14
COST CHAPTER OF CAPITAL
Answers to Concepts Review and Critical Thinking Questions
1.
It is the minimum rate of return the firm must earn overall on its existing assets. If it earns
more than this, value is created.
2.
Book values for debt are likely to be much closer to market values than are equity book
values.
3.
No. The cost of capital depends on the risk of the project, not the source of the money.
4.
Interest expense is tax-deductible. There is no difference between pretax and aftertax equity
costs.
5.
The primary advantage of the DCF model is its simplicity. The method is disadvantaged in
that (1) the model is applicable only to firms that actually pay dividends; many do not; (2)
even if a firm does pay dividends, the DCF model requires a constant dividend growth rate
forever; (3) the estimated cost of equity from this method is very sensitive to changes in g,
which is a very uncertain parameter; and (4) the model does not explicitly consider risk,
although risk is implicitly considered to the extent that the market has impounded the
relevant risk of the stock into its market price. While the share price and most recent
dividend can be observed in the market, the dividend growth rate must be estimated. Two
common methods of estimating g are to use analysts earnings and payout forecasts or to
determine some appropriate average historical g from the firms available data.
6.
Two primary advantages of the SML approach are that the model explicitly incorporates the
relevant risk of the stock and the method is more widely applicable than is the dividend
discount model model, since the SML doesnt make any assumptions about the firms
dividends. The primary disadvantages of the SML method are (1) three parameters (the riskfree rate, the expected return on the market, and beta) must be estimated, and (2) the method
essentially uses historical information to estimate these parameters. The risk-free rate is
usually estimated to be the yield on very short maturity T-bills and is, hence, observable; the
market risk premium is usually estimated from historical risk premiums and, hence, is not
observable. The stock beta, which is unobservable, is usually estimated either by
determining some average historical beta from the firm and the markets return data, or by
using beta estimates provided by analysts and investment firms.
7.
The appropriate aftertax cost of debt to the company is the interest rate it would have to pay
if it were to issue new debt today. Hence, if the YTM on outstanding bonds of the company
is observed, the company has an accurate estimate of its cost of debt. If the debt is privatelyplaced, the firm could still estimate its cost of debt by (1) looking at the cost of debt for
similar firms in similar risk classes, (2) looking at the average debt cost for firms with the
same credit rating (assuming the firms private debt is rated), or (3) consulting analysts and
investment bankers. Even if the debt is publicly traded, an additional complication is when
the firm has more than one issue outstanding; these issues rarely have the same yield
because no two issues are ever completely homogeneous.
8.
a.
b.
c.
9.
This only considers the dividend yield component of the required return on equity.
This is the current yield only, not the promised yield to maturity. In addition, it is based
on the book value of the liability, and it ignores taxes.
Equity is inherently more risky than debt (except, perhaps, in the unusual case where a
firms assets have a negative beta). For this reason, the cost of equity exceeds the cost
of debt. If taxes are considered in this case, it can be seen that at reasonable tax rates,
the cost of equity does exceed the cost of debt.
RSup = .12 + .75(.08) = .1800 or 18.00%
Both should proceed. The appropriate discount rate does not depend on which company is
investing; it depends on the risk of the project. Since Superior is in the business, it is closer
to a pure play. Therefore, its cost of capital should be used. With an 18% cost of capital, the
project has an NPV of $1 million regardless of who takes it.
10. 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 markets 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.
Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require
multiple steps. Due to space and readability constraints, when these intermediate steps are
included in this solutions manual, rounding may appear to have occurred. However, the final
answer for each problem is found without rounding during any step in the problem.
Basic
1.
With the information given, we can find the cost of equity using the dividend growth model.
Using this model, the cost of equity is:
RE = [$2.40(1.055)/$52] + .055 = .1037 or 10.37%
2.
Here we have information to calculate the cost of equity using the CAPM. The cost of equity
is:
RE = .053 + 1.05(.12 .053) = .1234 or 12.34%
3.
We have the information available to calculate the cost of equity using the CAPM and the
dividend growth model. Using the CAPM, we find:
RE = .05 + 0.85(.08) = .1180 or 11.80%
And using the dividend growth model, the cost of equity is
RE = [$1.60(1.06)/$37] + .06 = .1058 or 10.58%
Both estimates of the cost of equity seem reasonable. If we remember the historical return on
large capitalization stocks, the estimate from the CAPM model is about two percent higher
than average, and the estimate from the dividend growth model is about one percent higher
than the historical average, so we cannot definitively say one of the estimates is incorrect.
