Exam 2 Finance 470
1. When is EAC analysis appropriate for comparing two or more projects? Why is this
method used? Are there any implicit assumptions required by this method that you find
troubling? Explain.
The EAC approach is appropriate when comparing mutually exclusive projects with different
lives that will be replaced when they wear out. This type of analysis is necessary so that the
projects have a common life span over which they can be compared; in effect, each project is
assumed to exist over an infinite horizon of N-year repeating projects. Assuming that this type of
analysis is valid implies that the project cash flows remain the same forever, thus ignoring the
possible effects of, among other things: (1) inflation, (2) changing economic conditions, (3) the
increasing unreliability of cash flow estimates that occur far into the future, and (4) the possible
effects of future technology improvement that could alter the project cash flows.
2. The Army has requested a bid for multiple use digitizing devices (MUDDs). They will
require the winner of the bid to deliver 4 units each year for the next 3 years. You have
estimated that labor and materials costs will be $10,000 per unit. Production space can
be leased for $12,000 per year. The project will require $50,000 in fixed assets with
expected salvage of $10,000 at the end of the project (depreciate straight-line to salvage
value) and an initial $10,000 increase in NWC. Your marginal tax rate = 34% and the
required return = 15%. What is your minimum bid?
NPV = 0 = -60,000 + OCF(PVIFA15%,3) + 20,000(PVIF15%,3)
NPV = 0 = -60,000 + (NI + Dep)(2.2832) + 20,000(0.6575)
NPV = 0 = -60,000 + [(S – VC – FC - Dep)(1 – T) + Dep](2.2832) + 13,150.32
46,849.68 = [(4P – 4(10,000) – 12,000 – 13,333.33)(1 - .34) + 13,333.33](2.2832)
20,519.31 = (4P – 65,333.33)(0.66) + 13,333.33
7,185.98 = (4P – 65,333.33)(0.66)
10,887.85 = 4P – 65,333.33
76,221.18 = 4P
19,055.21 = P
3. As a shareholder of a firm that is contemplating a new project, would you be more
concerned with the accounting break-even point, the cash break-even point, or the
financial break-even point? Why?
From the shareholder perspective, the financial break-even point is the most important. A
project can exceed the accounting and cash break-even points but still be below the financial
break-even point. This causes a reduction in shareholder (your) wealth.
4. In an effort to capture the large jet market, Airbus invested $13 billion developing its
A380, which is capable of carrying 800 passengers. The plane has a list price of $280
million. In discussing the plane, Airbus stated that the company would break even when
249 A380s were sold.
a. Assuming the break-even sales figure given is the cash flow break-even, what is the
cash flow per plane?
The cash flow per plane is the initial cost divided by the breakeven number of planes, or:
Cash flow per plane = $13,000,000,000 / 249
Cash flow per plane = $52,208,835
b. Airbus promised its shareholders a 20 percent rate of return on the investment. If
sales of the plane continue in perpetuity, how many planes must the company sell per
year to deliver on this promise?
In this case the cash flows are a perpetuity. Since we know the cash flow per plane, we need
to determine the annual cash flow necessary to deliver a 20 percent return. Using the
perpetuity equation, we find:
PV = C /R
$13,000,000,000 = C / .20
C = $2,600,000,000
This is the total cash flow, so the number of planes that must be sold is the total cash flow
divided by the cash flow per plane, or:
Number of planes = $2,600,000,000 / $52,208,835
Number of planes = 49.80 or about 50 planes per year
c. Suppose instead that the sales of the A380 last for only 10 years. How many planes
must Airbus sell per year to deliver the same rate of return?
In this case the cash flows are an annuity. Since we know the cash flow per plane, we need
to determine the annual cash flow necessary to deliver a 20 percent return. Using the
present value of an annuity equation, we find:
PV = C(PVIFA20%,10)
$13,000,000,000 = C(PVIFA20%,10)
C = $3,100,795,839
This is the total cash flow, so the number of planes that must be sold is the total cash flow
divided by the cash flow per plane, or:
Number of planes = $3,100,795,839 / $52,208,835
Number of planes = 59.39 or about 60 planes per year
5. Explain why a characteristic of an efficient market is that investments in that market have
zero NPVs.
