FIN 470 Exam2 (Chapters 1-14) Spring 2012
1.
Given the choice, would a firm prefer to use MACRS depreciation or straight-line depreciation?
Why?
For tax purposes, a firm would choose MACRS because it provides for larger depreciation
deductions earlier and probably more closely reflects the true timing of the cash flows. These larger
deductions reduce taxes, but have no other cash consequences. Notice that the choice between
MACRS and straight-line is purely a time value issue; the total depreciation is the same, only the
timing differs. On the other hand, straight-line is a more conservative method in that it makes
marginal projects more difficult to accept.
2.
You are evaluating two different silicon wafer milling machines. The Techron I costs $194,000, has
a 3-year life, and has pretax operating costs of $31,000 per year. The Techron II costs $327,000, has
a 5-year life, and has pretax operating costs of $17,000 per year. For both milling machines, use
straight-line depreciation to zero over the project's life and assume a salvage value of $20,000. If
your tax rate is 34 percent and your discount rate is 12 percent. Calculate the EAC for each. Which
do you prefer, Why?
We will need the aftertax salvage value of the equipment to compute the EAC. Even though the
equipment for each product has a different initial cost, both have the same salvage value. The
aftertax salvage value for both is:
Both cases: aftertax salvage value = $20,000(1 – 0.34) = $13,200
To calculate the EAC, we first need the OCF and NPV of each option. The OCF and NPV for
Techron I is:
OCF = $-31,000(1 – 0.34) + 0.34($194,000/3) = $1,526.67
NPV = -194,000 + $1,526.67(PVIFA12%,3) + ($13,200/1.12 3) = $-180,937.7
EAC = $-180,937.7 / (PVIFA12%,3) = $-75,333.23
And the OCF and NPV for Techron II is:
OCF =$-17,000(1 – 0.34) + 0.34($327,000/5) = $11,016
NPV = $-327,000 + $11,016(PVIFA12%,5) + ($13,200/1.12 5) = $-279,799.75
EAC = $-279,799.75 / (PVIFA12%,5) = $-77,619.17
The two milling machines have unequal lives, so they can only be compared by expressing both on
an equivalent annual basis, which is what the EAC method does. Thus, you prefer the Techron I
because it has the lower (less negative) annual cost.
3.
Assume a firm is considering a new project that requires an initial investment and has equal sales and
costs over its life. Will the project reach the accounting, cash, or financial break- even point first?
Which will it reach next? Last? Will this ordering always apply?
The project will reach the cash break-even first, the accounting break-even next and finally the
financial break-even. For a project with an initial investment and sales after, this ordering will always
apply. The cash break-even is achieved first since it excludes depreciation. The accounting breakeven is next since it includes depreciation. Finally, the financial break-even, which includes the time
value of money, is achieved.
4.
Consider a project to supply Detroit with 42,000 tons of machine screws annually for automobile
production. You will need an initial $1,848,000 investment in threading equipment to get the project
started; the project will last for 6 years. The accounting department estimates that annual fixed costs
will be $546,000 and that variable costs should be $210 per ton; accounting will depreciate the initial
fixed asset investment straight-line to zero over the 6-year project life. It also estimates a salvage
value of $584,000 after dismantling costs. The marketing department estimates that the automakers
will let the contract at a selling price of $290 per ton. The engineering department estimates you will
need an initial net working capital investment of $546,000. You require a 10 percent return and face
a marginal tax rate of 39 percent on this project. Suppose you believe that the accounting
department's initial cost and salvage value projections are accurate only to within ±14 percent; the
marketing department's price estimate is accurate only to within ±11 percent; and the engineering
department's net working capital estimate is accurate only to within ±7 percent. What are the Best
and Worst case NPVs?
In the worst-case, the OCF is:
OCFworst = {[($290)(0.89) – 210](42,000) – $546,000}(1-0.39) + 0.39($2,106,720/6)
OCFworst = $1,036,198.8
And the worst-case NPV is:
NPVworst = –$2,106,720 – $546,000(1+0.07) + $1,036,198.8(PVIFA10%,6) + [$546,000(1+0.07) +
$584,000(1-0.14)(1 – 0.39)]/1.16
NPVworst = –$2,324,688.72
The best-case OCF is:
OCFbest = {[$290(1.11) – 210](42,000) – $546,000}(1-0.39) + 0.39($1,589,280/6)
OCFbest = $2,637,121.2
And the best-case NPV is:
NPVbest = – $1,589,280 – $546,000(1-0.07) + $2,637,121.2(PVIFA10%,6) +
[$546,000(1-0.07) + $584,000(1.14)(1 – 0.39)]/1.16
NPVbest = $9,904,159.43
5.
