FIN 470 Exam 2 KEY
1.
NAME________________________
The cash flows in this problem occur every two years, so we need to find the effective two year rate. One
way to find the effective two year rate is to use an equation similar to the EAR, except use the number of
days in two years as the exponent. (We use the number of days in two years since it is daily compounding;
if monthly compounding was assumed, we would use the number of months in two years.) So, the
effective two-year interest rate is:
Effective 2-year rate = [1 + (.11/365)]365(2) – 1 = .246 or 24.6%
We can use this interest rate to find the PV of the perpetuity. Doing so, we find:
PV = $15,000 /.246 = $60,966.83
This is an important point: Remember that the PV equation for a perpetuity (and an ordinary annuity) tells
you the PV one period before the first cash flow. In this problem, since the cash flows are two years apart,
we have found the value of the perpetuity one period (two years) before the first payment, which is one
year ago. We need to compound this value for one year to find the value today. The value of the cash
flows today is:
PV = $67,760.07(1 + .11/365)365 = $68,054.81
2.
If a project has a positive NPV for a certain discount rate, then it will also have a positive NPV for a zero
discount rate; thus, the payback period must be less than the project life. Since discounted payback is
calculated at the same discount rate as is NPV, if NPV is positive, the discounted payback period must be
less than the project’s life. If NPV is positive, then the present value of future cash inflows is greater than
the initial investment cost; thus PI must be greater than 1. If NPV is positive for a certain discount rate R,
then it will be zero for some larger discount rate R*; thus the IRR must be greater than the required return.
3.
For tax purposes, a firm would choose MACRS because it provides for larger depreciation deductions
earlier. 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.
4.
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 – 0.3) = $14,000
To calculate the EAC, we first need the OCF and NPV of each option. The OCF and NPV for Techron I
is:
OCF = $-33,000(1 – 0.3) + 0.3($189,000/3) = $-4,200
NPV = -189,000 + $-4,200(PVIFA14%,3) + ($14,000/1.14)3 = $-189,301.25
EAC = $-189,301.25 / (PVIFA14%,3) = $-81,538.01
And the OCF and NPV for Techron II is:
OCF =$-21,000(1 – 0.3) + 0.3($322,000/6) = $1,400
NPV = $-322,000 + $1,400(PVIFA14%,6) + ($14,000/1.14)6 = $-310,177.65
EAC = $-310,177.65 / (PVIFA14%,6) = $-79,764.51
5.
We need to find the bid price for a project, but the project has extra cash flows. Since we don't already
produce the keyboard, the sales of the keyboard outside the contract are relevant cash flows. Since we
know the extra sales number and price, we can calculate the cash flows generated by these sales. The cash
flow generated from the sale of the keyboard outside the contract is:
Sales
Variable costs
EBT
Tax
Net income (and OCF)
1
2
3
4
$669,600 $1,339,200 $1,785,600 $1,116,000
402,300
804,600 1,072,800
670,500
$267,300 $534,600 $712,800 $445,500
104,247
208,494
277,992
173,745
$163,053 $326,106 $434,808 $271,755
So, the addition to NPV of these market sales is:
NPV of market sales = $163,053/1.11 + $326,106/1.112 + $434,808/1.113 + $271,755/1.114
NPV of market sales = $908,510.84
You may have noticed that we did not include the initial cash outlay, depreciation or fixed costs in the
calculation of cash flows from the market sales. The reason is that it is irrelevant whether or not we
include these here. Remember, we are not only trying to determine the bid price, but we are also
determining whether or not the project is feasible. In other words, we are trying to calculate the NPV of
the project, not just the NPV of the bid price. We will include these cash flows in the bid price calculation.
The reason we stated earlier that whether we included these costs in this initial calculation was irrelevant
is that you will come up with the same bid price if you include these costs in this calculation, or if you
include them in the bid price calculation.
