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Unformatted text preview: Spring 1999 Problem 1
VS = AT Operating Margin * (1 Reinvestment Rate) * (1 + g)/(WACC g)
Reinvestment Rate = g / ROC = g / (AT Operating Margin * Sales/Capital)
Let the margin for Generic Office be x,
VS for Generic Office = 1.5 = x (1.05/2x)(1.05)/(.10.05)
Solve for x,
x = (1.5*.05+(.05/2)*1.05)/1.05
x =
9.64%
HK's aftertax operating margin = 9.64% (1.05) =
HK's VS ratio =.1013 (1.05/2*.1013)(1.05)/(.10.05) = 10.13% ! I also gave full credit if you added 5% to get 14.64%
1.6023
! Note that if you do not adjust the reinvestment rate, you
get 1.575.
Problem 2
a. Value of Developed Reserves = 100,000 * (300200) * (PV of Annuity, 5 years, 9%) = $38,896,513 b. Value of Undeveloped Reserves (on DCF basis) Value of oil in the ground = 40,000 * (300200) * (PV of Annuity, 9%, 12.5 years) =
### ! 40000 barrels a year for 12.5 years Value of oil in the ground allowing for development lag = 29,309,311/1.08 =
### Fixed cost of development =
### DCF Value of Undeveloped reserves =
###
I also gave full credit for a number of variations, including
a. Assuming that costs and prices are in present value dollars, in which case the value of reserves is [500000*(300200)]/1.08 = 46,296,296
c. Inputs for Option Pricing Model
y = Annual Production Revenue/Reserves = 40,000/500,000 =
8.00% ! Many of you used 1/15. You actually lose more because
your production potential is much higher.
S = PV of reserves discounted back by development lag = $27,138,251 ! Full credit also for $ 46,296,296
K = Upfront Cost of Developing Reserves = $50,000,000 t = Period for which firm has rights =
15
Variance = Expected variance in ln(gold prices) =
0.09 ! Use forward looking variance
r = Riskfree rate =
6.00%
d. The developed reserves will become less valuable, since oil prices are down.
The undeveloped reserves may become more or less valuale depending upon whether the effect of S or the effect of variance is greater on the option value. Spring 2000 Problem 1
Adjusted EBIT = 1500 100 =
Adjusted EBIT (1t) = Reinvestment =
FCFF 1400 840
336
504 Total Beta = 0.80/0.5 =
Levered beta = 1.6 (1 + (1.4)(3/7)) =
Cost of Equity = 6% + 2.01 (4%) =
Cost of Capital = 14.04% (.7) + 7% (1.4)(.3) = 1.6 Tax rate = 480/1200 = 40% (Do not divide by EBIT. That
will result in a double counting of the interest tax benefit
which is already being counted in the cost of capital) 2.0114285714
14.04% Use total beta rather than illiquidity discount, since you have
11.09% insufficient information for such a discount. Value of private firm = 504 (1.05)/(.1109.05) = $8,692.51 Problem 2
Present Value of FCFF from developed reserves = 300 (PVA,10 years, 9.375%) =
Cost of Capital = 12%(25/40) + 5% (15/40) =
Value of undeveloped reserves = 4000 1894 =
Problem 3
d1 = 0.15
d2= 0.90 N(d1) =
N(d2) = $1,894 9.38% $2,106 ! Do not subtract from the value of equity. 0.4404
0.1841 Value of Equity = 400 (.4404) 800 exp (.06*6) (.1841) =
Value of Debt = 400 73.41
Interest rate on debt = (800/326.59)^(1/6) 1 =
Default spread on debt = 16.08% 6% = $73.41 $326.59 16.08%
10.08% Spring 2002
Problem 1 Aftertax Margin
Sales/ Capital
ROC
Reinvestment rate
Value/Sales
Value BigName 12%
2
24.00%
16.67%
2.08
10.4 Problem 2
Net Income
ROE
Total Beta
PBV =
MV of Equity = NoName 6%
2
12.00%
33.33%
0.832
4.16 Brand Name ! ROC = Aftertax operating margin * Sales/BV of capital
! Reinvestment rate = g/ ROC 6.24 2 ! Remember to subtract aftertax expense = 2.6 1(1.4)
20.00%
2.75
1.94
19.4 Problem 3
S =
K =
t =
Variance =
Riskless rate =
cost of delay= 106.698524
131.698524
12
0.0225
5%
0.083333333 ! I think you can also make a reasonable case for 1/8 if you argued
that competition would kick in after the 8th year.