Several celebrated investors and stock pickers frequently mentioned in the financial press have
recorded huge returns on their investments over the past two decades. Is the success of these
particular investors an invalidation of the EMH? Explain.
The EMH only says, within the bounds of increasingly strong assumptions about the information
processing of investors, that assets are fairly priced. An implication of this is that, on average, the
typical market participant cannot earn excessive profits from a particular trading strategy. However,
that does not mean that a few particular investors cannot outperform the market over a particular
investment horizon. Certain investors who do well for a period of time get a lot of attention from the
financial press, but the scores of investors who do not do well over the same period of time generally
get considerably less attention from the financial press.
6.
Suppose the returns on an asset are normally distributed. Suppose the historical average annual return
for the asset was 6.8 percent and the standard deviation was 9.6 percent. Based on these values, the
approximate probability that your return on these bonds will be less than -2.8 percent in a given year
is _____ percent. Approximately 95 percent of the time you would expect to see returns that range
from as low as _____ percent to as high as _____ percent. Approximately 99 percent of the time you
would expect to see returns that range from as low as _____percent to as high as _____percent.
The mean return for the asset was 6.8 percent, with a standard deviation of 9.6 percent. In the normal
probability distribution, approximately 2/3 of the observations are within one standard deviation of
the mean. This means that 1/3 of the observations are outside one standard deviation away from the
mean. Or:
Pr(R < -2.8 or R >16.4) ≈ 1/3
But we are only interested in one tail here, that is, returns less than -2.8 percent, so:
Pr(R < -2.8) ≈ 1/6
You can use the z-statistic and the cumulative normal distribution table to find the answer as well.
Doing so, we find:
z = (X − μ)/σ
z = (-2.8% − 6.8)/9.6% = -1
Looking at the z-table, this gives a probability of 15.87%, or:
Pr(R < -2.8) ≈ 0.1587 or 15.87%
The range of returns you would expect to see 95 percent of the time is the mean plus or minus 2
standard deviations, or:
95% level: Rε μ ± 2σ = 6.8% ± 2(9.6%) = -12.4% to 26%
The range of returns you would expect to see 99 percent of the time is the mean plus or minus 3
standard deviations, or:
99% level: Rε μ ± 3σ = 6.8% ± 3(9.6%) = -22% to 35.6%
7.
Is it possible that a risky asset could have a beta of zero? Explain. Based on the CAPM, what is the
expected return on such an asset? Is it possible that a risky asset could have a negative beta? What
does the CAPM predict about the expected return on such an asset? Can you give an explanation for
your answer?
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.
A stock has an expected return of 16 percent, the risk-free rate is 8.8 percent, and the market risk
premium is 6 percent. The beta of this stock must be
We are given the values for the CAPM except for the β of the stock. We need to substitute these
values into the CAPM, and solve for the β of the stock. One important thing we need to realize is that
we are given the market risk premium. The market risk premium is the expected return of the market
minus the risk-free rate. We must be careful not to use this value as the expected return of the
market. Using the CAPM, we find:
E(Ri) = 0.16 = 0.088+ 0.06βi
βi = 1.2
9.
You want to create a portfolio equally as risky as the market, and you have $1,000,000 to invest.
Given this information, fill in the rest of the following table.
Asset
Stock A
Stock B
Stock C
Risk-free asset
Investment
$
250,000
$
150,000
$
$
Beta
0.6
1.3
1.6
Since the portfolio is as risky as the market, the β of the portfolio must be equal to one. We also
know the β of the risk-free asset is zero. We can use the equation for the β of a portfolio to find the
weight of the third stock. Doing so, we find:
βp = 1.0 = wA(0.6) + wB(1.3) + wC(1.6) + wRf(0)
Solving for the weight of Stock C, we find:
wC = 0.409375
So, the dollar investment in Stock C must be:
Invest in Stock C = 0.409375($1,000,000) = $409,375
We know the total portfolio value and the investment of two stocks in the portfolio, so we can find
the weight of these two stocks. The weights of Stock A and Stock B are:
wA = $250,000 / $1,000,000 = 0.25
wB = $150,000/$1,000,000 = 0.15
We also know the total portfolio weight must be one, so the weight of the risk-free asset must be one
minus the asset weight we know, or:
1 = wA + wB + wC + wRf = 1 – 0.25 – 0.15 – 0.409375 = wRf
wRf = 0.190625
So, the dollar investment in the risk-free asset must be:
Invest in risk-free asset = 0.190625($1,000,000) = $190,625
10.
