1. If the bank debt is treated as permanent financing, the capital structure proportions are:
Bank debt (r_{D} = 10 percent) 
$280 

9.4% 

Longterm debt (r_{D} = 9 percent) 
1800 

60.4 

Equity (r_{E} = 18 percent, 90 x 10 million shares) 
900 

30.2 


$2980 

100.0% 

WACC* = [0.10´(1  0.35)´0.094] + [0.09´(1  0.35)´0.604] + [0.18´0.302] 

= 0.096 = 9.6% 


2. Forecast aftertax incremental cash flows as explained in Section 6.1. Interest is not included; the forecasts assume an allequity financed firm.
3. Calculate APV by subtracting $4 million from basecase NPV.
4. We make three adjustments to the balance sheet:
· Ignore deferred taxes; this is an accounting entry and represents neither a liability nor a source of funds
· ‘Net out’ accounts payable against current assets
· Use the market value of equity (7.46 million x $46)
Now the righthand side of the balance sheet (in thousands) looks like:
Shortterm debt $75,600
Longterm debt 208,600
Share
holder equity 343,160
Total $627,360
The aftertax weightedaverage cost of capital formula, with one element for each source of funding, is:
WACC = [r_{DST}´(1 – T_{c})´(DST/V)]+[r_{DLT}´(1 – T_{c})´(DLT/V)]+[r_{E} ´(E/V)]
WACC = [0.06´(1  0.35)´(75,600/627,360)] + [0.08´(1  0.35)´(208,600/627,360)]
+ [0.15´(343,160/627,360)]
= 0.004700 + 0.017290 + 0.082049 = 0.1040 = 10.40%
5. Assume that shortterm debt is temporary. From Practice Question 4:
Longterm debt $208,600
Share
holder equity 343,160
Total $551,760
Therefore:
(D/V) = ($208,600/$551,760) = 0.378
(E/V) = ($343,160/$551,760) = 0.622
Step 1:
r = r_{D} (D/V) + r_{E} (E/V) = (0.08 ´ 0.378) + (0.15 ´ 0.622) = 0.1235
Step 2:
r_{E} = r + (r – r_{D}) (D/E) = 0.1235 + (0.1235  .08) ´ (0.4) = 0.1409
Step 3:
WACC = [r_{D} ´ (1 – T_{C}) ´ (D/V)] + [r_{E} ´ (E/V)]
= (0.08 ´ 0.65 ´ 0.286) + (0.1409 ´ 0.714) = 0.1155 = 11.55%
6.
Pretax operating income 