Given this, we will use the average of the two, so:
RE = (.1180 + .1058)/2 = .1119 or 11.19%
4.
To use the dividend growth model, we first need to find the growth rate in dividends. So, the
increase in dividends each year was:
g1 = ($1.12 1.05)/$1.05 = .0667 or 6.67%
g2 = ($1.19 1.12)/$1.12 = .0625 or 6.25%
g3 = ($1.30 1.19)/$1.19 = .0924 or 9.24%
g4 = ($1.43 1.30)/$1.30 = .1000 or 10.00%
So, the average arithmetic growth rate in dividends was:
g = (.0667 + .0625 + .0924 + .1000)/4 = .0804 or 8.04%
Using this growth rate in the dividend growth model, we find the cost of equity is:
RE = [$1.43(1.0804)/$45.00] + .0804 = .1147 or 11.47%
Calculating the geometric growth rate in dividends, we find:
$1.43 = $1.05(1 + g)4
g = .0803 or 8.03%
The cost of equity using the geometric dividend growth rate is:
RE = [$1.43(1.0803)/$45.00] + .0803 = .1146 or 11.46%
5.
The cost of preferred stock is the dividend payment divided by the price, so:
RP = $6/$96 = .0625 or 6.25%
6.
The pretax cost of debt is the YTM of the companys bonds, so:
P0 = $1,070 = $35(PVIFAR%,30) + $1,000(PVIFR%,30)
R = 3.137%
YTM = 2 3.137% = 6.27%
And the aftertax cost of debt is:
RD = .0627(1 .35) = .0408 or 4.08%
7.
a. The pretax cost of debt is the YTM of the companys bonds, so:
P0 = $950 = $40(PVIFAR%,46) + $1,000(PVIFR%,46)
R = 4.249%
YTM = 2 4.249% = 8.50%
b.
The aftertax cost of debt is:
RD = .0850(1 .35) = .0552 or 5.52%
c.
8.
The after-tax rate is more relevant because that is the actual cost to the company.
The book value of debt is the total par value of all outstanding debt, so:
BVD = $80,000,000 + 35,000,000 = $115,000,000
To find the market value of debt, we find the price of the bonds and multiply by the number
of bonds. Alternatively, we can multiply the price quote of the bond times the par value of
the bonds. Doing so, we find:
MVD = .95($80,000,000) + .61($35,000,000)
MVD = $76,000,000 + 21,350,000
MVD = $97,350,000
The YTM of the zero coupon bonds is:
PZ = $610 = $1,000(PVIFR%,14)
R = 3.594%
YTM = 2 3.594% = 7.19%
So, the aftertax cost of the zero coupon bonds is:
RZ = .0719(1 .35) = .0467 or 4.67%
The aftertax cost of debt for the company is the weighted average of the aftertax cost of debt
for all outstanding bond issues. We need to use the market value weights of the bonds. The
total aftertax cost of debt for the company is:
RD = .0552($76/$97.35) + .0467($21.35/$97.35) = .0534 or 5.34%
9.
a.
Using the equation to calculate the WACC, we find:
WACC = .60(.14) + .05(.06) + .35(.08)(1 .35) = .1052 or 10.52%
b.
Since interest is tax deductible and dividends are not, we must look at the after-tax cost
of debt, which is:
.08(1 .35) = .0520 or 5.20%
Hence, on an after-tax basis, debt is cheaper than the preferred stock.
10. Here we need to use the debt-equity ratio to calculate the WACC. Doing so, we find:
WACC = .15(1/1.65) + .09(.65/1.65)(1 .35) = .1140 or 11.40%
11. Here we have the WACC and need to find the debt-equity ratio of the company. Setting up
the WACC equation, we find:
WACC = .0890 = .12(E/V) + .079(D/V)(1 .35)
Rearranging the equation, we find:
.0890(V/E) = .12 + .079(.65)(D/E)
Now we must realize that the V/E is just the equity multiplier, which is equal to:
V/E = 1 + D/E
.0890(D/E + 1) = .12 + .05135(D/E)
Now we can solve for D/E as:
.06765(D/E) = .031
D/E = .8234
12. a.