On average, the only return that is earned is the required return—investors buy assets with
returns in excess of the required return (positive NPV), bidding up the price and thus causing the
return to fall to the required return (zero NPV); investors sell assets with returns less than the
required return (negative NPV), driving the price lower and thus causing the return to rise to the
required return (zero NPV).
6. A stock has had returns of 3 percent, 38 percent, 21 percent, 15 percent, 29 percent, and
13 percent over the last six years. What are the arithmetic and geometric returns for the
stock?
The arithmetic average return is the sum of the known returns divided by the number of
returns, so:
Arithmetic average return = (.03 + .38 + .21 – .15 + .29 – .13) / 6
Arithmetic average return = .1050 or 10.50%
Using the equation for the geometric return, we find:
Geometric average return = [(1 + R1) × (1 + R2) × … × (1 + RT)]1/T – 1
Geometric average return = [(1 + .03)(1 + .38)(1 + .21)(1 – .15)(1 + .29)(1 – .13)](1/6) – 1
Geometric average return = .0860 or 8.60%
Remember, the geometric average return will always be less than the arithmetic average return
if the returns have any variation.
7. Is it possible that a risky asset could have a beta of zero? Based on the CAPM, what is
the expected return on such an asset? Explain your answers.
Yes. It is possible, in theory, to construct a zero beta portfolio of risky assets whose return would
be equal to the risk-free rate. It is also possible to have a negative beta; the return would be less
than the risk-free rate. A negative beta asset would carry a negative risk premium because of its
value as a diversification instrument.
8. Stock Y has a beta of 1.3 and an expected return of 18.5 percent. Stock Z has a beta of
.70 and an expected return of 12.1 percent. If the risk-free rate is 8 percent and the market
risk premium is 7.5 percent, are these stocks correctly priced? Explain.
There are two ways to correctly answer this question. We will work through both. First, we can
use the CAPM. Substituting in the value we are given for each stock, we find:
E(RY) = .08 + .075(1.30) = .1775 or 17.75%
It is given in the problem that the expected return of Stock Y is 18.5 percent, but according to
the CAPM, the return of the stock based on its level of risk, the expected return should be 17.75
percent. This means the stock return is too high, given its level of risk. Stock Y plots above the
SML and is undervalued. In other words, its price must increase to reduce the expected return
to 17.75 percent. For Stock Z, we find:
E(RZ) = .08 + .075(0.70) = .1325 or 13.25%
The return given for Stock Z is 12.1 percent, but according to the CAPM the expected return of
the stock should be 13.25 percent based on its level of risk. Stock Z plots below the SML and is
overvalued. In other words, its price must decrease to increase the expected return to 13.25
percent.
We can also answer this question using the reward-to-risk ratio. All assets must have the same
reward-to-risk ratio. The reward-to-risk ratio is the risk premium of the asset divided by its .
We are given the market risk premium, and we know the  of the market is one, so the rewardto-risk ratio for the market is 0.075, or 7.5 percent. Calculating the reward-to-risk ratio for Stock
Y, we find:
Reward-to-risk ratio Y = (.185 – .08) / 1.30 = .0808
The reward-to-risk ratio for Stock Y is too high, which means the stock plots above the SML, and
the stock is undervalued. Its price must increase until its reward-to-risk ratio is equal to the
market reward-to-risk ratio. For Stock Z, we find:
Reward-to-risk ratio Z = (.121 – .08) / .70 = .0586
The reward-to-risk ratio for Stock Z is too low, which means the stock plots below the SML, and
the stock is overvalued. Its price must decrease until its reward-to-risk ratio is equal to the
market reward-to-risk ratio.
