, bond prices fall. Conversely, if market
YTM interest rates fall, bond prices rise. The suggestion that the Fed might raise interest
rates is enough to send the bond market reeling as bond traders unload their holdings.
In this section we examined bond valuation for bonds that pay annual and semiannual
interest. We also investigated how to find a bond’s yield to maturity and the relationship
between a bond’s YTM and its price. We turn next to preferred stock valuation. Preferred Stock Valuation
To value preferred stock, we adapt the discounted cash flow valuation formula,
Equation 121, to reflect the characteristics of preferred stock. First, recall that the
value of any security is the present value of its future cash payments. Second, review
the characteristics of preferred stock. Preferred stock has no maturity date, so it has no
maturity value. Its future cash payments are dividend payments that are paid to preferred
stockholders at regular time intervals for as long as they (or their heirs) own the stock.
Cash payments from preferred stock dividends are scheduled to continue forever. To
value preferred stock, then, we must adapt the discounted cash flow model to reflect
that preferred stock dividends are a perpetuity. Finding the Present Value of Preferred Stock Dividends
To calculate the value of preferred stock, we need to find the present value of its future
cash flows—which are a perpetuity. In Chapter 8 we learned how to find the present Figure 122 Bond YTM
versus Bond Price
Figure 122 shows the inverse
relationship between the price
and the YTM for a $1,000
face value, 20year, 7% coupon
interest rate bond that pays
annual interest. 350 Part III Capital Budgeting and Business Valuation value of a perpetuity. We use the formula for the present value of a perpetuity, Equation
85, but adapt the terms to reflect the nature of preferred stock.3
The preferred stock valuation calculations require that we find the present value
(VP) of preferred stock dividends (Dp), discounted at required rate of return, kp. The
formula for preferred stock valuation follows:
The Formula for the Present Value of Preferred Stock
VP = Dp
kp (124) where:VP = Current market value of the preferred stock
Dp = Amount of the preferred stock dividend per period
kp = Required rate of return per period for this issue of preferred stock
Let’s apply Equation 124 to an example. Suppose investors expect an issue of
preferred stock to pay an annual dividend of $2 per share. Investors in the market have
evaluated the issuing company and market conditions and have concluded that 10 percent
is a fair rate of return on this investment. The present value for one share of this preferred
stock, assuming a 10 percent required rate of return follows: $2 VP = .10 = $20 We find that for investors whose required rate of return (kp) is 10 percent, the value
of each share of this issue of preferred stock is $20. Take Note
With bonds, an investor’s
annual percent return
on investment is called
the yield to maturity, or
YTM. With preferred
and common stocks, an
investor’s percent return
on investment is simply
called the yield because
preferred and common
stock don’t have a
maturity date. The Yield on Preferred Stock
The yield on preferred stock represents the annual rate of return that investors would
realize if they bought the preferred stock for the current market price and then received
the promised preferred dividend payments.
Like bond investors, preferred stock investors want to know the percentage yield
they can expect if they buy shares of preferred stock at the current market price. That
way, investors can compare the yield with the minimum they require to decide whether
to invest in the preferred stock.
Fortunately, calculating the yield on preferred stock is considerably easier than
calculating the YTM for a bond. To calculate the yield, we rearrange Equation 124
so that we solve for kp. We are not solving for the value of the preferred stock, VP, but
rather are taking the market value as a given and solving for kp as follows:
Formula for the Yield on Preferred Stock
kP = 3 Equation 85 is PV = DP
VP PMT
. In Equation 124, VP substitutes for PV, Dp replaces PMT, and kp replaces k.
k (125) Chapter 12 Business Valuation 351 where: kp = Yield per period on investment that an investor can expect if the shares
are purchased at the current market price, PP, and if the preferred
dividend, Dp, is paid forever
Dp = Amount of the preferred stock dividend per period
VP = Current market value of the preferred stock
To illustrate how to find the yield using Equation 125, suppose SureThing
Corporation’s preferred stock is selling for $25 per share today and the dividend is $3
a share. Now assume you are a potential buyer of SureThing’s preferred stock, so you
want to find the expected annual percent yield on your investment. You know that the
current market value of the stock, VP, is $25, and the stock dividend, Dp, is $3. Applying
Equation 125, you calculate the yield as follows:
kP = $3
$25 = .12, or 12% You find that the yield for SureThing’s preferred stock is 12 percent. If your
minimum required rate of return is less than or equal to 12 percent, you would invest in
the SureThing preferred stock. If your required rate of return is greater than 12 percent,
you would look for another preferred stock that had a yield of more than 12 percent. Common Stock Valuation
The valuation of common stock is somewhat different from the valuation of bonds and
preferred stock. Common stock valuation is complicated by the fact that common stock
dividends are difficult to predict compared with the interest and principal payments on
a bond or dividends on preferred stock. Indeed, corporations may pay common stock
dividends irregularly or not pay dividends at all. Moreover, because owners of more than
50 percent of a corporation’s stock have control over the affairs of the business and can
force their will, the value of a controlling interest of common stock is relatively more
valuable than the value of one share. This means that different procedures must be used
to value controlling interests (or total common stockholders’ equity) than are used to
value one share. Often, ownership of less than 50 percent of a corporation’s common
stock can result in control if the percentage owned is significant and if the remaining
shares are widely disbursed among investors not working in concert with each other.
In the sections that follow, we examine the most popular methods of valuing
individual shares of common stock. We will then illustrate how these methods are
applied to the valuation of total common stockholders’ equity. Valuing Individual Shares of Common Stock
As with bonds and preferred stock, we value individual shares of common stock by
estimating the present value of the expected future cash flows from the common stock.
Those future cash flows are the expected future dividends and the expected price of the
stock when the stock is sold. The discounted cash flow valuation model, Equation 121,
adapted for common stock is shown in Equation 126: Interactive Module
Go to www.textbookmedia.
com and find the free
companion material for this
book. Follow the instructions
there. See how the various
input variables affect the
estimated value. 352 Part III Capital Budgeting and Business Valuation The DCF Valuation Model Applied to Common Stock
P0 = where: D1
+
(1 + k s )1 D2
+
(1 + k s )2 D3
+ ... +
(1 + k s )3 Pn
(1 + k s ) n (126) P0 = Present value of the expected dividends, the current price of the
common stock D1, D2, D3, etc. = Common stock dividends expected to be received at the end of
periods 1, 2, 3, and so on until the stock is sold
Pn = Anticipated selling price of the stock in n periods
ks = Required rate of return per period on this common stock
investment
In practice, however, using Equation 126 to value shares of common stock is
problematic because an estimate of the future selling price of a share of stock is often
speculative. This severely limits the usefulness of the model.
Instead, some analysts use models that are a variation of Equation 126 that do
not rely on an estimate of a stock’s future selling price. We turn to those models next.
The Constant Growth Dividend Model Common stock dividends can grow at different
rates. The two growth patterns we examine here are constant growth and nonconstant,
or supernormal, growth.
The constant growth dividend model assumes common stock dividends will be
paid regularly and grow at a constant rate. The constant growth dividend model (also
known as the Gordon growth model because financial economist Myron Gordon helped
develop and popularize it) is shown in Equation 127:
The Constant Growth Version of the Dividend Valuation Model
P0 = where: D1
ks − g (127) P0 = Current price of the common stock
D1 = Dollar amount of the common stock dividend expected one
period from now
ks = Required rate of return per period on this common stock
investment
g = Expected constant growth rate per period of the company’s
common stock dividends Equation 127 is easy to use if the stock dividends grow at a constant rate. For
example, assume your required rate of return (ks) for Wendy’s common stock is 10
percent. Suppose your research leads you to believe that Wendy’s Corporation will pay
a $0.25 dividend in one year (D1), and for every year after the dividend will grow at
a constant rate (g) of 8 percent a year. Using Equation 127, we calculate the present
value of Wendy’s common stock dividends as follows: Chapter 12 P0 =
= 353 Business Valuation $0.25
.10 − .08
$0.25
.02 = $12.50 We find that with a common stock dividend in one year of $0.25, a constant growth
rate of 8 percent, and a required rate of return of 10 percent, the value of the common
stock is $12.50.
In a nogrowth situation, g, in the denominator of Equation 127 becomes zero. To
value stocks that have no growth is particularly easy because the value is simply the
expected dividend (D1) divided by ks.