The book value of equity is the book value per share times the number of shares, and
the book value of debt is the face value of the companys debt, so:
BVE = 11,000,000($6) = $66,000,000
BVD = $70,000,000 + 55,000,000 = $125,000,000
So, the total value of the company is:
V = $66,000,000 + 125,000,000 = $191,000,000
And the book value weights of equity and debt are:
E/V = $66,000,000/$191,000,000 = .3455
D/V = 1 E/V = .6545
b.
The market value of equity is the share price times the number of shares, so:
MVE = 11,000,000($68) = $748,000,000
Using the relationship that the total market value of debt is the price quote times the par
value of the bond, we find the market value of debt is:
MVD = .93($70,000,000) + 1.04($55,000,000) = $122,300,000
This makes the total market value of the company:
V = $748,000,000 + 122,300,000 = $870,300,000
And the market value weights of equity and debt are:
E/V = $748,000,000/$870,300,000 = .8595
D/V = 1 E/V = .1405
c.
The market value weights are more relevant.
13. First, we will find the cost of equity for the company. The information provided allows us to
solve for the cost of equity using the dividend growth model, so:
RE = [$4.10(1.06)/$68] + .06 = .1239 or 12.39%
Next, we need to find the YTM on both bond issues. Doing so, we find:
P1 = $930 = $35(PVIFAR%,42) + $1,000(PVIFR%,42)
R = 3.838%
YTM = 3.838% 2 = 7.68%
P2 = $1,040 = $40(PVIFAR%,12) + $1,000(PVIFR%,12)
R = 3.584%
YTM = 3.584% 2 = 7.17%
To find the weighted average aftertax cost of debt, we need the weight of each bond as a
percentage of the total debt. We find:
wD1 = .93($70,000,000)/$122,300,000 = .5323
wD2 = 1.04($55,000,000)/$122,300,000 = .4677
Now we can multiply the weighted average cost of debt times one minus the tax rate to find
the weighted average aftertax cost of debt. This gives us:
RD = (1 .35)[(.5323)(.0768) + (.4677)(.0717)] = .0484 or 4.84%
Using these costs we have found and the weight of debt we calculated earlier, the WACC is:
WACC = .8595(.1239) + .1405(.0484) = .1133 or 11.33%
14. a.
Using the equation to calculate WACC, we find:
WACC = .094 = (1/2.05)(.14) + (1.05/2.05)(1 .35)RD
RD = .0772 or 7.72%
b.
Using the equation to calculate WACC, we find:
WACC = .094 = (1/2.05)RE + (1.05/2.05)(.068)
RE = .1213 or 12.13%
15. We will begin by finding the market value of each type of financing. We find:
MVD = 8,000($1,000)(0.92) = $7,360,000
MVE = 250,000($57) = $14,250,000
MVP = 15,000($93) = $1,395,000
And the total market value of the firm is:
V = $7,360,000 + 14,250,000 + 1,395,000 = $23,005,000
Now, we can find the cost of equity using the CAPM. The cost of equity is:
RE = .045 + 1.05(.08) = .1290 or 12.90%
The cost of debt is the YTM of the bonds, so:
P0 = $920 = $32.50(PVIFAR%,40) + $1,000(PVIFR%,40)
R = 3.632%
YTM = 3.632% 2 = 7.26%
And the aftertax cost of debt is:
RD = (1 .35)(.0726) = .0472 or 4.72%
The cost of preferred stock is:
RP = $5/$93 = .0538 or 5.38%
Now we have all of the components to calculate the WACC. The WACC is:
WACC = .0472(7.36/23.005) + .1290(14.25/23.005) + .0538(1.395/23.005) = .0983 or
9.83%
Notice that we didnt 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.
16. a.
We will begin by finding the market value of each type of financing. We find:
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 companys 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.
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%
17. a.
b.
Projects X, Y and Z.
Using the CAPM to consider the projects, we need to calculate the expected return of
the project given its level of risk. This expected return should then be compared to the
expected return of the project. If the return calculated using the CAPM is lower than
the project expected return, we should accept the project, if not, we reject the project.
After considering risk via the CAPM:
E[W] = .05 + .80(.11 .05)
E[X] = .05 + .90(.11 .05)
E[Y] = .05 + 1.45(.11 .05)
E[Z] = .05 + 1.60(.11 .05)
= .0980 < .10, so accept W
= .1040 < .12, so accept X
= .1370 > .13, so reject Y
= .1460 < .15, so accept Z
c. Project W would be incorrectly rejected; Project Y would be incorrectly accepted.