$100.5 

Shortterm interest 

4.5 

Longterm interest 

16.7 

Earnings before tax 

$79.3 

Tax 

27.8 

Net income 

$51.5 

Value of equity = $51.5/0.15 = $343.3 

Value of firm = $343.3 + $75.6 + $208.6 = $627.5 
7. The problem here is that issue costs are a onetime expenditure, while adjusting the WACC implies a correction every year. The only way to account for issue costs in project evaluation is to use the APV formulation and adjust directly by subtracting the issue costs from the base case NPV.
8. a. Base case NPV = 1,000 + (600/1.12) +
(700/1.12^{2}) = $93.75 or $93,750
Year 
Debt Outstanding at Start Of Year 
Interest 
Interest Tax Shield 
PV (Tax Shield) 
1 
300 
24 
7.20 
6.67 
2 
150 
12 
3.60 
3.09 
APV = 93.75 + 6.67 + 3.09 = 103.5 or $103,500
9. [$100,000 ´ (1  0.35)] + [$100,000 ´ (1  0.35) ´ (Annuity Factor_{5/9 (1 – 0.35)%})]
= $65,000 + $274,925 = $339,925
10. a. Basecase NPV = $1,000,000 + ($85,000/0.10) = $150,000
PV(tax shields) = 0.35 ´ $400,000 = $140,000
APV = $150,000 + $140,000 = $10,000
b. PV(tax shields, approximate) = (0.35 ´ 0.07 ´ $400,000)/0.10 = $98,000
APV = $150,000 + $98,000 = $52,000
PV(tax shields, exact) = $98,000 ´ (1.10/1.07) = $100,748
APV = $150,000 + $100,748 = $49,252
The present value of the tax shield is higher when the debt is fixed and therefore the tax shield is certain. When borrowing a constant proportion of the market value of the project, the interest tax shields are as uncertain as the value of the project, and therefore must be discounted at the project’s opportunity cost of capital.
11. The immediate source of funds (i.e., both the proportion borrowed and the expected return on the stocks sold) is irrelevant. The project would not be any more valuable if the university sold stocks offering a lower return. If borrowing is a zeroNPV activity for a taxexempt university, then basecase NPV equals APV, and the adjusted cost of capital r* equals the opportunity cost of capital with allequity financing. Here, basecase NPV is negative; the university should not invest.
12. r* is the aftertax adjusted weighted average cost of capital. An adjusted discount rate does not equal the WACC when it takes into account major changes in expected capital structure or costs.
13. Note the following:
· The costs of debt and equity are not 8.5% and 19%, respectively. These figures assume the issue costs are paid every year, not just at issue.
· The fact that Bunsen can finance the entire cost of the project with debt is irrelevant. The cost of capital does not depend on the immediate source of funds; what matters is the project’s contribution to the firm’s overall borrowing power.
· The project is expected to support debt in perpetuity. The fact that the first debt issue is for only 20 years is irrelevant.
Assume the project has the same business risk as the firm’s other assets. Because it is a perpetuity, we can use the firm’s weightedaverage cost of capital. If we ignore issue costs:
WACC = [r_{D} ´ (1  T_{C}) ´ (D/V)] + [r_{E} ´ (E/V)]
WACC = [0.07 ´ (1  .35) ´ (0.4)] + [0.14 ´ 0.6] = 0.1022 = 10.22%
Using this discount rate:
_{}
The issue costs are:
Stock issue: 
(0.050 ´ $1,000,000) = $50,000 
Bond issue: 
(0.015 ´ $1,000,000) = $15,000 
Debt is clearly less expensive. Project NPV net of issue costs is reduced to:
($272,016  $15,000) = $257,016. However, if debt is used, the firm’s debt ratio will be above the target ratio, and more equity will have to be raised later. If debt financing can be obtained using retaining earnings, then there are no other issue costs to consider. If stock will be issued to regain the target debt ratio, an additional issue cost is incurred.
A careful estimate of the issue costs attributable to this project would require a comparison of Bunsen’s financial plan ‘with’ as compared to ‘without’ this project.
14. From the text, Section 19.6, footnote 29, solving for b_{A}, we find that:
_{}
_{}
_{}
Using the Security Market Line, we calculate the opportunity cost of capital for Sphagnum’s assets:
r_{A} = r_{f} + b_{A} (r_{m} – r_{f}) = 0.09 + (0.6738 ´ 0.085) = 0.147 = 14.7%
Following MM’s original analysis and considering only corporate taxes, we have:
r* = r (1 – T_{C} L)
r* = 0.147 ´ [1 – (0.35 ´ 0.55)] = 0.1187 or approximately 12%
This matches the consultant’s estimate for the weightedaverage cost of capital.
15. Disagree. The Banker’s Tryst calculations are based on the assumption that the cost of debt will remain constant, and that the cost of equity capital will not change even though the firm’s financial structure has changed. The former assumption is appropriate while the latter is not.
16. Tax or financing side effects in international projects:
§ Project financing issues, such as early cash flows going to debt service resulting in a nonconstant debt ratio.
§ Subsidized financing rates.
§ Guaranteed contracts for output.
§ Government restrictions on the flow of funds.
17. a.
Year 
Principal at Start of Year 
Principal Repayment 
Interest 
Interest Less Tax 
Net Cash Flow On Loan 
1 
5000.0 
397.5 
250.0 
162.5 
560.0 
2 
4602.5 
417.4 
230.1 
149.6 
567.0 
3 
4185.1 
438.2 
209.3 
136.0 
574.2 
4 
3746.9 
460.2 
187.3 
121.7 
581.9 
5 
3286.7 
483.2 
164.3 
106.8 
590.0 
6 
2803.5 
507.3 
140.2 
91.1 
598.4 
7 
2296.2 
532.7 
114.8 
74.6 
607.3 
8 
1763.5 
559.3 
88.2 
57.3 
616.6 
9 
1204.2 
587.3 
60.2 
39.1 
626.4 
10 
616.9 
616.9 
30.8 
20.0 
636.9 
Therefore:
_{}
Value of subsidy = $5,000,000  $4,530,000 = $470,000
b. Yes. The value of the subsidy measures the additional value to the firm from a government loan at 5 percent, compared to an unsubsidized loan at 10 percent. Therefore, the company should calculate APV, including
PV (tax shields) on the unsubsidized loan, and then add in the value of subsidy.
18. a. Assume that the expected future Treasurybill rate is equal to the 20year Treasury bond rate (5.8%) less the average historical premium of Treasury bonds over Treasury bills (1.8%), so that the riskfree rate (r_{f}) is 4%. Also assume that the market risk premium (r_{m} – r_{f}) is 8%. Then, using the CAPM, we find r_{E} as follows:
r_{E} = r_{f} + b_{A} ´ [r_{m}  r_{f}] = 4% + (0.66 ´ 8%) = 9.28%
Market value of equity (E) is equal to: 256.2 ´ $59 = $15,115.8 so that:
V = $6,268 + $15,115.8 = $21,383.8
D/V = $6,268/$21,383.8 = 0.293
E/V = $15,115.8/$21,383.8 = 0.707
WACC = (0.707 ´ 9.28%) + (0.293 ´ 0.65 ´ 7.4%) = 7.97%
b. Step 1. Calculate the opportunity cost of capital.
Opportunity cost of capital = r = r_{D} ´ (D/V) + r_{E} ´ (E/V)
= 7.4% ´ 0.293 + 9.28% ´ 0.707 = 8.73%
Step 2. Estimate the cost of debt and calculate the new cost of equity.
Assume that the interest rate on the debt falls to 7.2% so that:
r_{E} = r + (r  r_{D}) ´ (D/E) = 8.73% + (8.73%  7.2%) ´ (0.25/0.75) = 9.25%
Step 3. Recalculate WACC.
WACC = (0.75 ´ 9.25%) + (0.25 ´ 0.65 ´ 7.2%) = 8.11%
19. The company weightedaverage cost of capital is appropriate for evaluating capital budgeting projects that are exact replicas of the firm as it currently exists. If the project in question is more like the industry as a whole than it is like the company, then the industry weightedaverage cost of capital would be a better choice.
Challenge Questions
1. a. For a oneperiod project to have zero APV:
Rearranging gives:
For a oneperiod project, the lefthand side of this equation is the project IRR. Also, (D/ C_{0}) is the project’s debt capacity. Therefore, the minimum acceptable return is:
b. For a company that follows Financing Rule 2, all of the variables in the MilesEzzell formula are constant. For example, we know that debt is assumed to be a constant proportion of market value, so that the adjusted cost of capital (r^{*}) is also constant over time. In other words, when we are at period 1, the MilesEzzell formula gives the same value for r^{*} as at period 0. We know from part (a) that the formula is correct for a oneperiod cash flow. So the value, in period 1, of the period 2 cash flow is:
PV_{1} = C_{2}/(1 + r ^{* })
The value today is:
PV_{0} = PV_{1}/(1 + r ^{* }) = C_{2}/(1 + r ^{* })^{2}
By analogy, we would discount the period 3 cash flow, at r^{*}, in period 2 to give:
PV_{2} = C_{3}/(1 + r ^{* })
Therefore, the value today is:
PV_{0} = C_{3}/(1 + r ^{* })^{3}
2.
D/V 
E/V 
D/E 
r 
r_{d} 
r_{E} 
WACC 
ME 