The Nonconstant, or Supernormal, Growth Model In addition to the constant growth
dividend cash flow pattern that we discussed in the previous section, some companies
have very high growth rates, known as supernormal growth of the cash flows. Valuing
the common stock of such companies presents a special problem because high growth
rates cannot be sustained indefinitely. A young hightechnology firm may be able to
grow at a 40 percent rate per year for a few years, but that growth must slow down
because it is not sustainable given the population and productivity growth rates. In fact,
if the firm’s growth rate did not slow down, its sales would surpass the gross domestic
product of the entire nation over time. Why? The company has a 40 percent growth
rate that will compound annually, whereas the gross domestic product may grow at a 4
percent compounded average annual growth rate.
The constant growth dividend model for common stock, Equation 127, then, must be
adjusted for those cases in which a company’s dividend grows at a supernormal rate that
will not be sustained over time. We do this by dividing the projected dividend cash flow
stream of the common stock into two parts: the initial supernormal growth period and the
next period, in which normal and sustainable growth is expected. We then calculate the
present value of the dividends during the fastgrowth time period first. Then we solve for
the present value of the dividends during the constant growth period that are a perpetuity.
The sum of these two present values determines the current value of the stock.
To illustrate, suppose Supergrowth Corporation is expected to pay an annual dividend
of $2 per share one year from now and that this dividend will grow at a 30 percent annual
rate during each of the following four years (taking us to the end of year 5). After this
supernormal growth period, the dividend will grow at a sustainable 5 percent rate each
year beyond year 5. The cash flows are shown in Figure 123. $2
$2.00
t0 t1 $2 × 1.3
$2.60 t2 $2 × 1.32
$3.38
t3 $2 × 1.33
$4.39 t4 Figure 123 Timeline
of Supergrowth Common
Stock Dividend with Initial
Supernormal Growth $2 × 1.34 × 1.05 $2 × 1.34 × 1.053
$6.61
$2 × 1.34 × 1.052
$6.30 $2 × 1.34
$5.71
t5 t6 t7 t8 354 Part III Capital Budgeting and Business Valuation The valuation of a share of Supergrowth Corporation’s common stock is described
in the following three steps.
Step 1: Add the present values of the dividends during the supernormal growth period. Assume that the required rate of return, ks, is 14 percent.
$2.00 × 1/1.141 = $ 1.75
$2.60 × 1/1.142 = $ 2.00
$3.38 × 1/1.143 = $ 2.28
$4.39 × 1/1.144 = $ 2.60
$5.71 × 1/1.145 = $ 2.97
∑ = $11.60 Step 2: Calculate the sum of the present values of the dividends during the normal
growth period, from t6 through infinity in this case. To do this, pretend for a
moment that t6 is t1. The present value of the dividend growing at the constant rate of 5 percent to perpetuity could be computed using Equation 127.
P0 = D1
ks − g Substituting our values we would have:
P0 = $6.00
.14 − .05 = $66.67 Because the $6.00 dividend actually occurs at t6 instead of t1, the $66.67 figure is not
a t0 value, but rather a t5 value. Therefore, it needs to be discounted back five years at our
required rate of return of 14 percent. This gives us $66.67 × (1/1.145) = $34.63. The result
of $34.63 is the present value of the dividends from the end of year 6 through infinity.
Step 3: Finally we add the present values of the dividends from the supernormal
growth period and the normal growth period. In our example we add $11.60
+ $34.63 = $46.23. The sum of $46.23 is the appropriate market price of Supergrowth Corporation’s common stock, given the projected dividends and
the 14 percent required rate of return on those dividends.
The P/E Model Many investment analysts use the price to earnings, or P/E, ratio to
value shares of common stock. As we discussed in Chapter 6, the P/E ratio is the price
per share of a common stock divided by the company’s earnings per share:
P / E ratio = Price per Share
Earnings per Share Chapter 12 Business Valuation The P/E ratio indicates how much investors are willing to pay for each dollar of a
stock’s current earnings. So, a P/E ratio of 20 means that investors are willing to pay
$20 for $1 of a stock’s earnings. A high P/E ratio indicates that investors believe the
stock’s earnings will increase, or that the risk of the stock is low, or both.
Financial analysts often use a P/E model to estimate common stock value for
businesses that are not public. First, analysts compare the P/E ratios of similar companies
within an industry to determine an appropriate P/E ratio for companies in that industry.
Second, analysts calculate an appropriate stock price for firms in the industry by
multiplying each firm’s earnings per share (EPS) by the industry average P/E ratio. The
P/E model formula, Equation 128, follows:
The P/E Model
Appropriate Stock Price = Industry P/E Ratio × EPS (128) To illustrate how to apply the P/E model, let’s value the common stock of the
Zumwalt Corporation. Suppose that Zumwalt Corporation has current earnings per share
of $2 and, given the risk and growth prospects of the firm, the analyst has determined
that the company’s common stock should sell for 15 times current earnings. Applying the
P/E model, we calculate the following price for Zumwalt Corporation’s common stock:
Appropriate Stock Price = Industry P/E Ratio × EPS
= 15 × $2
= $30 Our P/E model calculations show that $30 per share is the appropriate price for
common stock that has a $2 earnings per share and an industry P/E ratio of 15. The
industry P/E ratio would be adjusted up or down according to the individual firm’s
growth prospects and risk relative to the industry norm. Valuing Total Common Stockholders’ Equity
As we said earlier, different procedures must be used to value total common stockholders’
equity than are used to value one share of common stock. The primary reason for this
is that owners of some large percentage of a corporation’s stock have control over the
affairs of the business and can force their will on the remaining shareholders. This
makes the value of a controlling interest of common stock relatively more valuable
than a noncontrolling interest. Therefore, to value controlling interests of common
stock, or total stockholders’ equity, we must use models that account for this “control
premium.” In the sections that follow, we examine the most popular methods of valuing
total stockholders’ equity.
Book Value One of the simplest ways to value total common stockholders’ equity is to
subtract the value of the firm’s liabilities and preferred stock, if any, as recorded on the
balance sheet from the value of its assets. The result is the book value, or net worth.
Book Value of Common Equity (129) Book Value of Common Equity = Total Assets – Total Liabilities – Preferred Stock 355 356 Part III Capital Budgeting and Business Valuation The book value approach has severe limitations. The asset values recorded on a
firm’s balance sheet usually reflect what the current owners originally paid for the assets,
not the current market value of the assets. Due to these and other limitations, the book
value is rarely used to estimate the market value of common equity.
Liquidation Value The liquidation value and book value valuation methods are similar,
except that the liquidation method uses the market values of the assets and liabilities,
not book values, as in Equation 129. The market values of the assets are the amounts
the assets would earn on the open market if they were sold (or liquidated). The market
values of the liabilities are the amounts of money it would take to pay off the liabilities.
The liquidation value is the amount each common stockholder would receive if the
firm closed, sold all assets and paid off all liabilities and preferred stock, and distributed
the net proceeds to the common stockholders.
Although more reliable than book value, liquidation value is a worstcase valuation
assessment. A company’s common stock should be worth at least the amount generated
at liquidation. Because liquidation value does not consider the earnings and cash flows
the firm will generate in the future, it may provide misleading results for companies
that have significant future earning potential. The Free Cash Flow DCF Model
The Free Cash Flow DCF Model is very similar to the nonconstant, or supernormal,
dividend growth model discussed earlier, but instead of discounting dividend cash flows,
the free cash flow model discounts the total cash flows that would flow to the suppliers
of the firm’s capital. Once the present value of those cash flows is determined, liabilities
and preferred stock (if any) are subtracted to arrive at the present value of common
stockholders’ equity.
Free Cash Flows Free cash flows represent the total cash flows from business operations
that flow to the suppliers of a firm’s capital each year. In forecasts, free cash flows are
calculated as follows:
Cash Revenues
– Cash Expenses
= Earnings Before Interest, Taxes, Depreciation, and Amortization (EBITDA)
– Depreciation and Amortization
= Earnings Before Interest and Taxes (EBIT)
– Federal and State Income Taxes
= Net Operating Profit AfterTax (NOPAT)
+ Add Back Depreciation and Amortization
– Capital Expenditures
– New Net Working Capital
= Free Cash Flow Free cash flow represents those amounts in each operating period that are “free”
to be distributed to the suppliers of the firm’s capital—that is, the debt holders, the
preferred stockholders, and the common stockholders. In the previous calculation, you
can see that free cash flow is that amount remaining after cash expenses, income taxes,
capital expenditures, and new net working capital are subtracted from cash revenues. Chapter 12 Business Valuation A Real World Example In July 2001, the Abiomed Corporation of Danvers,
Massachusetts, received a lot of publicity when the company’s AbioCor selfcontained
artificial heart was implanted in a terminally ill patient, marking the first time that such
a device was used on a human being. Let us put ourselves in the shoes of someone
valuing this company on April 1, 2006, and that you work for a firm that is interested
in acquiring Abiomed. In support of the acquisition analysis, you have been asked to
prepare an estimate of the market value of the firm’s common equity. The methodology
you have chosen is the discounted free cash flow model.