Next, we need to calculate the aftertax salvage value, which is:
Aftertax salvage value = $180,000(1 – 0.39) = $109,800
Instead of solving for a zero NPV as is usual in setting a bid price, the company president requires an NPV
of $90,000, so we will solve for a NPV of that amount. The NPV equation for this project is (remember to
include the NWC cash flow at the beginning of the project, and the NWC recovery at the end):
NPV = $90,000 = –$2,160,000 – 67,500 + 908,510.84 + OCF (PVIFA11%,4) + [($109,800 + 67,500) /
1.114]
Solving for the OCF, we get:
OCF = $1,231,689.16 / PVIFA11%,4 = $416,508.87
Now we can solve for the bid price as follows:
OCF = $416,508.87 = [(P – v)Q – FC ](1 – tC) + tCD
$416,508.87 = [(P – $149)(9,000) – $450,000](1 – 0.39) + 0.39($2,160,000/4)
P = $236.51
6.
Forecasting risk is the risk that a poor decision is made because of errors in projected cash flows. The
danger is greatest with a new product because the cash flows are probably harder to predict.
7.
Using the tax shield approach, the OCF is:
OCF = [($330 − 270)(49,000) − $637,000](1-0.39) + 0.39($2,009,000/5)
OCF = $1,561,532
8.
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).
9.
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.
10.
R1 = ($52.79 − 44.39 + 0.58) / $44.39 = 0.2022 or 20.22%
R2 = ($47.88 − 52.79 + 0.52) / $52.79 = -0.0832 or -8.32%
R3 = ($48.63 − 47.88 + 0.53) / $47.88 = 0.0266 or 2.66%
R4 = ($58.13 − 48.63 + 0.66)/ $48.63 = 0.2089 or 20.89%
R5 = ($64.95 − 58.13 + 0.71) / $58.13 = 0.1295 or 12.95%
The arithmetic average return was:
RA = ((0.2022) + (-0.0832) + (0.0266) + (0.2089) + (0.1295))/5 = 0.0968 or 9.68%
And the geometric average return was:
RG = [(1 + (0.2022))(1 + (-0.0832))(1 + (0.0266))(1 + (0.2089))(1 + (0.1295))]1/5 − 1 =
0.0909 or 9.09%
11.
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.
12.
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) = 0.31(0.25) + 0.31(0.65) + 0.38(0.55) = 0.488 or 48.8%
Normal: E(Rp) = 0.31(0.2) + 0.31(0.26) + 0.38(0.04) = 0.1578 or 15.78%
Bust: E(Rp) = 0.31(0.02) + 0.31(-0.07) + 0.38(-0.48) = -0.1979 or -19.79%
And the expected return of the portfolio is:
E(Rp) = 0.35(0.488) + 0.5(0.1578) + 0.15(-0.1979) = 0.220015 or 22%
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 = 0.35(0.488 – 0.220015)2 + 0.5(0.1578 – 0.220015)2 + 0.15(-0.1979 – 0.220015)2
σ2p = 0.053269
σp = (0.053269)1/2 = 0.2308 or 23.08%
E[RA] = 0.35(0.25) + 0.5(0.2) + 0.15(0.02) = 0.1905
E[RB] = 0.35(0.65) + 0.5(0.26) + 0.15(-0.07) = 0.347
σAB = 0.35(0.25 - 0.1905)(0.65 – 0.347) + 0.5(0.2 – 0.1905)(0.26 – 0.347) + 0.15(0.02 – 0.1905)(-0.07 –
0.347) = 0.0166
13.
If an asset plots above the line it is providing more return for the amount of risk than is needed to
compensate investors and all investors will buy the asset. This forces the current price up and the
expected return down to the SML. If the asset plots below the line it is providing less return than is
needed to compensate investors for the risk and they will sell the asset. This forces the current price down
and the expected return up to the SML.
14.
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.
15.