9. Under what circumstances would it be appropriate for a firm to use different costs of
capital for its different operating divisions? If the overall firm WACC were used as the
hurdle rate for all divisions, would the riskier divisions or the more conservative divisions
tend to get most of the investment projects? Why? If you were to try to estimate the
appropriate cost of capital for different divisions, what problems might you encounter?
What are two techniques you could use to develop a rough estimate for each division’s
cost of capital?
If the different operating divisions were in much different risk classes, then separate cost of
capital figures should be used for the different divisions; the use of a single, overall cost of
capital would be inappropriate. If the single hurdle rate were used, riskier divisions would tend
to receive more funds for investment projects, since their return would exceed the hurdle rate
despite the fact that they may actually plot below the SML and, hence, be unprofitable projects
on a risk-adjusted basis. The typical problem encountered in estimating the cost of capital for a
division is that it rarely has its own securities traded on the market, so it is difficult to observe
the market’s valuation of the risk of the division. Two typical ways around this are to use a pure
play proxy for the division, or to use subjective adjustments of the overall firm hurdle rate based
on the perceived risk of the division.
10. Titan Mining Corporation has 9 million shares of common stock outstanding, 250,000
shares of 6 percent preferred stock outstanding, and 105,000 7.5 percent semiannual
bonds outstanding. The common stock currently sells for $34 per share and has a beta of
1.25, the preferred stock currently sells for $91 per share, and the bonds have 15 years to
maturity and sell for 93 percent of par. The market risk premium is 8.5 percent, T-bills
are yielding 5 percent, and Titan Mining’s tax rate is 35 percent.
a. What is the firm’s market value capital structure?
MVD = 105,000($1,000)(0.93) = $97,650,000
MVE = 9,000,000($34) = $306,000,000
MVP = 250,000($91) = $22,750,000
And the total market value of the firm is:
V = $97,650,000 + 306,000,000 + 22,750,000 = $426,400,000
So, the market value weights of the company’s financing is:
D/V = $97,650,000/$426,400,000 = .2290
P/V = $22,750,000/$426,400,000 = .0534
E/V = $306,000,000/$426,400,000 = .7176
b. If Titan Mining is evaluating a new investment project that has the same risk as the
firm’s typical project, what rate should the firm use to discount the project’s cash flows?
For projects equally as risky as the firm itself, the WACC should be used as the discount rate.
First we can find the cost of equity using the CAPM. The cost of equity is:
RE = .05 + 1.25(.085) = .1563 or 15.63%
The cost of debt is the YTM of the bonds, so:
P0 = $930 = $37.5(PVIFAR%,30) + $1,000(PVIFR%,30)
R = 4.163%
YTM = 4.163% × 2 = 8.33%
And the aftertax cost of debt is:
RD = (1 – .35)(.0833) = .0541 or 5.41%
The cost of preferred stock is:
RP = $6/$91 = .0659 or 6.59%
Now we can calculate the WACC as:
WACC = .0541(.2290) + .1563(.7176) + .0659(.0534) = .1280 or 12.80%
10. Why do noninvestment-grade bonds have much higher direct costs than investment-grade
issues?
They are riskier and harder to market from an investment bank’s perspective.
11. The Educated Horses Corporation needs to raise $ 60 million to finance its expansion into
new markets. The company will sell new shares of equity via a general cash offering to
raise the needed funds. If the offer price is $ 21 per share and the company’s underwriters
charge a 9 percent spread, how many shares need to be sold?
Using X to stand for the required sale proceeds, the equation to calculate the total sale
proceeds, including floatation costs is:
X(1 – .09) = $60,000,000
X = $65,934,066 required total proceeds from sale.
So the number of shares offered is the total amount raised divided by the offer price, which is:
Number of shares offered = $65,934,066/$21 = 3,139,717
13. You’ve collected the following information about St. Pierre, Inc.: Sales $195,000; Net
income $17,500; Dividends $9,300; Total debt $86,000; Total equity $58,000. What is
the sustainable growth rate for St. Pierre, Inc.? If it does grow at this rate, how much new
borrowing will take place in the coming year, assuming a constant debt– equity ratio?