! In fact, you can even make a reasonable case for it being 0. If you entered
0 and want to justify it, give me your reason… Fall 2002 Problem 1
First, clean up the market value of equity for the cross holdings
Total market value of equity =
3000 ! 150 *20 Value of equity in Coleman Holdings = 500 ! 20% of 2500 Value of equity in Silicon Tech =
1200 ! 60% of 2000
Value of Equity in Steel business =
1300
Next clean up the debt for the consolidated debt from Silicon
Value of debt =
2000 Value of Debt in Silicon Tech =
500 ! Silicon Tech's debt is consolidated in balance sheet
Value of debt in Steel business =
1500
Finally, clean up the EBITDA
Consolidated EBITDA = EBITDA of Silicon Tech =
EBITDA of Steel Business = 700
300
400 EV of Steel Business =
EV/ EBITDA of Steel Business = 2800
7.00 Problem 2
a. Estimated PS in year 5 =
3.5 ! Net margin = 10%; 1.5 + .2 (10) = 3.5 Estimated Equity value in year 5 =
1750 ! 3.5 * 500
b. Total beta =
2.25 Cost of equity =
14.00%
c. Value of equity today (going concern) =
$908.90 ! 1750/1.14^5 Survival adjusted equity value =
$363.56 ! 908.90 * .40 Spring 2003 Problem 1
a. Unlevered beta =
Total beta =
Cost of equity = 1
2.5
15.00% ! Use total beta because buyer is not diversified Return on capital =
Reinvestment rate = 0.175 ! 280/1600
0.228571429 !4%/17.5% EBIT (1t) Reinvestment
FCFF $280.00
$64.00 ! 22.86% of EBIT (1t)
$216.00 Value of firm = $2,042.18 ! 224 (1.04)/(.15.04) b. Unlevered beta =
Cost of equity =
Return on capital=
Reinvestment rate =
EBIT (1t) Reinvestment
FCFF 1 ! IPO valuation: use market beta
9.00%
0.15 ! Using reestimated return on capital
0.266666667 ! 3.5%/15%
$240.00 ! Reestimate operating income with 40% tax rate
$64.00 ! 23.33% of 240
$176.00 Value of firm = $3,660.80 ! 176 (1.04)/(.09.04) c. There should be an illiquidity discount in the private transaction but not on the IPO.
Problem 2
Part a
Value of commercial product =
Value of R&D =
Total = $88.63
$45.00
$133.63 Market value of firm =
Value of patent = $240.00
$106.37 Part b
If the firm develops the patent today, you will replace the option value above with the NPV
NPV =
$49.39
Change in value =
$56.98 ! 49.39 106.37
New firm value =
$183.02 ! 240 56.98 Fall 2003 Problem 1
a. Intrinsic price to book ratio = 0.833333333 ! (ROE g)/ (COE g); ROE =8%, Cost of equity = 5+4% = 9%)
Stock is undervalued slightly. b. if the market is correct
Price to book ratio = .8 = (.08.03)/(r.03)
Solving for r, Cost of equity =
9.25%
Problem 2
Levered beta =
EV/Sales based upon regression=
Actual EV/Sales ratio =
Stock is overvalued by
Problem 3
Total beta =
Cost of equity =
Reinvestment rate =
Status quo value of firm =
Value of 25% stake in firm = 1.56
2.028 ! 0.30 + .08 (15/100) 1.2 (1.56) + .12 (20)
2.5 ! (200 + 100 50)/100
23.27% ! Divided the actual by the expected value ! You cannot compare the predicted value to the average for the sector. That tells you very little. 3 ! Sale in a private transaction. Divided beta by correlation.
17.00% ! 5% + 3*4%
0.4 ! G/ROC = 4%/10%
6.923076923 ! 1.5 (1.4)/(.17.04); I don't need a (1+g) because 1.5 is next year's income
1.730769231 With a doubled return on capital
Reinvestment rate =
0.2 ! Doubled return on capital only on new investments. So existing operating income unaffected
Optimal firm value =
9.230769231 ! 1.5 (1.2)/(.17.04)
Value of 51% stake in firm =
4.707692308
For IPO valuation
Market beta =
Cost of equity =
Status quo value =
Optimal firm value =
Value per voting share =
Value per voting share = 0.9
8.600%
$19.57 ! 1.5 (1.4)/(.086.04)
$26.09 ! 1.5 (1.2)/(.086.04)
$4.89
$5.54 !4.89+.2(26.0919.57)/2 Since this is an IPO valuation, you have to revalue the company with a market beta. Spring 2004
Problem 1 Aftertax Operating Margin
Return on Capital
Reinvestment Rate
EV/Sales
Enterprise Value Gloria Inc.