Following a lengthy analysis of the artificial heart market, the medical equipment
industry, and Abiomed’s financial statements, you produce the discounted free cash flow
forecast and valuation shown in Figure 124. In the following paragraphs we explain the
procedure. The forecasting variables that form the basis for the valuation are listed at
the top of Figure 124 (these are the product of your lengthy analysis). For convenience,
we have numbered each line in the figure at the lefthand side.
The “Actual 2006” column in Figure 124 contains Abiomed’s operating results for
the fiscal year ended March 31, 2006, as recorded on the firm’s SEC Form 10K.4 The
remaining columns contain the forecast for the next 10 years.
Product revenues (line 12) are expected to accelerate from 20 to 50 percent annual
growth over four years, with the growth rate decreasing 10 percentage points a year
after that until the ninth year of the forecast, when revenue growth settles out at an
expected longterm growth rate of 5 percent a year (the growth factor is on line 1).
Funded research and development revenue (line 13), on the other hand, is expected to
decrease 50 percent a year until it is almost negligible after 10 years (the growth factor
is on line 2). These factors produce total revenues (line 14) exceeding $52 million in
2007 and $376 million in 2016.
Direct costs of revenues on line 15 are a function of the expected gross profit margin
on line 3. In Abiomed’s forecast, 2006’s gross margin of 77 percent is extended for each
year through 2016. This produces gross profits (see line 16) ranging from just over $40
million in 2007 to over $289 million in 2016. Given the forecasted gross profit figures,
direct costs on line 15 are “plugged” by subtracting gross profit from total revenues.
Research and development expenses (line 17) are expected to grow by 10 percent
in 2007 and then to decrease by 10 percent a year through 2016. Selling, general, and
administrative expenses (line 18) are forecast as a percentage of revenue, starting at 70
percent of revenue in 2007 (the same percentage as in 2006) and declining to 54 percent
in 2016. Subtracting these operating expenses from gross profit leaves earnings before
interest, taxes, depreciation, and amortization (EBITDA on line 19) of negative $15.176
million in 2007, positive $2.067 million in 2010, and positive $78.966 million in 2016.
Although they are noncash expenses, depreciation and amortization are included
in discounted free cash flow forecasts in order to calculate income tax expense. In the
case of Abiomed, depreciation and amortization expense (line 20) is forecast to be 6
percent of revenue each year. Subtracting depreciation and amortization expense from
EBITDA produces earnings before interest and taxes (EBIT), also known as operating
income (see line 21).
As shown in Figure 124, line 22, Abiomed has $94.159 million in taxloss
carryforwards at the beginning of FY 2006. Operating income was a negative $16.985
million in 2006, so $94.159 million + $16.985 million = $111.144 million in taxloss 4 Source: the “Edgar” database at www.sec.gov. 357 358 Part III Capital Budgeting and Business Valuation Line Forecasting Variables:
1
2
3
4
5
6
7
8 Product revenue growth factor
Research revenue growth factor
Expected gross profit margin
R&D expense growth factor
S, G, & A expense % of revenue
Depr. & Amort. % of revenue
Capital expenditure growth factor
Net working capital to sales ratio 9 Income tax rate
10 Assumed longterm sustainable growth rate
11 Discount rate
Forecast and Valuation:
12 Product revenue
13 Funded research and development revenue
14 Total revenue Actual
2006
14%
77%
71%
6% 2007
20%
–10%
77%
10%
71%
6%
0%
10% 2008
30%
–10%
77%
–10%
70%
6%
–10%
10% 40%
5% per year
20%
Actual
2006 2007 2008 $ 43,322
348
43,670 $ 51,986
313
52,299 $ 67,582
282
67,864 15 Direct costs 10,251 12,029 15,609 16 Gross profit 33,419 40,270 52,255 17 Research and development expenses
18 Selling, general and administrative
expenses
19 Earnings before interest, taxes,
depr. & amort. (EBITDA) 16,739 18,413 16,572 30,923 37,033 47,574 (14,243) (15,176) (11,891) 2,742 3,138 4,072 (16,985)
(94,159)
(16,985) (18,314)
(111,144)
(18,314) (15,963)
(129,458)
(15,963) 0 0 0 (16,985) (18,314) (15,963) 2,742
(2,920)
0 3,138
(2,920)
(866) 4,072
(2,628)
(1,560) ($17,163) ($18,962) ($16,079) (15,802) (11,166) 20 Depreciation and amortization
21 Earnings before interest and
taxes (EBIT)
22 Available taxloss carryforwards
23 Net taxable earnings
24 Federal and state income taxes
25 Net operating profit aftertax
(NOPAT)
26 Add back depreciation and amortization
27 Subtract capital expenditures
28 Subtract new net working capital
29 Free cash flow
30 Terminal value, 2016
31 Present value of free cash flows @ 20%
32 Total present value of company
operations $100,140 33 Plus current assets
34 Less current liabilities Figure 12 4 Discounted
Free Cash Flow Forecast
and Valuation for Abiomed
(in $ thousands) 46,443*
(8,739)* 35 Less longterm debt (310)* 36 Less preferred stock 0* 37 Net market value of
common equity $137,534 *from Abiomed’s March 31, 2006 Balance Sheet Chapter 12 359 Business Valuation Years Ending March 31
Forecast
2009 2010 2011 2012 2013 2014 2015 2016 40%
–10%
77%
–10%
68%
6%
–10%
10% 50%
–10%
77%
–10%
66%
6%
–10%
10% 40%
–10%
77%
–10%
64%
6%
–10%
10% 30%
–10%
77%
–10%
62%
6%
–10%
10% 20%
–10%
77%
–10%
60%
6%
–10%
10% 10%
–10%
77%
–10%
58%
6%
–10%
10% 5%
–10%
77%
–10%
56%
6%
–10%
10% 5%
–10%
77%
–10%
54%
6%
–10%
10% Years Ending March 31
Forecast
2009 2010 2012 2013 2014 2015 $94,615
254
94,869 $141,923
229
142,152 $198,692
206
198,898 $258,300
185
258,485 $309,960
167
310,127 $340,956
150
341,106 $358,004
135
358,139 $375,904
122
376,026 21,820 32,695 45,747 59,452 71,329 78,454 82,372 86,486 73,049 109,457 153,151 199,033 238,798 262,652 275,767 289,540 14,915 13,424 12,082 10,874 9,787 8,808 7,927 7,134 64,608 93,966 127,499 160,526 186,394 198,191 200,925 203,440 (6,474) 2,067 13,570 27,633 42,617 55,653 66,915 78,966 5,692 8,529 11,934 15,509 18,608 20,466 21,488 22,562 (12,166)
(45,421)
(12,166) (6,462)
(157,587)
(6,462) 1,636
(164,049)
0 12,124
(162,413)
0 24,009
(150,289)
0 35,187
(126,280)
0 45,427
(91,093)
0 56,404
(45,666)
10,738 0 0 0 0 0 0 0 4,295 (12,166) (6,462) 1,636 12,124 24,009 35,187 45,427 52,109 5,692
(2,365)
(2,703) 8,529
(2,129)
(4,731) 11,934
(1,916)
(5,677) 15,509
(1,724)
(5,961) 18,608
(1,552)
(5,166) 20,466
(1,397)
(3,100) 21,488
(1,257)
(1,705) 22,562
(1,131)
(1,790) 5,977 $ 19,948 $ 35,899 $ 51,156 $ 63,953 $ 71,750 ($ 11,542) ($ 2011 4,793) $ 2016 $502,250
(6,679) (2,311) 2,402 6,681 10,019 11,897 12,395 92,704 360 Part III Capital Budgeting and Business Valuation carryforwards are available at the beginning of 2007. This situation continues until 2016,
when the carryforwards are finally used up, and Abiomed reports $10.738 million in
net taxable earnings. After 2016, operating income is fully taxable.
The forecast assumes a combined federal and state income tax rate of 40 percent
(see line 9). Applying this rate to Abiomed’s net taxable earnings (line 23) in 2016, and
$0 to the earlier years, produces the income tax expenses shown on line 24. Subtracting
taxes from EBIT produces the company’s net operating profit after tax (NOPAT on line
25), which is negative $18.314 million in 2007 rising to positive $52.109 million in 2016.