0.20 
0.80 
0.250 
12.00% 
8.00% 
13.00% 
11.44% 
11.42% 

0.40 
0.60 
0.667 
12.00% 
8.00% 
14.67% 
10.88% 
10.84% 

0.60 
0.40 
1.500 
12.00% 
10.00% 
15.00% 
9.90% 
9.86% 

T* = T_{C} = 0.35 








Different values result because the MilesEzzell formula assumes debt is rebalanced at the end of every period (Financing Rule 2).
3. The expected cash flow from the firm is: (V_{u }r + T_{c }r_{D }D) where r is the return on assets and r_{D} is the rate on debt (the interest tax shield has the same level of risk). The cash flow to the stockholders and bondholders is:
Er* + Dr_{D}
Because the firm generates a perpetual cash flow stream:
Er* + Dr_{D} = V_{u}r + T_{c }r_{D }D
Divide by E and subtract Dr_{D}:
Substitute L = D/E
We know that: V_{u} = E + (1  T_{c})D:
a. Whenever r > r_{D}, r* increases with leverage.
b. The formulas for levering and relevering the cost of equity implicitly assume ongoing corporate profitability so that the interest tax shields can be exploited.
4. This is not necessarily true. Note that, when the debt is rebalanced, next year’s interest tax shields are fixed and, thus, discounted at a lower rate. The following year’s interest is not known with certainty for one year and, hence, is discounted for one year at the higher risky rate and for one year at the lower rate. This is much more realistic since it recognizes the uncertainty of future events.