COMM 371 – THEORY OF FINANCE
This assignment is to be solved in groups, and these groups are the same conformed
groups you used for the first case (and will use for the last case). You cannot switch
groups, or submit individual answers.
You should submit only one answer per group.
You do not need to type the answers. However, you should submit one clean and legible
copy written in ink (we will not accept pencil writing).
Be precise in your answers. Carefully explain and should all details of your work.
The assignment is due the last day of classes (Wednesday, April 6), at the beginning of
We will post solutions on the website that same day.
We will take any time we need to grade this assignment carefully, and do not
compromise to return it before the final exam.
Thus, you MUST keep one copy of your work, so that you can start checking your
answers right away by comparing your solutions with the solutions on the web.
Question 1 (30 points) General Motors (GM) is considering the construction of a new
plant in Minnesota. Construction costs are expected to be $2 million, and can be
amortized straight line during the first 10 years. The plant will generate EBIT of
$100,000 for years 1-3, $150,000 for years 4-10, in years 11-20 it would grow at 7%, but
in years 21 and after growth slows down to 5% forever. GM’s marginal tax rate is 40%.
The firm can raise $1.5 million in debt, consisting of $1 million (before flotation costs)
with a 10-year bond at 12%, and $500 thousands with a 10-year government-sponsored
bond at 7% that will be risk-free. Both bonds have annual interest payments and principal
repayable in the last year. Flotation costs for the first bond are 1% of the amount raised,
and can be amortized straight line over the life of the bond (GM still has to pay interest
on the full amount raised). The government absorbs the flotation costs of the second bond.
Interest from both bonds is tax-deductible.
After the debt issue Moody’s will likely downgrade GM’s debt from Aaa to Baa due to GM’s increase in financial leverage. A study of default on debt payments shows that 5%
of firms with ratings Aaa and 10% of firms with rating Baa default on their interest
payments and enter financial distress. Industry specialists estimate that a typical firm in
the auto industry suffers permanent loses equivalent to about 15% of its value during
Then 10-year Treasury Bonds rate is 10%. GM has an equity beta of .9, and its book debt
represents 45% of firm value. The average return on the value-weighted market index
during the last 20 years is 16%. Currently, GM’s combined market value of debt and
equity is $30 million.
Should GM build the new plant? Carefully explain and show your work!
1. Calculate GM's unlevered cost of capital (Ro)
Tax rate 0.4 Rf 0.1 GM's (levered) equity beta 0.9 GM's B/(B+S) 0.45 Rm 0.16
At GM, B/(B+S) = .45, B/S=? If B=1, then S = 1.222 So B/S = 0.818
GM's Unlev. beta = levered beta / [1+(B/S)(1-t)] 0.604
Using CAPM, Ro = Rf + unl beta[Rm - Rf] = 0.136
2. Compute the new plant's UCFs (remaining years in following page)
Year 0 1 2 3 4 5 6 7 8 9 10
EBIT 100,000 100,000 100,000 150,000 150,000 150,000 150,000 150,000 150,000 150,000
Taxes 40,000 40,000 40,000 60,000 60,000 60,000 60,000 60,000 60,000 60,000
(1-t) x EBIT 60,000 60,000 60,000 90,000 90,000 90,000 90,000 90,000 90,000 90,000
TV as of year 20 (uses Ro)
Depreciation 200,000 200,000 200,000 200,000 200,000 200,000 200,000 200,000 200,000 200,000
Initial Investment -2,000,000
UCFs for years 1-20 (including TV in year 20) -2,000,000 260,000 260,000 260,000 290,000 290,000 290,000 290,000 290,000 290,000 290,000
3. Compute all-equity value (remaining years in following page)
All-equity discount factor 1/1.000 1/1.136 1/1.291 1/1.467 1/1.667 1/1.894 1/2.152 1/2.445 1/2.778 1/3.156 1/3.586
UCFs as of year 0 -2,000,000 228,829 201,395 177,250 174,000 153,139 134,780 118,621 104,400 91,884 80,868
2. Compute the new plant's UCFs (cont.)
Year 11 12 13 14 15 16 17 18 19 20
EBIT 160,500 171,735 183,756 196,619 210,383 225,110 240,867 257,728 275,769 295,073
Taxes 64,200 68,694 73,503 78,648 84,153 90,044 96,347 103,091 110,308 118,029
(1-t) x EBIT 96,300 103,041 110,254 117,972 126,230 135,066 144,520 154,637 165,461 177,044
TV as of year 20 (uses Ro) 2,156,076
UCFs for years 1-20 (including TV in year 20) 96,300 103,041 110,254 117,972 126,230 135,066 144,520 154,637 165,461 2,333,119