If you can borrow all the money you need for a project at 6 percent, doesn’t it follow that 6 percent is
your cost of capital for the project?
No. The cost of capital depends on the risk of the project, not the source of the money.
11.
Given the following information for Evenflow Power Co., the WACC is _____ percent. Assume the
company's tax rate is 31 percent.
Debt:
5,500 8.5 percent coupon bonds outstanding, $1,000 par value, 20 years to
maturity, selling for 104 percent of par; the bonds make semiannual payments.
Common stock: 110,000 shares outstanding, selling for $65 per share; the beta is 1.11.
Preferred stock: 16,500 shares of 8 percent preferred stock outstanding, currently selling for $107
per share.
Market:
10 percent market risk premium and 8 percent risk-free rate.
We will begin by finding the market value of each type of financing. We find:
MVD = 5,500($1,000)(1.04) = $5,720,000
MVE = 110,000($65) = $7,150,000
MVP = 16,500($107) = $1,765,500
And the total market value of the firm is:
V = $5,720,000 + 7,150,000 + 1,765,500 = $14,635,500
Now, we can find the cost of equity using the CAPM. The cost of equity is:
RE = 0.08 + 1.11(0.10) = 0.191 or 19.1%
The cost of debt is the YTM of the bonds, so:
P0 = $1,040 = $42.5(PVIFAR%,40) + $1,000(PVIFR%,40)
R = 3.013%
YTM = 4.0465% × 2 = 8.093%
And the aftertax cost of debt is:
RD = (1 – 0.31)(0.08093) = 0.05584 or 5.584%
The cost of preferred stock is:
RP = $8/$107 = 0.07477 or 7.48%
Now we have all of the components to calculate the WACC. The WACC is:
WACC = 0.191(7.15/14.6355) + 0.05584(5.72/14.6355) + 0.07477(1.7655/14.6355) = 0.1242 or
12.42%
Notice that we didn't include the (1 – tC) term in the WACC equation. We used the aftertax cost of
debt in the equation, so the term is not needed here.
12.
How does a bond issuer decide on the appropriate coupon rate to set on its bonds? Explain the
difference between the coupon rate and the required return on a bond.
Bond issuers look at outstanding bonds of similar maturity and risk. The yields on such bonds are
used to establish the coupon rate necessary for a particular issue to initially sell for par value. Bond
issuers also simply ask potential purchasers what coupon rate would be necessary to attract them.
The coupon rate is fixed and simply determines what the bond’s coupon payments will be. The
required return is what investors actually demand on the issue, and it will fluctuate through time. The
coupon rate and required return are equal only if the bond sells for exactly at par.
13.
Consider the prices in the following three Treasury issues as of May 15, 2007: The bond in the
middle is callable in February 2008. The implied value of the call feature is
6.5
8.2
12
May 13n
May 13
May 13
106:10
101:15
134:25
106:12
101:16
134:31
-13
-3
-15
5.28
5.24
5.32
To calculate this, we need to set up an equation with the callable bond equal to a weighted average of
the noncallable bonds. We will invest X percent of our money in the first noncallable bond, which
means our investment in Bond 3 (the other noncallable bond) will be (1 – X). The equation is:
C2 = C1 X + C3(1 – X)
8.2 = 6.5 X + 12(1 – X)
8.2 = 6.5 X + 12 – 12 X
X = 0.69091
So, we invest about 69 percent of our money in Bond 1, and about 31 percent in Bond 3. This
combination of bonds should have the same value as the callable bond, excluding the value of the
call. So:
P2 = 0.69091 P1 + 0.30909 P3
P2 = 0.69091(106.375) + 0.30909(134.96875)
P2 = 115.2131
The call value is the difference between this implied bond value and the actual bond price. So, the
call value is:
Call value = 115.2131 – 101.5 = 13.7131
Assuming $1,000 par value, the call value is $137.13.
14.
Storico Co. just paid a dividend of $1.50 per share. The company will increase its dividend by 16
percent next year and will then reduce its dividend growth rate by 4 percentage points per year until
it reaches the industry average of 4 percent dividend growth, after which the company will keep a
constant growth rate forever. If the required return on Storico stock is 14 percent, a share of stock
will sell for $_______ today.