Generic
Brand Name Value
0.15
0.075
0.25
0.125
0.2
0.4
2.4
0.9
2400
900
1500 Problem 2
Cost of equity =
Part a. Under existing management
EBIT (1t)
Return on capital =
Reinvestment Rate =
Value of firm = 10.0% ! Use market beta since this is for initial public offering
5
0.1
0.4 ! 4./10
50 ! No surprise here. If you earn your cost of capital, MV = BV Part b. Under new management
EBIT (1t) Return on capital =
Reinvestment Rate =
Value of firm = $6.50
13.00%
30.77% ! 4/13
$75.00 Value of control = $5.00 ! (100 75) *.20 Value per nonvoting share =
Value per voting share = $10.00 ! Divide status quo value by total number of shares
$12.50 ! Add Value of control/ Number of voting shares Fall 2004 Problem 1
EV/Sales = Aftertax operating margin ( 1 g/ ROC)/ (Cost of capital g)
1.20 = .10 (1 .04/ ROC)/ (.09 .04)
! There are other ways to get to the same solution. You could set up firm value
Solving for return on capital, we get
3000 = 250 (1.04/ROC)/ (.09.04)
Return on capital =
10.00%
! While technically you do not need a (1+g) in the numerator since I have given you next year's operating income
I did give full credit to those who used it.
Problem 2
Bank
PBV
ROE Hibernia Bank
1.25
Bancomer
1.1
North Fork Bank
0.9
North Fork Bank is the most
undervalued bank…..
If we use the regression,
Hibernia Bank
Bancomer
North Fork Bank 16%
14%
12% PBV 1.25
1.1
0.9 Predicted PBV
1.2 Overvalued
1.1 Correctly valued
1 Under valued b. Low Price to book, high ROE, low risk, high growth
Problem 3
Corrected income =
Aftertax income= $300,000.00
$180,000.00 Total beta =
Cost of equity = ! Subtracted out rent (75,000), accounting expense (25,000) and dental salary of 150,000.
Why subtract out the dentist salary? If you don't, you will be paying a premium to the owner of the
practice for something that does not belong to him. Another way to think of this is as a pure
business. You could be a nondentist, buy this business and hire a dentist to work for you for 150,000….. 2.4 ! 0.80*3
13.85% Value of practice = ! On the total beta calculation, I did give full credit if you assumed that the R squared was 33% and took the square root of it. ### Spring 2005 Problem 1
a. Tax Rate: The higher the tax rate, the lower the EV/EBITDA multiple should be (not higher) b. EV/EBITDA = 2.26 + .1513 (Tax Rate) + .2156 (Return on Capital) – .1335
EV/EBITDA =
7.9059
Problem 2
Market value fo equity =
Net Income next year = Problem 3
Total Beta =
Cost of equity = 5% + 3*4% =
Reinvestment rate = Value of firm = ! You cannot change the sign on a regression coefficient if you don't agree with it. 1800
1500 MV of Equity/ Forward Earnings =
PE =1.2 = Payout Ratio / (.10 .04) Payout ratio = Return on equity = g/ (1 Payout ratio) = 1.2 ! 1800/1500
! Cost of equity = 10%; Growth rate = 4% 7.20% 1.2/.4 = 4.31% ! Loser company but dem's the breaks… 3 ! Market beta/ Square root of R squared
17.00%
0.25 ! G/ ROC
$66.21 Cost of equity to publicly traded firm =
new return on capital =
New reinvestment rate =
Value of firm =
Value of 51% = 151.470588
77.25 0.098
0.18
0.16666667 ! Investors in publicly traded firm are diversified.
! I also gave full credit if you adjusted the growth rate upwards to 4.5%
! Only the growth rate or reinvestment rate will be affected…. Existing operating income remains unchanged. Fall 2007 Problem 1
Enterprise value = Equity + Debt Cash
EV/Sales = 2500
1.25 ! 2500/2000 b. Estimated ROC =
0.075 ! Assumed book equity = 1000
b. If the market value is right,
! The book value of capital was missing on this problem. So, I gave full credit to any book
EV/Sales = Expected operating margin next year/(1RIR) (Cost of capital g)
value of capital that was rasonable. The solution assumes that the book value of equity
1.25 = 0.075(1 .03/.075)/ (Cost of capital .03)
! Aftertax Margin = 150/2000
is $ 1 billion and the book value of capital is $ 2 billion.