18. a.
b.
He should look at the weighted average flotation cost, not just the debt cost.
The weighted average floatation cost is the weighted average of the floatation costs for
debt and equity, so:
fT = .05(.75/1.75) + .08(1/1.75) = .0671 or 6.71%
c.
The total cost of the equipment including floatation costs is:
Amount raised(1 .0671) = $20,000,000
Amount raised = $20,000,000/(1 .0671) = $21,439,510
Even if the specific funds are actually being raised completely from debt, the flotation
costs, and hence true investment cost, should be valued as if the firms target capital
structure is used.
19. We first need to find the weighted average floatation cost. Doing so, we find:
fT = .65(.09) + .05(.06) + .30(.03) = .071 or 7.1%
And the total cost of the equipment including floatation costs is:
Amount raised(1 .071) = $45,000,000
Amount raised = $45,000,000/(1 .071) = $48,413,125
Intermediate
20. Using the debt-equity ratio to calculate the WACC, we find:
WACC = (.90/1.90)(.048) + (1/1.90)(.13) = .0912 or 9.12%
Since the project is riskier than the company, we need to adjust the project discount rate for
the additional risk. Using the subjective risk factor given, we find:
Project discount rate = 9.12% + 2.00% = 11.12%
We would accept the project if the NPV is positive. The NPV is the PV of the cash outflows
plus the PV of the cash inflows. Since we have the costs, we just need to find the PV of
inflows. The cash inflows are a growing perpetuity. If you remember, the equation for the
PV of a growing perpetuity is the same as the dividend growth equation, so:
PV of future CF = $2,700,000/(.1112 .04) = $37,943,787
The project should only be undertaken if its cost is less than $37,943,787 since costs less
than this amount will result in a positive NPV.
21. The total cost of the equipment including floatation costs was:
Total costs = $15,000,000 + 850,000 = $15,850,000
Using the equation to calculate the total cost including floatation costs, we get:
Amount raised(1 fT) = Amount needed after floatation costs
$15,850,000(1 fT) = $15,000,000
fT = .0536 or 5.36%
Now, we know the weighted average floatation cost. The equation to calculate the
percentage floatation costs is:
fT = .0536 = .07(E/V) + .03(D/V)
We can solve this equation to find the debt-equity ratio as follows:
.0536(V/E) = .07 + .03(D/E)
We must recognize that the V/E term is the equity multiplier, which is (1 + D/E), so:
.0536(D/E + 1) = .08 + .03(D/E)
D/E = 0.6929
22. To find the aftertax cost of debt for the company, we need to find the weighted average of
the four debt issues. We will begin by calculating the market value of each debt issue, which
is:
MV1 = 1.03($40,000,000)
MV1 = $41,200,000
MV2 = 1.08($35,000,000)
MV2 = $37,800,000
MV3 = 0.97($55,000,000)
MV3 = $53,500,000
MV4 = 1.11($40,000,000)
MV4 = $55,500,000
So, the total market value of the companys debt is:
MVD = $41,200,000 + 37,800,000 + 53,350,000 + 55,500,000
MVD = $187,850,000
The weight of each debt issue is:
w1 = $41,200,000/$187,850,000
w1 = .2193 or 21.93%
w2 = $37,800,000/$187,850,000
w2 = .2012 or 20.12%
w3 = $53,500,000/$187,850,000
w3 = .2840 or 28.40%
w4 = $55,500,000/$187,850,000
w4 = .2954 or 29.54%
Next, we need to find the YTM for each bond issue. The YTM for each issue is:
P1 = $1,030 = $35(PVIFAR%,10) + $1,000(PVIFR%,10)
R1 = 2.768%
YTM1 = 3.146% 2
YTM1 = 6.29%
P2 = $1,080 = $42.50(PVIFAR%,16) + $1,000(PVIFR%,16)
R2 = 3.584%
YTM2 = 3.584% 2
YTM2 = 7.17%
P3 = $970 = $41(PVIFAR%,31) + $1,000(PVIFR%,31)
R3 = 3.654%
YTM3 = 4.276% 2
YTM3 = 8.54%
P4 = $1,110 = $49(PVIFAR%,50) + $1,000(PVIFR%,50)
R4 = 4.356%
YTM4 = 4.356% 2
YTM4 = 8.71%
The weighted average YTM of the companys debt is thus:
YTM = .2193(.0629) + .2012 (.0717) + .2840(.0854) + .2954(.0871)
YTM = .0782 or 7.82%
And the aftertax cost of debt is:
RD = .0782(1 .034)
RD = .0516 or 5.16%
23. a.