Once NOPAT has been determined, three further adjustments are necessary to
calculate free cash flow. First, on line 26, depreciation and amortization are added back
to NOPAT, because these noncash items were subtracted earlier only for the purpose
of calculating income tax expense. Next, on line 27, expected capital expenditures
are subtracted. Capital expenditures are amounts expected to be spent to procure new
plant and equipment. For this forecast, we assume that your research indicates that
Abiomed will need to spend about the same amount on plant and equipment in 2007
than it did in 2006 (see line 7), and that this spending may be decreased 10 percent
a year in each year after 2007. The resulting capital expenditure budget, shown in
Figure 124, line 27, gradually decreases from $2.92 million in 2007 to just over
$1.13 million in 2016.
Finally, on line 28, new net working capital investment is subtracted. Net working
capital is the difference between current assets and current liabilities that must be
financed from longterm capital sources (debt and equity). When businesses grow, they
typically need more working capital in the form of cash, inventory, and receivables,
and not all of it can be financed spontaneously from current liabilities. For this reason,
the company’s longterm debt and equity holders must invest additional amounts
each year to “take up the slack.” In the case of Abiomed, we will assume that your
research indicates that the typical ratio of net working capital to sales in the medical
equipment industry is 10 percent (see line 8). In other words, for every $10 of new
sales a company realizes, $1 of new net working capital will be needed. In Figure
124, line 28, this is calculated by multiplying the difference in product revenue each
year by .10. In 2007, for example, ($51,986 – $43,322) × .10, and rounded to even
thousands = $866,000 of new net working capital is needed. The remaining years are
calculated similarly.
After all the calculations have been completed, the resulting figures on line 29 represent
amounts that are free to be distributed to the suppliers of Abiomed’s capital, either in
the form of interest to the debt holders or dividends to the stockholders. These free cash
flows range from negative $18.962 million in 2007 to positive $71.750 million in 2016.
In the previous paragraphs, we explicitly forecast the free cash flows for 2007
through 2016. But what about the years after that? After all, Abiomed is not expected
to suddenly cease operating at the end of 2016 but to continue operating indefinitely
into the future as a going concern.
To forecast the free cash flows in the years beyond 2016, we rely on a variation of
the constant growth dividend valuation model, Equation 127. After 2016, Abiomed’s
free cash flows are expected to grow at a constant rate of 5 percent a year indefinitely.
We adapt Equation 127 to value these constantly growing free cash flows as follows:
Constant Growth Free Cash Flow Valuation Model
Vfcf t = FCFt (1 + g)
k−g (1210) Chapter 12 Business Valuation 361 where: Vfcf t = the value of future free cash flows at time t
FCFt = free cash flow at time t
k = the discount rate per period
g = the longterm constant growth rate per period of free cash flows
According to Equation 1210, and assuming a discount rate of 20 percent (see
line 11),5 the value as of the end of 2016 of Abiomed’s free cash flows in years 2017
and beyond, in thousands, would be
Vfcf 2016 = $71, 750 (1 + .05)
.20 − .05 = $502, 250 The value of the free cash flows at the end of 2016 and beyond is called the terminal
value of the company’s operations at the end of 2016. The amount is shown in Figure
124 on line 30.
On line 31, the present value of the free cash flows is calculated using Equation
82a, assuming a discount rate of 20 percent. The present values are then summed up
on line 32 to produce the total value of Abiomed’s operations on April 1, 2006, which
is $100.140 million.
Let us say a few words about this value before proceeding. As we said earlier, the present
value of the company’s free cash flows ($100.140 million in the case of Abiomed) represents
the market value of the firm’s core incomeproducing operations. In the world of finance
and investing, this is sometimes called the firm’s enterprise value. It is NOT the total market
value of the entire company, however, or the total market value of the company’s assets,
because the current, or nonoperating, assets of the company have not yet been accounted for.
We shall have more to say about this issue later in the chapter in the section on
valuing complete businesses. For now, just remember that the present value of the
company’s free cash flows equals the market value of the firm’s core incomeproducing
operations (called enterprise value). The relationship is illustrated in Figure 125.
In the analysis in Figure 124, we have calculated the market value of Abiomed’s
operating, or incomeproducing assets, as shown in the lowerleft portion of Figure
125. Observing Figure 125, it is clear that to obtain the value of Abiomed’s common
stock (which is our ultimate goal), we must take line 32 and add the value of the firm’s
current assets and then subtract the values of current liabilities, longterm debt, and
preferred stock. In Figure 124, this is done on lines 33, 34, 35, and 36. The values for
current assets, current liabilities, longterm debt, and preferred stock were taken from
Abiomed’s March 31, 2006, balance sheet.6
Line 37 of Figure 124 shows the final result after adding Abiomed’s current assets
($46.443 million) and subtracting current liabilities ($8.739 million), longterm debt
($.310 million), and preferred stock ($0) from the present value of the firm’s operations
5 The discount rate represents the weighted average required rates of return of Abiomed’s debt holders and common
stockholders. Calculating this weighted average return was discussed in detail in Chapter 9. 6 To be precise, we should have calculated the market values of Abiomed’s current assets, current liabilities, and longterm debt
before making the adjustments. In practice, however, the book values from the balance sheet are often used instead, because the
process of valuing the items is difficult and the market values often do not differ materially from the book values. 7 In fact, Abiomed’s stock closed at $12.90 on Friday, March 31, 2006, the day before our valuation date. $12.90 per share
equates to a total common equity value of $341.438 million, not including a control premium. This is almost $204 million
higher than the $137.534 million estimated by our model. Could investors have been overcome by speculative fever on that
date? We leave that for you to decide. Take Note
Do not confuse the market
value of Abiomed’s
common equity, as
calculated here, with
the actual price of the
firm’s common stock on
the open market. The
$137.534 million is what
the company’s stock is
worth to an investor with
a required rate of return
of 20 percent a year,
given the assumptions
in the model in Figure
124. Stock traders in the
market may be making
any number of different
assumptions about
Abiomed and may have
different required rates
of return. As a result, the
actual price of Abiomed’s
stock in the market may
be completely different
than the intrinsic value
shown here.7 362 Part III Capital Budgeting and Business Valuation
Total Market Value of a Business Market Value of
Nonoperating
(Current) Assets Figure 125 Total
Market Value of a Business
This figure is an extension of
Figure 121, showing how
total assets are made up of
operating (incomeproducing)
assets plus nonoperating
(current) assets. Present Value of Current Liabilities Present Value of LongTerm Debt
Market Value
of Operating
(IncomeProducing)
Assets Present Value of Preferred Stock
Present Value
of Common Stock ($100.140 million). This final result, $137.534 million, is the total market value of
Abiomed’s common equity as of April 1, 2006. The Yield on Common Stock
We calculate the yield for common stock by rearranging the terms in Equation 127 to
arrive at the constant growth dividend model, as shown in Equation 1211:
The Yield, or Total Return, on Common Stock
ks = D1
+g
P0 (1211) where: D1 = Amount of the common stock dividend anticipated in one period
P0 = Current market price of the common stock
g = Expected constant growth rate of dividends per period
ks = Expected rate of return per period on this common stock
investment
Equation 1211 is also called the formula for an investor’s total rate of return from
common stock. The stock’s dividend yield is the term D1/P0.
To demonstrate how Equation 1211 works, suppose you found that the price of
BP common stock today was $52 per share. Then suppose you believe that BP will pay
a common stock dividend next year of $4.80 a share, and the dividend will grow each
year at a constant annual rate of 4 percent. If you buy one share of BP common stock at
the listed price of $52, your expected annual percent yield on your investment will be Chapter 12 ks =
= Business Valuation D1
+g
P0
$4.80
+ .04
$52 = .0923 + .04
= .1323, or 13.23% If your minimum required rate of return for BP common stock, considering its risk,
were less than 13.23 percent, you would proceed with the purchase. Otherwise you
would look for another stock that had an expected return appropriate for its level of risk. Valuing Complete Businesses
Up to this point in the chapter, we have dealt with the values of business components as
shown in the righthand “pillar” in Figure 121. Now we turn our attention to valuing
the complete business all at once, or the total value of the business’s assets as shown in
the lefthand “pillar” in Figure 121. The Free Cash Flow DCF Model Applied to a Complete Business
As it turns out, using the Free Cash Flow Model to value a complete business is quite
straightforward once you have learned how to use it to value common equity. This is
because the Free Cash Flow Model values the complete business as a part of the procedure
to value common equity. Refer again to Figure 125, which shows that the value of a
complete business is the sum of the values of the operating, or incomeproducing, assets
plus the value of the nonoperating, or current, assets. All that is necessary to use the
Free Cash Flow Model to value a complete business is to add the value of the company’s
current assets, taken from the most recent balance sheet,8 to the value of the company’s
operations, calculated exactly the same way as in Figure 124 for Abiomed. Following
this procedure, the complete business value for Abiomed would be
Present value of company operations (or enterprise value)
+ Value of current assets
= Complete business value of Abiomed $100.140 million
46.443 million
$146.583 million (see Figure 124, lines 32 and 33) The Replacement Value of Assets Method
The replacement value of assets valuation method is similar to the liquidation model
covered earlier in the chapter. According to the concept underlying the model, the market
value of a complete business cannot exceed the amount it would take to buy all of the
firm’s assets on the open market. For example, you would not be willing to pay the
owners of Abiomed $146.583 million for the company if you could buy all the assets
necessary to duplicate the company for $100 million.