What growth rate could be supported with no outside financing at all?
To calculate the sustainable growth rate, we first must calculate the retention ratio and ROE.
The retention ratio is:
b = 1 – $9,300 / $17,500
b = .4686
And the ROE is:
ROE = $17,500 / $58,000
ROE = .3017 or 30.17%
So, the sustainable growth rate is:
Sustainable growth rate = (ROE × b) / [1 – (ROE × b)]
Sustainable growth rate = [.3017(.4686)] / [1 – .3017(.4686)]
Sustainable growth rate = .1647 or 16.47%
If the company grows at the sustainable growth rate, the new level of total assets is:
New TA = 1.1647($86,000 + 58,000) = $167,710.84
To find the new level of debt in the company’s balance sheet, we take the percentage of debt in
the capital structure times the new level of total assets. The additional borrowing will be the
new level of debt minus the current level of debt. So:
New TD = [D / (D + E)](TA)
New TD = [$86,000 / ($86,000 + 58,000)]($167,710.84)
New TD = $100,160.64
And the additional borrowing will be:
Additional borrowing = $100,160.04 – 86,000
Additional borrowing = $14,160.64
The growth rate that can be supported with no outside financing is the internal growth rate. To
calculate the internal growth rate, we first need the ROA, which is:
ROA = $17,500 / ($86,000 + 58,000)
ROA = .1215 or 12.15%
This means the internal growth rate is:
Internal growth rate = (ROA × b) / [1 – (ROA × b)]
Internal growth rate = [.1215(.4686)] / [1 – .1215(.4686)]
Internal growth rate = .0604 or 6.04%
14. Why is NPV considered a superior method of evaluating the cash flows from a project?
Suppose the NPV for a project’s cash flows is computed to be $2,500. What does this
number represent with respect to the firm’s shareholders?
NPV is superior to the other methods of analysis presented in the text because it has no serious
flaws. The method unambiguously ranks mutually exclusive projects, and can differentiate
between projects of different scale and time horizon. The only drawback to NPV is that it relies
on cash flow and discount rate values that are often estimates and not certain, but this is a
problem shared by the other performance criteria as well. A project with NPV = $2,500 implies
that the total shareholder wealth of the firm will increase by $2,500 if the project is accepted
and all estimates of cash flows and required rate are in fact realized.
15. What is the value of an investment that pays $16,000 every other year forever, if the first
payment occurs one year from today and the discount rate is 12 percent compounded
daily?
The cash flows occur every two years, so the nominal per-period rate = 12% x 2 = 24%
A period here is two years long. Compounding occurs more often than the cash flows, so we
need the effective per-period rate
The present value of a series of cash flows is always calculated one period prior to the first cash
flow. The first cash flow in this problem occurs at time one. One period prior to this is time
minus one.
PV-1 = 16,000/.2712 = 58,997.27
We need the annual effective rate to find the value today
PV0 = PV-1(1 + r) = 58,997.27(1 + .1275) = 66,517.92
Bonus:
Previously we have shown that the present value of a perpetuity is PV = C/r. Your book
gives the following formula for the present value of an annuity. Show that this is true.
Assume two perpetuities. Perpetuity A has cash flows that begin at the end of the first
period and perpetuity B has cash flows that begin at the end of period N+1.
A: ----C1----C2----C3----C4--//--C----CN----CN+1--…
B: ---- 0 ---- 0 ---- 0 ---- 0 --//--0----0 ---- CN+1--…
PVA = C/r
PVB (at time N) = C/r
PVB (at time 0) = (C/r)/(1 + r)N
PVA – PVB is an N-period annuity
The Present Value of this annuity is:
PV = PVA – PVB = C/r - (C/r)/(1 + r)N
Factor out C
PV = C x [1/r – (1/r)/(1 + r)N]
Factor out 1/r to get above result