250 125 375 125 250 375 500 400 100 200 300 500 0 125 250 375 125 250 375 500
10%
11-24
a.
10 15 20 25 10 20 30 40 50 0 WACC1=(1.181)3 /1(1.10)/1.10 (1.10)2 /10% /1.1812 1 / 1 3 2 .10 / 1 1 (1.181) (1.10) 10 1 Crossover Rate 1 9% IRR
18.1%
ALLIED COMPONENTS COMPANY
BASICS OF CAPITAL BUDGETING
S
= 23.6% IRR
L
What is capital budgeting? Are there any similarities between a firms capital budgeting decisions and an individuals investment decisions? WACC (%)
= 18.1% Project S Project L
Capital budgeting is the process of analyzing fixed assets additions. It is important because the fixed asset decisions chart a companys course for the future. In addition, the NPV NPV ($) apital budgeting process is relatively identical to the same decision making process by (Thousands of Dollars) c 5 r (%) 10 ndividual investors. i
100 200 300 500 0 125 250 375 125 250 375 500 400 15 20 25 10 20 30 40 50 0 10 Crossover Rate 1 9% IRR
S
i. ii. iii. iv. v.
= 23.6% IRR
L
Listed below are the same steps used by both processes: Estimate the cash flows Assess the riskiness of the cash flows Determine the discount rate based on the riskiness of the cash flows as well as interest rates. This process is called the project cost of capital. Find the PV of the expected cash flows/the asset rate of return. If the inflow is greater than the outflow of the PV (meaning the NPV is greater than zero), or if the IRR is higher than the project cost of capital, you would accept the project. projects with normal and nonnormal cash flows? Projects are independent if the cash flows of one are not affected by the acceptance of the other. Therefore, two projects are mutually exclusive if acceptance of one affects adversely the cash flows of the other; that is, at most one of two or more such projects may be accepted. Projects with normal cash flows have outflows, or costs, in the first year (or years) followed by a series of inflows. Projects with nonnormal cash flows have one or more outflows after the inflow stream has begun.
b. = What is the difference between independent and mutually exclusive projects? Between 18.1%
WACC (%)
Project S Project L
c. (1) Define the term net present value (NPV). What is each projects NPV?
The NPV defines the present values of a projects cash flows:
NPV =. Project Ls NPV is $18.79: 0 | 80 60.11 18.79 = NPVL 1 | 2 | 3 |
-100.00 9.09 49.59
10
60
NPVs are easy to determine using a calculator with an NPV function. Enter the cash flows sequentially, with outflows entered as negatives; enter the WACC; and then press the NPV button to obtain the projects NPV, $18.78. The NPV of Project S is NPVS = $19.98. (2) What is the rationale behind the NPV method? According to NPV, which project(s) should be accepted if they are independent? Mutually exclusive? The rationale behind the NPV method is direct by definition meaning if a project has NPV = $0, then the project generates exactly enough cash flows to recover the cost of the investment as well as to enable investors to earn their required rates of return (the opportunity cost of capital). In addition, if NPV = $0, then in a financial situation (not an accounting), the project breaks even. Furthermore, if the NPV is positive, then more than enough cash flow is generated, and conversely if NPV is negative. Consider Project Ls cash inflows, which total $150. They are sufficient for the following reasons: i. to return the $100 initial investment ii. to provide investors with their 10% aggregate opportunity cost of capital iii. Still have $18.78 left over on a present value basis. This $18.78 excess PV belongs to the shareholdersthe debt holders claims are fixed so the shareholders wealth will be increased by $18.78 if Project L is accepted. Consequently, Allieds shareholders gain $19.98 in value if Project S is accepted.
If Projects L and S are independent, then both should be accepted, because both add to shareholders wealth, hence to the stock price. If the projects are mutually exclusive, then Project S should be chosen over L, because S adds more to the value of the firm. (3) Would the NPVs change if the WACC changed? Explain. The NPV of a project is dependent on the WACC used. If the WACC changes, the NPV of each project will change also. The NPV will decline if the WACC increases and the NPV will increase if the WACC declines.
d. (1) Define the term internal rate of return (IRR). What is each projects IRR?
The IRR is that discount rate which forces the NPV of a project to equal zero: 0 | CF0 PVCF1 PVCF2 PVCF3 1 | CF1 2 | CF2 3 | CF3
0 = Sum of PVs = NPV.
The IRR may also be expressed as an equation. Please see below:
IRR: = $0 = NPV Both the IRR and NPV use the same equation; however, in order to find the IRR the equation is solved for the particular discount rate, IRR, which forces the projects NPV to equal zero (the IRR) rather than using the WACC in the denominator and finding NPV. In other words, the two approaches differ in only one respect: In the NPV method, a discount rate is specified (the projects WACC) and the equation is solved for NPV, while in the IRR method, the NPV is specified to equal zero and the discount rate (IRR) that forces this equality is found.
Project Ls IRR is 18.1% 0 1 2 10 3 60 | 80 48.57 0.06 | | |
-100.00 8.47 43.02
$0 if IRRl = 18.1% is used as the discount rate.