8 As we said earlier, to be precise, one should use the market value of the current assets, rather than the book value from the
balance sheet. However, because estimating the market value of the current assets is timeconsuming and the results are often
not materially different from the book value, many analysts simply use the book value in their complete business valuations. 363 364 Part III Capital Budgeting and Business Valuation Although it is simple in concept, the replacement value of assets method is not often
applied to complete business valuations for two reasons:
1. It is frequently very difficult to locate similar assets for sale on the open market.
2. Some of a business’s assets are difficult to define and quantify (how do you
quantify a business’s reputation, for example, or the strength of its brands?).
Although it is difficult to use the replacement value of assets method to value a
complete business, the model can be quite useful for estimating the value of individual
assets in a business. For example, the value of a company’s nonproprietary software can
be estimated by listing the various programs in use and then noting the prices of those
programs in retail stores, catalogs, and on the Internet. The sum of the lowest prices
at which the programs could be obtained is the replacement value of the company’s
software. In another example, it is possible to estimate the value of a company’s
machinery and equipment by calculating what it would cost to replace all the machinery
and equipment. This is normally done by noting the prices for machinery and equipment
of similar age and in similar condition on the open market. Alternatively, analysts
sometimes note the prices of new machinery and equipment and adjust those prices to
reflect the age and condition of the machinery and equipment belonging to the company.
Individual asset valuations of this type are most often employed when one business
buys another and it is necessary to allocate the purchase price among the assets purchased.
In such cases, the “fair market value” of the individual assets is estimated (using the
replacement value of assets method, the discounted free cash flow method, or some
other method), and any amounts remaining are assigned to “goodwill.” What’s Next
In this chapter we investigated valuation methods for bonds, preferred stock, common
stock, and complete businesses. The valuation methods applied risk and return, and
time value of money techniques learned in Chapters 7 and 8, respectively. In the next
chapter, we will explore capital structure issues. Summary
1. Explain the importance of business valuation.
When corporations contemplate selling their businesses, they do not want to undervalue
the businesses because they want to raise the most money possible. Likewise, wouldbe
purchasers of businesses use valuation methods to avoid paying more than the businesses
are worth.
2. Discuss the concept of business valuation.
To value any business, business asset, or security, we apply risk and return and time
value of money techniques. In sum, the value of a business, asset, or security is the
present value of the expected future cash flows. Bond cash flows are the periodic interest
payments and the principal at maturity. Stock and business cash flows come from the
future earnings that the assets produce for the firm, usually leading to cash dividend
payments. Chapter 12 Business Valuation To value businesses, assets, and securities, investors and financial managers use a
general valuation model to calculate the present value of the expected future cash flows.
That model incorporates risk and return, and time value of money concepts.
3. Compute the market value and the yield to maturity of a bond.
The market value of a bond is the sum of the present values of the coupon interest
payments plus the present value of the face value to be paid at maturity, given a market’s
required rate of return.
The yield to maturity of a bond (YTM) is the average annual rate of return that
investors realize if they buy a bond for a certain price, receive the promised interest
payments and principal on time, and reinvest the interest payments at the YTM rate.
A bond’s market price and its YTM vary inversely. That is, when the YTM rises,
the market price falls, and vice versa. When a bond has a YTM greater than its coupon
rate, it sells at a discount to its face value. When the YTM is equal to the coupon rate,
the market price equals the face value. When the YTM is less than the coupon rate, the
bond sells at a premium over face value.
4. Compute the market value and expected yield of preferred stock.
The market value of preferred stock is the present value of the stream of preferred stock
dividends, discounted at the market’s required rate of return for that investment. Because
the dividend cash flow stream is a perpetuity, we adapt the present value of a perpetuity
formula, Equation 85, to value preferred stock.
The yield on preferred stock represents the annual rate of return that investors
realize if they buy the stock for the current market price and then receive the promised
dividend payments on time.
5. Compute the market value per share of common stock.
The market value of common stock is estimated in a number of ways, including
(1) finding the present value of all the future dividends the stock is expected to pay,
discounted at the market’s required rate of return for that stock; and (2) finding the
price implied, given the level of earnings per share and the appropriate P/E ratio. The
dividend growth model and the P/E valuation approaches assume the firm will be a
going concern. That is, the models value the future cash flows that a firm’s assets are
expected to produce. Two versions of the dividend growth model are commonly used,
one for situations in which the future growth of the firm’s dividends is expected to be
constant, and the other for situations in which the future growth of the firm’s dividends
is expected to be nonconstant, or supernormal. Supernormal growth implies a period of
high growth followed by a settling out at the longterm constant growth rate.
6. Compute the market value of total common equity.
The market value of total common equity is estimated in a number of ways, including
(1) estimating common equity value based on the book value of the firm’s assets
as recorded on the balance sheet, less all liabilities and preferred stock (if any); (2)
estimating the value of the firm’s assets if they were to be liquidated on the open market
and all claims on the firm were to be paid off; and (3) employing a discounted free cash
flow model that calculates the present value of expected free cash flows to the suppliers
of the firm’s capital. The discounted free cash flow model is similar to the nonconstant
dividend growth model in that it involves making a forecast of free cash flows during a
specified period (usually 7 to 10 years). This is followed by the calculation of the value
of the cash flows expected to be received after the forecast period (called the terminal 365 366 Part III Capital Budgeting and Business Valuation value). The present values of the free cash flows and the present value of the terminal
value are summed to produce the total present value of the firm’s operations. This figure,
in turn, is adjusted by adding current assets and subtracting current liabilities, longterm
debt, and preferred stock (if any) to produce the total value of common equity.
7. Compute the expected yield of common stock.
The yield on common stock is the percentage return investors can expect if they
purchase the stock at the prevailing market price and receive the expected cash flows.
It is calculated by solving for k in the constant growth dividend model.