Solving for the cost of capital,
Cost of capital = 6.60% ! If you assume a 5% return on capital, this number will be lower (5.4%)
Problem 2
Market value of equity of parent company =
Debt of parent company =
Cash of parent company =
Enterprise value of parent company =
EBITDA of parent company =
EV/EBITDA for parent company = 650 ! 1000*10 0.1*500 0.75*400
300 ! 500 200
50 ! 150 100
900
150 ! 250 100
6 ! 900/150 Problem 3
C. Best combination: Low P/BV, Low risk, High growth, High ROE ! One point for D and F. They were close but failed one one dimension (D on growth and F on risk) b. Expected price to book for company A =
Actual price to book ratio =
Company is overvalued by apprroximately 0.8
1.25
36.00% ! Mechanical errors: 0.5 point c. PBV of C = 1.2 = 0.80 + 0.75 X 0.5 (1)
Solving for X
ROE for company C would have to be
12%
The ROE would have to be approximately 12%… it is actually 20% ! Used intrinsic equation: 1 point
! Set up equation in way to make solution impossible: 1 point
! Mechanical erorrs: 0.5 point Fall 2008 Problem 1
Current price to book ratio =
1.5
Current cost of equity =
9%
Expected growth rate=
3%
PBV = 1.5 = (ROE g)/ (Cost of equity g)
1.5 = (ROE .03)/ (.09.03)
ROE =
12%
b. Book equity increases by =
New return on equity =
New cost of equity=
New price to book ratio =
Problem 2
Company Used wrong cost of equity: 0.5 point
Math error: 0.5 point each New ROE incorrect: 1 point
New cost of equity incorrect: 1 point 20%
10.00% ! Old ROE/ (1 + Capital increase)
11% ! Riskfree rate + New ERP
0.875 ! (10%3%)/(11%3%)
Primary shares
Price/Share Net Income # Options Zap Tech
InfoRock
Lo Software 100
500
80 $20
$6
$5 $100
$150
$20 Value/option 10
80
20 $10 Using regular PE completely misses the options oustanding: 2 points
$1.50 Using diluted PE treats all options as equal: 1 point
$0.50 Market Cap Net Income PE Ratio
Diluted EPS Diluted PE Total Equity Value
Modified PE
Zap Tech
$2,000 $100.00
20.00
$0.91
22.00
$2,100 21.00
InfoRock
$3,000 $150.00
20.00
$0.26
23.20
$3,120 20.80
Lo Software
$400 $20.00
20.00
$0.20
25.00
$410 20.50
Lo Software is the cheapest stock. It's modified PE ratio is the lowest.
Problem 3
Value of private firm =
EBIT (1t) next year =
Reinvestment rate =
FCFF next year = 2000
300
20% ! g/ ROC = 3/15 = 20%
240 Used EBIT (1t) as FCFF: 1 point
Reinvestment rate wrong: 0.5 point
Math errors: 0.5 point each To solve for the cost of equtiyt used:
! Market beta computation wrong: 1 point
Value of firm = 2000 = 240/ (r .03)
Cost of capital = Cost ofequity =
15%
Cost of equity = 15% = 4% + Beta (5%) Total beta used =
2.2
Market beta =
1.1 ! Total beta * Correlation with the market
Cost of equity = 4% +1.1*5% =
9.50%
Correct value of the firm =
3692.307692
! 240/ (.095.03) Fall 2009 Problem 1
Part a
Return on capital =
0.15 ! Aftertax operating margin* Sales/Bv oF Capital
Reinvestment Rate =
0.2 ! g/ ROC
EV/Sales Ratio =
1.333333333 ! AT Oprating Margin (1RIR)/ (Cost of capital g)
Part b
New Return on Capital =
0.16 ! 0.08 *(1.5*1.3333)
Reivestment Rate =
0.1875
EV/Sales Ratio =
1.083333333
New EV =
1.444440833 ! Remember that revenues are higher by 33.33%
Value of the firm increaases by about
8.33%
Problem 2 SunTrust
SouthEast
Market value of equity
$150.00
$100.00
Book Value of equity
$90.00
$80.00
Expected Net income next year
$18.00
$12.00
P/BV
1.666666667
1.25
ROE
20.00%
0.15
If SunTrust Bank is fairly valued,
P/BV = 1.6667 = (.20.03)/(Cost of equity .03)
Cost of equity = !Did not compute return on capital: 1 point
! Math errors: 1/2 point
! Did not recompute sales/cap ratio: 1/2 poitn
! Did not recompute value: 1/2 point ! Wrong cost of equity: 1 point
1 Did not compare to actual P/BV: 0.5 point 0.132 Valuing SouthEast Bank with this cost of equity
Intrinsic P/BV =
1.17647059
Actual P/BV =
1.25
Overvalued by
6.25%
Problem 3
Expected EBIT(1t)
170 ! 200 50 (1.4)