Using the dividend discount model, the cost of equity is:
RE = [(0.80)(1.05)/$61] + .05
RE = .0638 or 6.38%
b.
Using the CAPM, the cost of equity is:
RE = .055 + 1.50(.1200 .0550)
RE = .1525 or 15.25%
c.
When using the dividend growth model or the CAPM, you must remember that both
are estimates for the cost of equity. Additionally, and perhaps more importantly, each
method of
estimating the cost of equity depends upon different assumptions.
Challenge
24. We can use the debt-equity ratio to calculate the weights of equity and debt. The debt of the
company has a weight for long-term debt and a weight for accounts payable. We can use the
weight given for accounts payable to calculate the weight of accounts payable and the
weight of long-term debt. The weight of each will be:
Accounts payable weight = .20/1.20 = .17
Long-term debt weight = 1/1.20 = .83
Since the accounts payable has the same cost as the overall WACC, we can write the
equation for the WACC as:
WACC = (1/1.7)(.14) + (0.7/1.7)[(.20/1.2)WACC + (1/1.2)(.08)(1 .35)]
Solving for WACC, we find:
WACC = .0824 + .4118[(.20/1.2)WACC + .0433]
WACC = .0824 + (.0686)WACC + .0178
(.9314)WACC = .1002
WACC = .1076 or 10.76%
We will use basically the same equation to calculate the weighted average floatation cost,
except we will use the floatation cost for each form of financing. Doing so, we get:
Flotation costs = (1/1.7)(.08) + (0.7/1.7)[(.20/1.2)(0) + (1/1.2)(.04)] = .0608 or 6.08%
The total amount we need to raise to fund the new equipment will be:
Amount raised cost = $45,000,000/(1 .0608)
Amount raised = $47,912,317
Since the cash flows go to perpetuity, we can calculate the present value using the equation
for the PV of a perpetuity. The NPV is:
NPV = $47,912,317 + ($6,200,000/.1076)
NPV = $9,719,777
25. We can use the debt-equity ratio to calculate the weights of equity and debt. The weight of
debt in the capital structure is:
wD = 1.20 / 2.20 = .5455 or 54.55%
And the weight of equity is:
wE = 1 .5455 = .4545 or 45.45%
Now we can calculate the weighted average floatation costs for the various percentages of
internally raised equity. To find the portion of equity floatation costs, we can multiply the
equity costs by the percentage of equity raised externally, which is one minus the percentage
raised internally. So, if the company raises all equity externally, the floatation costs are:
fT = (0.5455)(.08)(1 0) + (0.4545)(.035)
fT = .0555 or 5.55%
The initial cash outflow for the project needs to be adjusted for the floatation costs. To
account for the floatation costs:
Amount raised(1 .0555) = $145,000,000
Amount raised = $145,000,000/(1 .0555)
Amount raised = $153,512,993
If the company uses 60 percent internally generated equity, the floatation cost is:
fT = (0.5455)(.08)(1 0.60) + (0.4545)(.035)
fT = .0336 or 3.36%
And the initial cash flow will be:
Amount raised(1 .0336) = $145,000,000
Amount raised = $145,000,000/(1 .0336)
Amount raised = $150,047,037
If the company uses 100 percent internally generated equity, the floatation cost is:
fT = (0.5455)(.08)(1 1) + (0.4545)(.035)
fT = .0191 or 1.91%
And the initial cash flow will be:
Amount raised(1 .0191) = $145,000,000
Amount raised = $145,000,000/(1 .0191)
Amount raised = $147,822,057
26. The $4 million cost of the land 3 years ago is a sunk cost and irrelevant; the $5.1 million
appraised value of the land is an opportunity cost and is relevant. The $6 million land value
in 5 years is a relevant cash flow as well. The fact that the company is keeping the land
rather than selling it is unimportant. The land is an opportunity cost in 5 years and is a
relevant cash flow for this project. The market value capitalization weights are:
MVD = 240,000($1,000)(0.94) = $225,600,000
MVE = 9,000,000($71) = $639,000,000
MVP = 400,000($81) = $32,400,000
The total market value of the company is:
V = $225,600,000 + 639,000,000 + 32,400,000 = $897,000,000
Next we need to find the cost of funds. We have the information available to calculate the
cost of equity using the CAPM, so:
RE = .05 + 1.20(.08) = .1460 or 14.60%
The cost of debt is the YTM of the companys outstanding bonds, so:
P0 = $940 = $37.50(PVIFAR%,40) + $1,000(PVIFR%,40)
R = 4.056%
YTM = 4.056% 2 = 8.11%
And the aftertax cost of debt is:
RD = (1 .35)(.0811) = .0527 or 5.27%
The cost of preferred stock is:
RP = $5.50/$81 = .0679 or 6.79%
a.