8. Compute the value of a complete business.
The market value of a complete business can be found by applying the discounted free
cash flow model used to estimate the value of common equity. In the complete business
application, current assets are added to the present value of the firm’s operations to
produce the value of the complete business. Sometimes the value of complete businesses
can also be found by calculating the amount that would be required to replace the
firm’s assets, but this method is usually more effective when applied to the valuation
of individual business assets. Equations Introduced in This Chapter
Equation 121. The Discounted Cash Flow Valuation Model:
V0 = where: CF1 (1 + k )1 + CF2 (1 + k )2 + CF3 (1 + k )3 + ... + CFn (1 + k ) n V0 = Present value of the anticipated cash flows from the asset,
its current value
CF1, 2, 3, and n = Cash flows expected to be received one, two, three, and so
on up to n periods in the future
k = Discount rate, the required rate of return per period Equation 122. The Bond Valuation Formula (Algebraic Method):
1
1 −
n (1 + k d )
VB = INT × kd where: M
+
n
1 + kd )
( VB = Current market value of the bond
INT = Dollar amount of each periodic interest payment
n = Number of times the interest payment is received (which is
also the number of periods until maturity)
M = Principal payment received at maturity
kd = Required rate of return per period on the bond debt
instrument Chapter 12 Business Valuation Equation 123. The Bond Valuation Formula (Table Method):
VB = (INT × PVIFAk, n) + (M × PVIFk, n) where: PVIFAk, n = Present Value Interest Factor for an Annuity from Table IV
PVIFk, n = Present Value Interest Factor for a single amount from
Table II
Equation 124. The Formula for the Present Value of Preferred Stock:
VP = where: Dp
kp VP = Current market value of the preferred stock
Dp = Amount of the preferred stock dividend per period
kp = Required rate of return for this issue of preferred stock Equation 125. Formula for the Yield on Preferred Stock:
kp = where: Dp
VP kp = Yield per period on investment that an investor can expect
if the shares are purchased at the current market price, PP,
and if the preferred dividend, Dp, is paid forever
Dp = Amount of the preferred stock dividend per period
VP = Current market value of the preferred stock Equation 126. The DCF Valuation Model Applied to Common Stock:
P0 = where: D1
D2
D3
Pn
1+
2+
3 + ... +
(1 + k s )
(1 + k s )
(1 + k s )
(1 + k s )n P0 = Present value of the expected dividends, the current price
of the common stock D1, D2, D3, etc. = Common stock dividends expected to be received at the
end of periods 1, 2, 3, and so on until the stock is sold
Pn = Anticipated selling price of the stock in n periods
ks = Required rate of return per period on this common stock
investment 367 368 Part III Capital Budgeting and Business Valuation Equation 127. The Constant Growth Version of the Dividend Valuation Model:
P0 = where: D1
ks − g P0 = Current price of the common stock
D1 = Dollar amount of the common stock dividend expected one
period from now
ks = Required rate of return per period on this common stock
investment
g = Expected constant growth rate per period of the company’s
common stock dividends Equation 128. The P/E Model for Valuing Common Stock:
Appropriate Stock Price = Industry P/E Ratio × EPS Equation 129. The Book Value of Common Stock:
Book Value of Common Stock = Total Assets – Total Liabilities – Preferred Stock Equation 1210. The Constant Growth Free Cash Flow Valuation Model
Vfcf t = where: FCFt (1 + g)
k−g Vfcf t = the value of future free cash flows at time t
FCFt = free cash flow at time t
k = the discount rate per period
g = the longterm constant growth rate per period of free cash
flows Equation 1211. The Yield, or Total Return, on Common Stock:
ks = where: D1
+g
P0 D1 = Amount of the common stock dividend anticipated in one period
P0 = Current market price of the common stock
g = Expected constant growth rate of dividends per period
ks = Expected rate of return per period on this common stock
investment Chapter 12 Business Valuation 369 SelfTest
ST1. The DaimlerChrysler Corporation has issued
a 10.95 percent annual coupon rate bond that
matures December 31, 2027. The face value is
$1,000. If the required rate of return on bonds
of similar risk and maturity is 9 percent, and
assuming the time now is January 1, 2007,
what is the current value of DaimlerChrysler’s
bond? ST2. DaimlerChrysler’s 10.95 percent coupon rate,
2027 bond is currently selling for $1,115. At
this price, what is the yield to maturity of the
bond? Assume the time is January 1, 2007. ST3. McDonald’s is offering preferred stock
that pays a dividend of $1.93 a share. The
dividend is expected to continue indefinitely.
If your required rate of return for McDonald’s
preferred stock is 8 percent, what is the value
of the stock? ST4. Pepsico’s next annual dividend is expected
to be $1.14 a share. Dividends have been
growing at a rate of 6 percent a year, and
you expect this rate to continue indefinitely.
If your required rate of return for this stock
is 9 percent, what is the maximum price you
should be willing to pay for it? ST5. Goodyear Corporation stock is currently
selling for $38. The company’s next annual
dividend is expected to be $1.00 a share.
Dividends have been growing at a rate of 5
percent a year, and you expect this rate to
continue indefinitely. If you buy Goodyear at
the current price, what will be your yield, or
total return? Review Questions
1. Describe the general pattern of cash flows from a
bond with a positive coupon rate.
2. How does the market determine the fair value of
a bond?
3. What is the relationship between a bond’s market
price and its promised yield to maturity? Explain.
4. All other things held constant, how would the
market price of a bond be affected if coupon
interest payments were made semiannually
instead of annually?
5. What is the usual pattern of cash flows for a
share of preferred stock? How does the market
determine the value of a share of preferred stock,
given these promised cash flows?
6. Name two patterns of cash flows for a share of
common stock. How does the market determine
the value of the most common cash flow pattern
for common stock?
7. Define the P/E valuation method. Under what
circumstances should a stock be valued using this
method? 8. Compare and contrast the book value and
liquidation value methods for common stock. Is
one method more reliable? Explain.
9. Answer the following questions about the
discounted free cash flow model illustrated in
Figure 124:
a. What are “free cash flows”?
b. Explain the terminalvalue calculation at
the end of the forecast period. Why is it
necessary?
c. Explain the term present value of the firm’s
operations (also known as enterprise value).
What does this number represent?
d. Explain the adjustments necessary to translate
enterprise value to the total present value of
common equity.
10. Explain the difference between the discounted
free cash flow model as it is applied to the
valuation of common equity and as it is applied to
the valuation of complete businesses.
11. Why is the replacement value of assets method
not generally used to value complete businesses? 370 Part III Capital Budgeting and Business Valuation Build Your Communication Skills
CS1. Check the current price of Texas Instruments
Corporation stock or a stock of your choice
in the financial press. Then research financial
information from last year predicting how
Texas Instruments stock (or the stock you
chose) would fare and analyze what valuation
methods the analysts used. Next, compare
the current price with the analysts’ price
predictions. Prepare a brief oral report that you
present to the class discussing your assessment
of the analysts’ stock valuation. CS2. Choose a stock in the financial press. Check
its current price. Then estimate the value of
the stock using the dividend growth model,
Equation 127. Compare the value of the
stock with its current price and prepare a short
memo in which you explain why the two
figures might differ. Problems
Bond Valuation 121. Owen Meany is considering the purchase of a $1,000 Amity Island
Municipal Bond. The city is raising funds for a much needed advertising
campaign to promote its East Coast resort community. The stated coupon
rate is 6 percent, paid annually. The bond will mature in 10 years. The YTM
for similar bonds in the market is 8 percent.
a. How much will the annual interest payments be?
b. What is the market price of the bond today?
c. Is the interest received on a municipal bond generally tax free? Bond Valuation 122. Assume Disney Studios is offering a corporate bond with a face value of
$1,000 and an annual coupon rate of 12 percent. The maturity period is 15
years. The interest is to be paid annually. The annual YTM for similar bonds
in the market is currently 8 percent.
a. What is the amount of interest to be paid annually for each bond?
b. What is the value of this $1,000 bond today?
c. What would be the present value of the interest and principal paid
to holders of one of their bonds if the interest payments were made
semiannually instead of annually? Bond Valuation 123. After a major earthquake, the San Francisco Opera Company is offering zero
coupon bonds to fund the needed structural repairs to its historic building.
Buster Norton is considering the purchase of several of these bonds. The
bonds have a face value of $2,000 and are scheduled to mature in 10
years. Similar bonds in the market have an annual YTM of 12 percent. If
Mr. Norton purchases three of these bonds today, how much money will he
receive 10 years from today at maturity? Chapter 12 371 Business Valuation 124. Two best friends, Thelma and Louise, are making longrange plans for a road
trip vacation to Mexico. They will embark on this adventure in five years
and want to invest during the fiveyear period to earn money for the trip.
They decide to purchase a $1,000 Grand Canyon Oil Company bond with an
annual coupon rate of 10 percent with interest to be paid semiannually. The
bond will mature in five years. The YTM of similar bonds is 8 percent. How
much should they be willing to pay for the bond if they purchase it today? Bonds with
Semiannual
Interest Payments 125. Assume that Intel Corporation’s $1,000 face value 9 percent coupon rate
bond matures in 10 years and sells for $1,100. If you purchase the bond
for $1,100 and hold it to maturity, what will be your average annual rate of
return on the investment? Expected Rate of
Return on a
Corporate Bond 126. Clancy Submarines, Inc. is offering $1,000 par value bonds for sale. The
bonds will mature 10 years from today. The annual coupon interest rate is 12
percent, with payments to be made annually. James Hobson just purchased
one bond at the current market price of $1,125.
a. Will the YTM of this bond be greater than or less than the coupon interest
rate? Answer this part without doing any calculations.
b. To the nearest whole percent, what is the YTM of Mr. Hobson’s bond?