Reinvestment rate =
0% ! Because growth is zero
Value to undiversifed investor =
850
Cost of equity to undiversified investor =0.00%
2
Impliws Total Beta =
2.666666667
Correlation with the market =
40%
Market beta =
1.066666667
Cost of equity =
10.400%
Value of business =
1634.615385 ! Aftertax operating income wrong: 1 point
! Did not compute correct cost of equity: 1 point
! Did not adjust for market beta: 1 point Fall 2010
Problem 1 Current EV/Sales Ratio =
1.7
Reinvestment Rate=
0.15 ! Growth rate/ ROC
EV/Sales = Aftertax margin (1RIR)/ (Cost of capital g)
1.7 = Aftertax margin (1.15)/(.09.03)
Aftertax margin =
12.00% ! Ignored reinvestment rate = 1 point
1 Math errors: 0.5 point each If you can reduce margins by 25% and increase sales turnover (sales/capital) by 50%
Aftertax margin (Generic) =
6.00%
! Did not recompute return on captial: 1 point
Current sales/capital =
1.67 ! ROC/Aftertax margin of Slim Joe's
! Math errors: 0.5 point each
Return on capital (Generic) =
10.00%
Reinvestment rate =
0.3
Sales to capital (Generic) =
0.70 Problem 2
Lugano Market value of equity
Book value of equity + Market value of debt
Book value of debt Cash Market value of minority holdings
Book value of minority holdings + Market value of minority interests
Book value of minority interests
Tax rate
Net Income
Interest expenses
EBIT
DA Stulz 9000
4000
5000
4500
1500
1500
500
1000
400
40%
600
500
1500
500 13000
6000
5000
4500
2000
1000
500
3000
1000
20%
1200
500
2000
1000 ! EV computed incorrectly: 0.5 to 1.5 points
! EBITDA computed incorrectly: 0.5 to 1 point
! Did not consider ROC or tax rate in making judgment: 0.5 point ! Net Income/ (1t) + Interest expenses EV =
12000
18000
! MV Equity + MV Debt Cash MV Minority Holdings + MV Minority Interests
EBITDA
2000
3000
! EBIT +DA
EV/Ebitda
6.00
6.00
ROC=
12.86%
18.82%
Since Stulz has a hgher ROC, lower tax rate and trades at the same multiple, it is cheaper. Problem 3 PBV = (ROEg)/(Cost of equity g)
For publicly traded firms
1.6 = (.12.04)/ (Cost of equity .04)
Cost of equity =
0.09
Given riskfree rate = 4% and ERP =5%
Beta =
1
Total beta =
2.5 ! Beta/ 0.4
Cost of equity =
16.50%
PBV ratio of Seacrest = ! Didnot solve correctly for beta: 1 point
! No total beta computation: 1 point
! Math errors: 0.5 point each 1.28 Fall 2011
Problem 1 a. Intrinsic PE = 0.60/(.08.02) =
b. Estimated value for equity = Value of options Value of equity in common stock
Value per share Problem 2 Value of equity =
Debt
Cash
EBITDA KMD 10 ! All or nothing (Ok if you use (1+g) and get 10.4…) 1000
50 ! 10*5
950
9.5 ! 950/100
9000
5000
2000
2100 Problem 3 Corrected aftertax EBIT
Aftertax Operating margin =
Total Beta =
Expected growth =
Estimated EV/Sales =
Estimated EV = !Used diluted number of shares = 1.5
!Did not subtract out value of options = 1 point
! Did not divide by actual number of shares: 1 point RAD holdingsKMD just steel
3000
6000 ! Net out 60% of market value of RAD
3000
2000
1000
1000
700
1400 Enterprise Value
EV/ EBITDA
The steel business is fairly valued. ! EBITDA for steel business wrong: 1 point
! Equity value of steel business wrong: 1 point
! Added minority interest or subracted it : 1 point
! Other errors: 0.5 point each 7000
5 250
0.25
3 ! 1.2/0.4
0.1
2.5
2500 ! Did not use any reinvestment: 0.5 point (No ROC would support this)
! Reinvestment rate wrong (given your ROC): 0.5 point
! Failed to consider operating margin: 0.5 point
! Other mechanical errors: 0.5 point each ! Did not net out cash of consolidated sub: 0.5 point
! Got parent EBITDA incorrect: 0.5 to 1 point
! Other computational errors: 0.5 point each ! Did not adjust margin correctly = 1 point
! Did not get total beta = 1 point
! Other errors: 0.5 to 1 point ...
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 Fall '11
 BANKO

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