The weighted average floatation cost is the sum of the weight of each source of funds
in the capital structure of the company times the floatation costs, so:
fT = ($639/$897)(.08) + ($32.4/$897)(.06) + ($225.6/$897)(.04) = .0692 or 6.92%
The initial cash outflow for the project needs to be adjusted for the floatation costs. To
account for the floatation costs:
Amount raised(1 .0692) = $35,000,000
Amount raised = $35,000,000/(1 .0692) = $37,602,765
So the cash flow at time zero will be:
CF0 = $5,100,000 37,602,765 1,3000,000 = $44,002,765
There is an important caveat to this solution. This solution assumes that the increase in
net working capital does not require the company to raise outside funds; therefore the
floatation costs are not included. However, this is an assumption and the company
could need to raise outside funds for the NWC. If this is true, the initial cash outlay
includes these floatation costs, so:
Total cost of NWC including floatation costs:
$1,300,000/(1 .0692) = $1,396,674
This would make the total initial cash flow:
CF0 = $5,100,000 37,602,765 1,396,674 = $44,099,439
b.
To find the required return on this project, we first need to calculate the WACC for the
company. The companys WACC is:
WACC = [($639/$897)(.1460) + ($32.4/$897)(.0679) + ($225.6/$897)(.0527)] = .1197
The company wants to use the subjective approach to this project because it is located
overseas. The adjustment factor is 2 percent, so the required return on this project is:
Project required return = .1197 + .02 = .1397
c.
The annual depreciation for the equipment will be:
$35,000,000/8 = $4,375,000
So, the book value of the equipment at the end of five years will be:
BV5 = $35,000,000 5($4,375,000) = $13,125,000
So, the aftertax salvage value will be:
Aftertax salvage value = $6,000,000 + .35($13,125,000 6,000,000) = $8,493,750
d.
Using the tax shield approach, the OCF for this project is:
OCF = [(P v)Q FC](1 t) + tCD
OCF = [($10,900 9,400)(18,000) 7,000,000](1 .35) + .35($35,000,000/8) =
$14,531,250
e.
The accounting breakeven sales figure for this project is:
QA = (FC + D)/(P v) = ($7,000,000 + 4,375,000)/($10,900 9,400) = 7,583 units
f.
We have calculated all cash flows of the project. We just need to make sure that in
Year 5 we add back the aftertax salvage value and the recovery of the initial NWC. The
cash flows for the project are:
Year
0
1
2
3
4
5
Flow Cash
$44,002,765
14,531,250
14,531,250
14,531,250
14,531,250
30,325,000
Using the required return of 13.97 percent, the NPV of the project is:
NPV = $44,002,765 + $14,531,250(PVIFA13.97%,4) + $30,325,000/1.13975
NPV = $14,130,713.81
And the IRR is:
NPV = 0 = $44,002,765 + $14,531,250(PVIFAIRR%,4) + $30,325,000/(1 + IRR)5
IRR = 25.25%
If the initial NWC is assumed to be financed from outside sources, the cash flows are:
Year
0
1
2
3
4
5
Flow Cash
$44,099,439
14,531,250
14,531,250
14,531,250
14,531,250
30,325,000
With this assumption, and the required return of 13.97 percent, the NPV of the project
is:
NPV = $44,099,439 + $14,531,250(PVIFA13.97%,4) + $30,325,000/1.13975
NPV = $14,034,039.67
And the IRR is:
NPV = 0 = $44,099,439 + $14,531,250(PVIFAIRR%,4) + $30,325,000/(1 + IRR)5
IRR = 25.15%