You’ll need to crunch some numbers for this part.
c. What would the YTM have to be to make the market price of the bond
equal to the face value? No number crunching is needed to answer. Bond YTM
and Pricing 127. A corporate bond has a face value of $1,000 and an annual coupon interest
rate of 7 percent. Interest is paid annually. Of the original 20 years to
maturity, only 10 years of the life of the bond remain. The current market
price of the bond is $872. To the nearest whole percent, what is the YTM of
the bond today? Bond YTM 128. The new Shattuck Corporation will offer its preferred stock for sale in the
very near future. These shares will have a guaranteed annual dividend of $10
per share. As you research the market, you find that similar preferred stock
has an expected rate of return of 12 percent. If this preferred stock could be
purchased today, what price per share would you expect to pay for it? Preferred Stock
Valuation 129. Lucky Jackson knows that one share of Grand Prix Enterprises preferred
stock sells for $20 per share on the open market. From its annual reports,
he sees that Grand Prix pays an annual dividend of $1.75 per share on
this preferred stock. What is the market’s required rate of return on Grand
Prix’s stock? Preferred Stock k 372
Preferred Stock
Valuation Common Stock
Valuation per Share Yield on
Common Stock Common Stock
Valuation per Share Part III Capital Budgeting and Business Valuation 1210. Tiny Shipping Corporation is planning to sell preferred stock that will pay
an annual dividend of $8 per share. The current expected rate of return from
similar preferred stock issues is 13 percent.
a. What price per share would you expect to have to pay to purchase this
stock?
b. If the stock is actually selling for $50 per share, what is the market’s
required rate of return for this stock?
1211. China S. Construction, Inc., is in the business of building electrical power
plants in the eastern United States. Jack Godell and the rest of the board
members of the firm have just announced a $4 per share dividend on the
corporation’s common stock to be paid in one year. Because the quality
of some of its recent projects is under attack by investigative television
reporters, the expected constant dividend growth rate is only estimated to
be 1 percent. The required rate of return for similar stocks in this industry is
16 percent.
a. What is the present value of the expected dividends from one share of
China S. Construction’s common stock?
b. What is the stock’s dividend yield (D1/P0)?
1212. The current listed price per share of a certain common stock is $15. The
cash dividend expected from this corporation in one year is $2 per share. All
market research indicates that the expected constant growth rate in dividends
will be 4 percent per year in future years. What is the rate of return on this
investment that an investor can expect if shares are purchased at the current
listed price?
1213. Golden Manufacturing Company is expected to pay a dividend of $8 per
share of common stock in one year. The dollar amount of the dividends
is expected to grow at a constant 3 percent per year in future years. The
required rate of return from shares of similar common stock in the present
environment is 14 percent.
a. What would you expect the current market price of a share of Golden
common stock to be?
b. Assuming the cash dividend amount and the growth rate are accurate,
what is the annual rate of return on your investment in Golden common
stock if you purchased shares at the stock’s actual listed price of $65 per
share? Bond Valuation 1214. Micron issues a 9 percent coupon bond with a maturity of 5 years. The face
value of the bond, payable at maturity, is $1,000. What is the value of this
bond if your required rate of return is 12 percent? Bond Valuation
(Semiannual Interest) 1215. Sam wants to purchase a bond that has a par value of $1,000, an annual
coupon rate of 7 percent, and a maturity of 10 years. The bond’s interest is
paid semiannually. Sam’s annual required rate of return is 11 percent. What
should Sam be willing to pay for this particular bond? Chapter 12 Business Valuation 1216. What is the value of a security that entitles you to receive the following
payments if your required rate of return for this type of security is
23 percent? 373
Discounted Cash
Flows (DCF) $80—end of year 1
$150—end of year 2
$1,500—end of year 3 1217. Tom expects the issue of InVest preferred stock to pay an annual dividend of
$3 per share. He also has researched the company and feels that 12 percent
is a fair rate of return for this investment. Calculate the value of each share
of stock. Preferred Stock
Valuation 1218. Analysts forecast that Dixie Chicks, Inc. (DCI) will pay a dividend of $2.20
a share at the end of this year, continuing a longterm growth trend of 9
percent a year. If this trend is expected to continue indefinitely and investors’
required rate of return for DCI is 18 percent, what is the market value per
share of DCI’s common stock? Common Stock
Valuation,
Constant Growth 1219. PepsiCo (NYSE: PEP) paid a dividend of $0.58 per share this year.
Dividends at the end of each of the next five years are expected to be as
follows: Common Stock
Valuation,
Nonconstant
Growth Year 1 $0.70 Year 2 $0.83 Year 3 $0.96 Year 4 $1.09 Year 5 $1.22 After year 5, dividends are expected to grow indefinitely at 10 percent a year.
If your required rate of return for PepsiCo common stock is 12 percent, what
is the most that you would pay per share for PepsiCo today?
1220. Regis knows that CRS stock sells for $82 per share, has a growth rate of 7
percent, and a dividend that was just paid of $3.82. What can Regis expect as
an annual percent yield if he purchases a share of CRS stock? Common Stock
Yield 1221. Gwenyth just purchased a bond for $1,250 that has a maturity of 10 years
and a coupon interest rate of 8.5 percent, paid annually. What is the YTM of
the $1,000 face value bond that she purchased? Yield to Maturity
(YTM) 1222. Analysts forecast that free cash flows from Dixie Chicks, Inc. (DCI) will be
$2.1 million in the coming year, continuing a longterm growth trend of 9
percent a year. If this trend is expected to continue indefinitely and investors’
required rate of return for DCI is 18 percent, what will be the total enterprise
value of DCI? Enterprise Value,
Constant Growth 374 Part III Enterprise Value,
Nonconstant
Growth Capital Budgeting and Business Valuation 1223. The free cash flow for PepsiCo (NYSE: PEP) this year was $1,026,600,000.
Free cash flows at the end of each of the next five years are expected to be as
follows:
Year 1 $1,231,920,000 Year 2 $1,453,665,600 Year 3 $1,686,252,096 Year 4 $1,922,327,389 Year 5 $2,153,006,676 After year 5, free cash flows are expected to grow indefinitely at 10 percent
a year.
If the weighted average cost of capital (WACC) for PepsiCo is 12 percent,
what is the enterprise value of the company today?
Book Value 1224. Jack and Frank Baker know their piano renditions of lounge songs have
limited appeal on the night club circuit, so they work parttime as investment
consultants. They are researching relatively unknown corporations, one of
which is Susie Diamond Enterprises. To get a quick idea of the value of
SDE’s common stock, they have taken the following numbers from the most
recent financial statements.
Total Assets $675,000 Total Liabilities $120,000 250,000 Shares of Common Stock Issued
100,000 Shares of Common Stock Outstanding What is the book value (net worth) of Susie Diamond Enterprises?
Book Value
Liquidation
Value, and
P/E Methods 1225. The most recent balance sheet of Free Enterprise, Inc., follows.
Free Enterprise, Inc., Balance Sheet December 31, 2009
(thousands of dollars)
Assets
Cash Liabilities + Equity
$ 4,000 Accounts Payable $ 4,400 Accounts Receivable 10,000 Notes Payable 4,000 Inventory 13,000 Accrued Expenses 5,000 Prepaid Expenses
Total Current Assets
Fixed Assets
Total Assets 400
27,400
11,000
$ 38,400 Total Current Liabilities
Bonds Payable
Common Equity
Total Liabilities + Equity 13,400
6,000
19,000
$ 38,400 a. What was Free Enterprise’s book value (net worth) at the beginning
of 2010?
b. If the company had 750,000 shares of common stock authorized and
500,000 shares outstanding, what was the book value per share of
common stock at the beginning of 2010? Chapter 12 Business Valuation 375 c. Net income of Free Enterprise, Inc. was $5,610,000 in 2009. Calculate the
earnings per share of Free Enterprise’s common stock.
d. The P/E ratio for a typical company in Free Enterprise, Inc.’s industry is
estimated to be 6. Using the EPS from part c) above, calculate the price
of one share of common stock at the beginning of 2007, assuming that
Free Enterprise commands a P/E ratio value equal to that of an average
company in its industry.
e. What would you infer about the company’s total assets shown on the
balance sheet when comparing this calculated stock price with the
company’s book value per share?
f. Calculate the liquidation value of Free Enterprise’s common stock
assuming the market value of the total assets is $50 million and the market
value of total liabilities is $20 million, as estimated by your analyst.
1226. Lucky Jackson is trying to choose from among the best of the three
investment alternatives recommended to him by his fullservice investment
broker. The alternatives are
a. The corporate bond of Star Mining Company has a face value of $1,000
and an annual coupon interest rate of 13 percent. The bond is selling in
the market at $1,147.58. Of the original 20 years to maturity, only 16
years of the life of the bond remain.
b. The preferred stock of Supernova Minerals Company has a par value of
$100 per share and it offers an annual dividend of $14 per share. The
market price of the stock is $140 per share.
c. The common stock of White Dwarf Ores Company sells in the market at
$300 per share. The company paid a dividend of $39 per share yesterday.
The company is expected to grow at 3 percent per annum in the future.