The IRRL = 18.1%. Unless you know how to use the functions and formulas within Microsoft Excel, the use of a financial calculator is extremely helpful when calculating IRRs. The cash flows are entered sequentially, and then the IRR button is pressed. For Project S, IRRS = 23.6%. Note that with many calculators, you can enter the cash flows into the cash flow register, also enter WACC = I/YR, and then calculate both NPV and IRR by pressing the appropriate buttons. (2) How is the IRR on a project related to the YTM on a bond? The IRR is to a capital project what the YTM is to a bondit is the expected rate of return on the project, just as the YTM is the promised rate of return on a bond. (3) What is the logic behind the IRR method? According to IRR, which project(s) should be accepted if they are independent? Mutually exclusive? IRR measures a projects profitability in the rate of return sense: If a projects IRR equals its cost of capital, then its cash flows are just sufficient to provide investors with their required rates of return. An IRR greater than WACC implies an economic profit, which accrues to the firms shareholders, while an IRR less than WACC indicates an economic loss, or a project that will not earn enough to cover its cost of capital. Projects IRRs are compared to their costs of capital, or hurdle rates. Since Projects L and S both have a hurdle rate of 10%, and since both have IRRs greater than that hurdle rate, both should be accepted if they were independent; however, if they were mutually exclusive, Project S would be selected, because it has the higher IRR. (4) Would the projects IRRs change if the WACC changed? IRRs are independent of the WACC. Therefore, neither IRRS nor IRRL would change if WACC changed; however, the acceptability of the projects could changeL would be rejected if WACC were greater than 18.1%, and S would be rejected if WACC were greater than 23.6%.
e. (1) Draw NPV profiles for Projects L and S. At what discount rate do the profiles
cross? Based on the graph below, the discount rate appear to cross somewhere between 8 9%.
(2) Look at your NPV profile graph without referring to the actual NPVs and IRRs. Which project(s) should be accepted if they are independent? Mutually exclusive? Explain. Are your answers correct at any WACC less than 23.6%? Since the NPV and IRR have virtually the same criteria, their profiles lead to the same decision of accepting/rejecting any independent project. According to the IRR rule, the x-axis intersects approximately at 18.1%. This would make the project acceptable if the WACC is less than that. In addition, this will conclude that having a WACC less than that of 18.1%; this will make the NPV profile above the x-axis making the NPV greater than zero. Assuming that Project L & S are mutually exclusive a conflict of interest may occur because IRRS = 23.6% > 18.1% = IRRL. Consequently, regardless of the size of the WACC, Project S will have a higher ranking based on the IRR criteria. On the other hand the NPV profile demonstrates that the value of NPVL > NPVS making the WACC lesser than the crossover rate. If the WACC is less than the crossover rate, the NPV rule to says choose Project L, while the IRR rule says to choose Project S. Unfortunately, this is where the conflict of interest occurs.
f.
(1) What is the underlying cause of ranking conflicts between NPV and IRR? With the consideration of normal projects, in order for NPV profiles to cross, one project must have both a higher vertical axis intercept and a steeper slope than the other must. A projects vertical axis intercept typically will be dependent upon the size of the project and its size and timing pattern of the cash flowslarge projects, and ones with large distant cash flows, would generally be expected to have relatively high vertical axis intercepts. The slope of the NPV profile depends entirely on the timing pattern of the cash flowslong-term projects have steeper NPV profiles than short-term ones. Furthermore, it is concluded that NPV profiles can cross in two situations while mutually exclusive projects differ in size and if the projects cash flows differ in terms of the timing pattern of their cash flows. (2) What is the reinvestment rate assumption, and how does it affect the NPV versus IRR conflict? The underlying cause of ranking conflicts is the reinvestment rate assumption. All DCF methods implicitly assume that cash flows can be reinvested at some rate, regardless of what is actually done with the cash flows. Unfortunately, discounting has the adverse effect of compounding. Inherently in the NPV calculation is the assumption that cash flows can be reinvested at the projects cost of capital, while the IRR calculation assumes reinvestment at the IRR rate. (3) Which method is best? Why? The NPVs assumption is better because a projects cash inflows are usually used as substitutes for outside capital. In addition, having an opportunity cost provides cash flows for reinvestment at the cost of capital.
g. (1) Define the term modified IRR (MIRR). Find the MIRRs for Projects L and S.
MIRR is that discount rate which equates the present value of the terminal value of the inflows, compounded at the cost of capital, to the present value of the costs. Here is the setup for calculating Project Ls modified IRR: 0 1 2 3 10 | 60 | 80.00 TV of inflows = MIRR =? 12.10 158.10 | |
PV of costs = (100.00) 66.00
PV of TV =
100.00
$100 =
PV costs =. After you calculate the TV, enter N = 3, PV = -100, PMT = 0, FV = 158.1, and then press I/YR to get the answer, MIRRL = 16.5%. We could calculate MIRRS similarly: MIRRS = 16.9%. Thus, Project S is ranked higher than L. This result is consistent with the NPV decision. (2) What are the MIRRs advantages and disadvantages vis--vis the NPV? MIRR does not always lead to the same decision as NPV when mutually exclusive projects are being considered. In particular, small projects often have a higher MIRR, but a lower NPV, than larger projects. Thus, MIRR is not a perfect substitute for NPV, and NPV remains the single best decision rule. However, MIRR is superior to the regular IRR, and if a rate of return measure is needed, MIRR should be used. Business executives agree. Business executives prefer to compare projects rates of return to comparing their NPVs. This is an empirical fact. As a result, financial managers are substituting MIRR for IRR in their discussions with other corporate executives. This fact was brought out in the October 1989 FMA meetings, where executives from Du Pont, Hershey, and Ameritech, among others, all reported a switch from IRR to MIRR.
h. (1) What is the payback period? Find the paybacks for Projects L and S.