Here we have a stock with supernormal growth, but the dividend growth changes every year for the
first four years. We can find the price of the stock in Year 3 since the dividend growth rate is
constant after the third dividend. The price of the stock in Year 3 will be the dividend in Year 4,
divided by the required return minus the constant dividend growth rate. So, the price in Year 3 will
be:
P3 = $1.5(1.16)(1.12)(1.08)(1.04) / (0.14 – 0.04) = $21.89
The price of the stock today will be the PV of the first three dividends, plus the PV of the stock price
in Year 3, so:
P0 = $1.5(1.16)/(1.14) + $1.5(1.16)(1.12)/1.142 + $1.5(1.16)(1.12)(1.08)/1.143 + $21.89/1.143
P0 = $19.22
15.
Who owns a corporation? Describe the process whereby the owners control the firm’s management.
What is the main reason that an agency relationship exists in the corporate form of organization? In
this context, what kinds of problems can arise?
In the corporate form of ownership, the shareholders are the owners of the firm. The shareholders
elect the directors of the corporation, who in turn appoint the firm’s management. This separation of
ownership from control in the corporate form of organization is what causes agency problems to
exist. Management may act in its own or someone else’s best interests, rather than those of the
shareholders. If such events occur, they may contradict the goal of maximizing the share price of the
equity of the firm.
16.
A firm has $100,000 in their capital budget and has identified the following projects. These projects
are not divisible which means that the firm can not accept only part of the project. Which project or
projects should the firm accept? Explain your answer.
Cost
PI
A
$40,000
1.25
B
$35,000
1.3
C
$30,000
1.15
D
$20,000
1.1
E
$10,000
1.05
First find NPV = Cost(PI – 1). Then sort by PI and find the combination of projects that result in the
highest overall NPV.
17.
Cost
NPV
PI
B
$35,000
$10,500
1.3
A
$40,000
$8,000
1.2
C
$30,000
$4,500
1.15
D
$20,000
$2,000
1.1
BAD
BCDE
ACDE
NPV
$20,500
$17,500
$15,000
+$5,000 cash left over
+$5,000 cash left over
E
$10,000
$500
1.05
Explain why in an efficient competitive market all assets should plot on the SML.
If an assets is above/below the SML it is offering a rate of return that is higher/lower than that
required to compensate the investors for the risk they are forced to bear and they will buy/sell the
asset until the current price rises/lowers to the point where the expected return is in line with that of
other freely traded assets of the same risk.
18.
You have recently identified a new project closely related to your firm’s business which has a very
positive NPV. Your firm operates in an industry with 20 direct competitors and limited barriers to
entry. What should be your reaction to this new project? Why? What further analysis should you
undertake?
You should be very skeptical of the positive NPV because if it is as good as you think, why haven’t
your competitors undertaken it? What has your firm brought to the table that your competitors can
not? You would probably want to perform sensitivity and scenario analysis at the very least.
19.
Consider the following information on three stocks:
State of
Probability of State of Economy
Rate of Return if State Occurs
Stock A Stock B Stock C
Economy
Boom
Normal
Bust
.35
.50
.15
.24
.17
.00
.36
.13
–.28
.55
.09
–.45
If your portfolio is invested 40 percent each in A and B and 20 percent in C, the portfolio
expected return is
deviation is
16.12 ± 0%
18.04 ± 0%
percent. The variance is
.03253
and standard
percent.
We need to find the return of the portfolio in each state of the economy. To do this, we will multiply
the return of each asset by its portfolio weight and then sum the products to get the portfolio return in
each state of the economy. Doing so, we get:
Boom: E(Rp) = .4(.24) + .4(.36) + .2(.55) = .3500 or 35.00% Normal: E(Rp) = .4(.17) + .4(.13) +
.2(.09) = .1380 or 13.80% Bust: E(Rp) = .4(.00) + .4(–.28) + .2(–.45) = –.2020 or –20.20% And the
expected return of the portfolio is: E(Rp) = .35(.35) + .50(.138) + .15(–.202) = .1612 or 16.12%
To calculate the standard deviation, we first need to calculate the variance. To find the variance, we
find the squared deviations from the expected return. We then multiply each possible squared
deviation by its probability, than add all of these up. The result is the variance. So, the variance and
standard deviation of the portfolio is:
σ2p = .35(.35 – .1612)2 + .50(.138 – .1612)2 + .15(–.202 – .1612)2 σ2p = .03253
σp = (.03253)1/2 = .1804 or 18.04%
20.
Explain why a characteristic of an efficient market is that investments in that market have zero
NPVs.
For the same reason that all assets should plot on the SML, all capital investments would have a zero
NPV in an efficient market. On average, the only return that is earned is the required return based on
the amount of risk—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).