We will begin by finding the market value of each type of financing. We find:
MVD =3,500($1,000)(1.03) = $3,605,000
MVE = 77,000($56) = $4,312,000
MVP = 11,000($104) = $1,144,000
And the total market value of the firm is:
V = $3,605,000 + 4,312,000 + 1,144,000 = $9,061,000
Now, we can find the cost of equity using the CAPM. The cost of equity is:
RE = 0.075 + 1.08(0.11) = 0.1938 or 19.38%
The cost of debt is the YTM of the bonds, so:
P0 = $1,030 = $45(PVIFAR%,38) + $1,000(PVIFR%,38)
R = 4.338%
YTM = 4.338% × 2 = 8.68%
And the aftertax cost of debt is:
RD = (1 − 0.34)(0.0868) = 0.0573 or 5.73%
The cost of preferred stock is:
RP = $8/$104 = 0.0769 or 7.69%
Now we have all of the components to calculate the WACC. The WACC is:
WACC = 0.0573(3.6/9.061) + 0.1938(4.31/9.061) + 0.0769(1.144/9.061) = 0.1247 or 12.47%
16.
They are riskier and harder to market from an investment bank’s perspective. The largest players in the
bond market are institutions that may only invest in investment grade bonds. This lowers the supply of
buyers and makes the market less liquid.
17.
The number of new shares will be the amount raised divided by the subscription price, so:
Number of new shares = $45,000,000/$32 = 1,406,250 shares
And the number of rights needed to buy one share will be the current shares outstanding divided by the
number of new share offered, so:
Number of rights needed = 4,590,000 shares outstanding/1,406,250 new shares = 3.26
shareholder can buy 3.26 rights on shares for:
3.26($40) = $130.56
The shareholder can exercise these rights for $32, at a total cost of:
$130.56 + 32 = $162.56
The investor will then have:
Ex-rights shares = 1 + 3.26
Ex-rights shares = 4.26
The ex-rights price per share is:
PX = [3.26($40) + $32]/4.26 = $38.12
So, the value of a right is:
Value of a right = $40 – 38.12 = $1.88
18.
Business risk is the equity risk arising from the nature of the firm’s operating activity, and is directly
related to the systematic risk of the firm’s assets. Financial risk is the equity risk that is due entirely to the
firm’s chosen capital structure. As financial leverage, or the use of debt financing, increases, so does
financial risk and, hence, the overall risk of the equity. Thus, Firm B could have a higher cost of equity if
it uses greater leverage.
19.
The earnings per share are:
EPS = $17,000/1,900 shares
EPS = $8.95
So, the cash flow for the company is:
Cash flow = $8.95(100 shares)
Cash flow = $894.74
To determine the cash flow to the shareholder, we need to determine the EPS of the firm under the
proposed capital structure. The market value of the firm is:
V = $70(1,900)
V = $133,000
Under the proposed capital structure, the firm will raise new debt in the amount of:
D = 0.36($133,000)
D = $47,880
in debt. This means the number of shares repurchased will be:
Shares repurchased = $47,880/$70
Shares repurchased = 684
Under the new capital structure, the company will have to make an interest payment on the new debt. The
net income with the interest payment will be:
NI = $17,000 – 0.07($47,880)
NI = $13,648.4
This means the EPS under the new capital structure will be:
EPS = $13,648.4/1,216 shares
EPS = $11.224
Since all earnings are paid as dividends, the shareholder will receive:
Shareholder cash flow = $11.224(100 shares)
Shareholder cash flow = $1,122.4
To replicate the proposed capital structure, the shareholder should sell 36 percent of their shares, or 36
shares, and lend the proceeds at 7 percent. The shareholder will have an interest cash flow of:
Interest cash flow = 36($70)(0.07)
Interest cash flow = $176.4
The shareholder will receive dividend payments on the remaining 64 shares, so the dividends received will
be:
Dividends received = $11.224(64 shares)
Dividends received = $718.34
The total cash flow for the shareholder under these assumptions will be:
Total cash flow = $176.4 + 718.34
Total cash flow = $894.74
20.
If the tax rate is 32%, the value of the unlevered firm is:
VU = EBIT(1 – tC)/RU
VU = $95,000(1 – 0.32)/0.2
VU = $323,000
If Frederick borrows $66,000, the value of the levered firm is:
VU = VU + tCD
VU = $323,000 + 0.32($66,000)
VU = $344,120