The payback period is the expected number of years required to recover a projects cost. We calculate the payback by developing the cumulative cash flows as shown below for Project L: Year 0 1 2 3 0 | -100 Expected NCF Annual Cumulative ($100) ($100) 10 (90) 60 (30) 80 50 1 | 10 -90 2 | 60 -30
Payback is between t = 2 and t = 3 3 | 80 50
Project Ls $100 investment has not been recovered at the end of Year 2, but it has been more than recovered by the end of Year 3. Thus, the recovery period is between 2 and 3 years. If we assume that the cash flows occur evenly over the year, then the investment is recovered $30/$80 = 0.375 0.4 into Year 3. Therefore, PaybackL = 2.4 years. Similarly, PaybackS = 1.6 years. (2) What is the rationale for the payback method? According to the payback criterion, which project(s) should be accepted if the firms maximum acceptable payback is 2 years, if Projects L and S are independent, if Projects L and S are mutually exclusive? Payback represents a type of breakeven analysis: The payback period tells us when the project will break even in a cash flow sense. With a required payback of 2 years, Project S is acceptable, but Project L is not. Whether the two projects are independent or mutually exclusive makes no difference in this case. (3) What is the difference between the regular and discounted payback methods? Discounted payback is similar to payback except that discounted rather than raw cash flows are used. (4) What are two main disadvantages of discounted payback? Is the payback method of any real usefulness in capital budgeting decisions? Explain. Regular payback has three critical deficiencies:
i. It ignores the time value of money ii. It ignores the cash flows that occur after the payback period iii. Unlike the NPV, which tells us by how much the project should increase shareholder
wealth, and the IRR, which tells us how much a project yields over the cost of capital, the payback merely, tells us when we get out investment back. Discounted payback does consider the time value of money, but it still fails to consider cash flows after the payback period and it gives us no specific decision rule for acceptance; hence, it has two basic flaws. In spite of its deficiency, many firms today still calculate the discounted payback and give some weight to it when making capital budgeting decisions; however, payback is not generally used as the primary decision tool. Rather, it is used as a rough measure of a projects liquidity and riskiness.
i.
As a separate project (Project P), the firm is considering sponsoring a pavilion at the upcoming Worlds Fair. The pavilion would cost $800,000, and it is expected to result in $5 million of incremental cash inflows during its 1 year of operation. However, it would then take another year, and $5 million of costs, to demolish the site and return it to its original condition. Thus, Project Ps expected net cash flows look like this (in millions of dollars): 0 | $-0.8 1 | $5.0 2 | $-5.0
The project is estimated to be of average risk, so its WACC is 10%.
(1) What is Project Ps NPV? What is its IRR? Its MIRR?
Here is the time line for the cash flows, and the NPV: 0 1 2 | -800,000 | 5,000,000 | -5,000,000
NPVP = -$386,776.86. You can find the NPV by entering the cash flows into the cash flow register, entering I/YR = 10, and then pressing the NPV button. In addition, calculating the IRR presents a problem. Furthermore, having the cash flows in the register, you have to press the IRR button. An HP-10BII financial calculator will give the message error-soln. This means that Project P has multiple IRRs. An HP-17BII will ask for a guess. If you guess 10%, the calculator will show IRR = 25%. If you guess a high number, such as 200%, it will show the second IRR, 400%. The MIRR of Project P = 5.6%, and is found by calculating the discount rate that equates the terminal value ($5.5 million) to the present value of costs ($4.93 million).
(2) Draw Project Ps NPV profile. Does Project P have normal or nonnormal cash flows?
Should this project be accepted? Explain.
You could put the cash flows in your calculator and then enter a series of I/YR values, get an NPV for each, and then plot the points to construct the NPV profile. We used a spreadsheet model to automate the process and then to draw the profile. Note that the profile crosses the X-axis twice, at 25% and at 400%, signifying two IRRs. Which IRR is correct? In one sense, they both areboth cause the projects NPV to equal zero. However, in another sense, both are wrongneither has any economic or financial significance. Project P has nonnormal cash flows; that is, it has more than one change of signs in the cash flows. Without this nonnormal cash flow pattern, we would not have the multiple IRRs. Since Project Ps NPV is negative, the project should be rejected, even though both IRRs (25% and 400%) are greater than the projects 10% WACC. The MIRR of 5.6% also supports the decision that the project should be rejected.