Which of the three alternatives should Lucky choose? Remember the priority
of claims for bondholders, preferred stockholders, and common stockholders
from Chapters 1 and 4. Comprehensive
Problem 1227. Suppose Flash in the Pan Corporation is expected to pay an annual dividend
of $3 per share one year from now and that this dividend will grow at the
following rates during each of the following four years (to the end of year 5):
Year 2, 20 percent; Year 3, 30 percent; Year 4, 20 percent; Year 5, 10 percent.
After this supernormal growth period, the dividend will grow at a sustainable
5 percent rate each year beyond year 5.
a. What is the present value of the dividends to be paid during the
supernormal growth period? Assume that the required rate of return, ks, is
15 percent.
b. What is the present value of the dividends to be paid during the normal
growth period (from year 6 through infinity)?
c. What is the total present value of one share of Flash in the Pan’s common
stock? Nonconstant
Dividend Growth
Model 376
Discounted
Free Cash Flow
Model for Total
Common Equity
(Challenge
Problem) Part III Capital Budgeting and Business Valuation 1228. Assume that you are the owner of a pet foods company and you are
interested in acquiring the stock of HardiPets, an upandcoming company
that markets a new type of dog food that causes pets that eat it to never get
sick and to never need shots. Selected financial data for HardiPets is shown.
HardiPets, Inc., Selected Financial Data for 2009
Total Revenue $ 1,000,000 Cost of Goods Sold 500,000 Gross Profit 500,000 Selling, General and Administrative Expenses 200,000 Earnings before Interest, Taxes, Depr. & Amort. (EBITDA) 300,000 Depreciation and Amortization 100,000 Earnings before Interest and Taxes (EBIT) 200,000 Capital Expenditures $ 15,000 Combined Federal and State Income Tax Rate 40% Current Assets, Dec. 31, 2009 $ 100,000
80,000 Current Liabilities, Dec. 31, 2009
LongTerm Debt, Dec. 31, 2009 500,000 Preferred Stock Outstanding, Dec. 31, 2009 0 Prepare a valuation analysis of HardiPets total common equity using the
discounted free cash flow model. Use a spreadsheet format similar to the
example shown in Figure 124. The following forecasting variables apply.
Assume that the time now is January 1, 2010.
Revenue Growth Factor
Expected Gross Profit Margin 2010
10% 2011
15% 2012
20% 2013
25% 2014
30% 2015
25% 2016
20% 2017
15% 2018
10% 2019
5% 50% 50% 50% 50% 50% 50% 50% 50% 50% 50% S, G, & A Exp % of Revenue 20% 20% 20% 20% 20% 20% 20% 20% 20% 20% Depr. & Amort. % of Revenue 10% 10% 10% 10% 10% 10% 10% 10% 10% 10% Capital Expend. Growth Factor 10% 10% 10% 10% –10% –10% –10% –10% –10% –10% Net Working Cap to Sales Ratio 10% 10% 10% 10% 10% 10% 10% 10% 10% 10% Income tax rate = 40%
Assumed longterm sustainable growth rate = 5% per year after 2019
Discount rate = 20%
Discounted Free
Cash Flow Model
for Complete
Business Valuation
(Challenge
Problem) 1229. The Great Expectations Company just finished its first year of operations in
which the company realized $2 million in revenue. Company managers are
looking forward to a number of years of rapid growth ahead, and to this end
they are seeking $10 million in longterm debt financing from the Capital
4 U Financing Company. However, before the loan can be approved, an
independent appraisal of Great Expectations is required to establish the fair
market value of the company.
Assume that you are a financial analyst working for Value Plus, Independent
Appraisers. Capital 4 U has engaged your firm to estimate the fair market value
of Great Expectations as a complete business. Selected financial data for Great
Expectations is shown. Chapter 12 377 Business Valuation Great Expectations, Inc., Selected Financial Data for 2009
Total Revenue $2,000,000 Cost of Goods Sold 1,200,000 Gross Profit 800,000 Selling, General and Administrative Expenses 1,200,000 Earnings before Interest, Taxes, Depr. & Amort. (EBITDA) (400,000) Depreciation and Amortization 200,000 Earnings before Interest and Taxes (EBIT) (600,000) Capital Expenditures $1,000,000 Combined Federal and State Income Tax Rate 40% Current Assets, Dec. 31, 2009 $ 500,000 Prepare a valuation analysis of Great Expectations as a complete business using
the discounted free cash flow model. Use a spreadsheet format similar to the
example shown in Figure 124, modified for a complete business. The following
forecasting variables apply. Assume that the time now is January 1, 2007.
2010
Revenue Growth Factor 2011 2012 2013 2014 2015 2016 2017 2018 2019 20% 30% 40% 50% 60% 50% 40% 30% 20% 10% Expected Gross Profit Margin 50% 51% 52% 53% 54% 55% 56% 57% 58% 59% S, G, & A Exp % of Revenue 50% 40% 30% 29% 28% 27% 26% 25% 24% 23% Depr. & Amort. % of Revenue 10% 10% 10% 10% 10% 10% 10% 10% 10% 10% Capital Expend. Growth Factor 40% 35% 30% 25% 20% –10% –15% –20% –25% –30% Net Working Cap to Sales Ratio 19% 18% 17% 16% 15% 14% 13% 12% 11% 10% Income tax rate = 40%
Assumed longterm sustainable growth rate = 5% per year after 2019
Discount rate = 20% 378 Part III Capital Budgeting and Business Valuation Answers to SelfTest
ST1. The present value of DaimlerChrysler’s 10.95 percent 2027 bond can be
found using Equation 122:
1 1 − (1 + k ) n
d
VB = INT × kd + (1 M
n
+ kd ) Face value is $1,000
The coupon interest payment is 10.95 percent of $1,000, or $109.50.
n = 21
kd = 9%
1 1 −
21 (1 + .09) VB = $109.50 × +
.09 $1, 000
21
1 + .09)
( $1, 000 = ($109.50 × 9.29224) + 6.108801
= $1, 017.50 + $163.70
= $1,181.20 So the present value of the bond is $1,181.20.
ST2. The bond’s YTM is found by trial and error. We know that the bond has a
price of $1,115; face value of $1,000; coupon interest payment of $109.50
(10.95% of $1,000); and matures in 21 years. Now we can find that value of
kd that produces a VB of $1,115. Use Equation 122 and solve for VB.
First try kd = 9%:
1 1 −
21 (1 + .09)
VB = $109.50 × +
.09 $1, 000 (1 + .09)21 $1, 000 = ($109.50 × 9.29224) + 6.108801
= $1, 017.50 + $163.70
= $1,181.20 > $1,115 Chapter 12 Business Valuation $1,181.20 is too high. Try again using a higher yield (remember, bond prices
and yields vary inversely).
Second try at kd = 10%:
1 1 −
21 (1 + .10) VB = $109.50 × +
.10 $1, 000 (1 + .10)21 $1, 000 = ($109.50 × 8.64869) + 7.40025 = $947.03 + $135.13
= $1, 082.16 < $1,115 $1,082.16 is too low. Try again using a lower yield.
Third try at kd = 9.65%:
1 1 −
21 (1 + .0965)
VB = $109.50 × +
.0965 $1, 000
(1 + .0965)21 $1, 000 = ($109.50 × 8.86545) + 6.92120 = $970.77 + $144.48
= $1,115.25 At kd = 9.65% the calculated value of VB is within $.25 of the current market
price. We conclude the bond’s YTM is 9.65 percent.9
ST3. Equation 125 is used to find the value of preferred stock as follows:
VP = Dp
kp Dp is $1.93 and kp is 8 percent.
VP = $1.93
.08 = $24.125 9 The exact YTM, found using a financial calculator or Excel’s RATE function, is 9.652590645 percent. 379 380 Part III ST4. Capital Budgeting and Business Valuation The maximum price you are willing to pay for Pepsico is what it is worth
to you, or its value. Because the characteristics of the stock fit the constant
dividend growth model, use Equation 127 to compute the value.
P0 = D1
ks − g D1 is $1.14, ks is 9 percent, and g is 6 percent.
Given these conditions, the value of Quaker Oats stock is
$1.14
.09 − .06 P0 = $1.14
.03 = = $38 ST5. The yield on common stock can be found using Equation 1211.
ks = D1
+g
P0 D1 is $1.00, P0 is $38, and g is 5 percent. Given these conditions, the yield on
Goodyear common stock is as follows:
ks = $1.00
+ .05
$38 = .0263 + .05
= .0763, or 7.63% ...
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This note was uploaded on 11/17/2011 for the course BUS 330 taught by Professor Nugent during the Fall '08 term at SUNY Stony Brook.
 Fall '08
 Nugent
 Valuation

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