3. Compute all-equity value (cont.)
All-equity discount factor 1/4.075 1/4.630 1/5.260 1/5.977 1/6.791 1/7.716 1/8.767 1/9.961 1/11.318 1/12.860
UCFs as of year 0 23,634 22,257 20,960 19,738 18,588 17,504 16,484 15,524 14,619 181,423
4. Compute financing side effects (NPVF)
4.1 Compute NPVF of regular financing
4.1.a Compute NPV (flotation costs)
Rb = .12, maturity 10 years, amount $1M
Flotation cost = 1% of $1M = 10,000 Annuity Factor: A(10 yrs, 12%) = 5.65 NPV (FC) = -10,000 + (10,000/10)x.4 x A(10 yrs,12%) -7,740
4.1.b Compute NPV (regular debt)
NPV (RD) =
$1M -.12x$1Mx.6xA(10 yrs, 12%) - $1M/(1.12
NPVF of regular financing = 263,471
4.2 Compute NPVF of govt. sponsored debt
Rb = .07, maturity 10 years, amount $500,000
Flotation costs absorbed by government
Annuity Factor: A(10 yrs, 10%) = 6.14
500K - .07x500Kx.6xA(10 yrs, 10%) - 500K(1.1010) 178,192
4.3 Compute the effect of financial distress costs
% of Aaa rated firms that become distressed: 5%
% of Baa rated firms that become distressed: 10%
Increase in the proability of financial distress: 5%
Cost of financial distress 15% of firm value
GM's market value: $30M
NPV(FDC) = -.05x.15x$30M = -225,000
Total NPVF 216,663
Net APV 32,560
Question 2 (20 points). General Motors (GM) is evaluating the acquisition of Hughes
Aircraft Corporation (HAC). Next year’s projected income statement for HAC is given
Taxable income 350
Taxes @ 30% 105
Net Income 245
In addition, HAC’s unlevered cash flow is expected to grow 5% per year forever, and the firm will not make any capital expenditures or additions to net working capital in the
future. HAC’s marginal tax rate is 30%. HAC has very little debt in its capital structure.
However, GM will impose a target debt-to-equity ratio of one for HAC after the
acquisition. Management believes that HAC has business risk similar to two firms in the
industry: Lockheed, with a debt-to-equity ratio of 0.9 and equity beta of 0.90, and
Northrop, with a debt-to-equity ratio of 0.7 and equity beta of 0.85. Both of these
companies have the same marginal tax rate as HAC. HAC’s cost of debt is 10% per year,
and it will not be affected by the acquisition. The risk free rate is 8% and the expected
return on the market is 14%. GM’s has a debt-to-equity ratio of 0.4 and its WACC is 12%.
a) What is the value of HAC? Carefully show and explain all steps of your work.
b) Suppose that management decided to use GM’s WACC to value HAC. What is the
estimate of HAC’s value? Under what circumstances would this be a correct way to value the target? Carefully show your work and explain your answer.
c) Suppose now that Lockheed and Northrop have “P/E ratios” (Price per share/ Earnings
per share) of 25 and 30, respectively. How would you obtain a quick (but rough) estimate
of HAC’s value? Carefully show your work and explain your answer.
a) i) Compute HAC’s UCFs in next year using the projected income statement provided.
UCF = EBIT + D – Taxes = (1-.30) EBIT + Depreciation = 0.7 x 450 + 50 = $365M
ii) Compute HAC’s WACC = [E / (E+D)] x R + [D / (D+E)] x R x (1-t) EHACDHAC
Recall that HAC’s cost of debt is 10%. We can use the CAPM to obtain HAC’s cost of
equity, R = R + ? x [E(R) - R]. But we need to estimate ?. Compute the EHACFHACMFHAC
all-equity betas of the two comparison companies using the levered betas provided.
? = ? x [1+(D/E)(1-t)] or ? = ? / [1+(D/E)(1-t)] EAAE
? = 0.9 / [1+ 0.9 x 0.7)] = 0.552 & ? = 0.85 / [1+ 0.7 x 0.7] = 0.571 ALockANorth
Estimate the beta of HAC’s unlevered assets by taking the average of the unlevered betas
of the two comparison companies: ? = (0.552 + 0.571) / 2 = 0.562 AHAC
Estimate the levered equity beta for HAC, levering the previous average up to the capital
structure that will be imposed on HAC: ? = 0.562 x [1 + 1 x 0.7] = 0.955 EHAC
Into the CAPM gives: R = 8% + 0.955 x [14% - 8%] = 13.73% EHAC
Thus, WACC = 0.5 x 13.73% + 0.5 x 10% x (1 - 0.3) = 10.365% HAC
iii) Compute HAC’s value: V = $365M / (10.365% - 5%) = $6803.4M HAC
b) If we use GM’s WACC to discount the target’s cash flows we get
V = $365M / (12% - 5%) = $5214.3M HAC
This is generally incorrect. It would only work if GM and HAC had the same capital
structure (or GM would impose its own capital structure on HAC), both firms had exactly
the same business risk, and could borrow at the same terms. All these things are unlikely
to be satisfied here, as aircraft and automobile production have quite different business
risk, the firms have different capital structures, and probably borrow at different rates.
c) Take an average P/E ratio of 27.5. Then equityNIequity????/??27.5 ????#shares#sharesNI????
Thus, using our forecasted earning for next year, we can estimate HAC’s value:
V = 27.5 x 245 = $6737.5M. This “multiples” method is popular among practitioners.HAC
Question 3 (20 points)
Part A. Your consulting firm has recently been awarded a grant from the government of
Canada for past work that demonstrated the competitiveness of Canadian industry. The
amount of the grant is $50,000 per year for three years, with the first payment arriving
one year from today, and the grant is not taxable. The borrowing rate is 7% for either
the government or your firm, your firm’s unlevered cost of equity is 12%, and the tax rate
You are in the process of calculating the present value of the grant, and get into an
argument with a colleague about whether it is more appropriate to use a pre-tax discount
rate or an after tax discount rate.
a) Calculate the value of the cash flows using the after-tax and pre-tax discount rates.
b) Carefully explain why the results are different.
c) Explain under what circumstances, each calculation would provide a good estimate of
the true value of the cash flows.
d) Carefully show how you would take advantage of changes in debt capacity.
With pre-tax disc. rate, PV=
With after-tax disc. rate, PV== 50,000 * 2.7646 = $138,229.5 50,000*A(3yrs,0.6x7%)
It would be appropriate to use the pre-tax discount rate if the firm does not plan to adjust
its borrowing to reflect its increased debt capacity. Even in this case, the firm will still
reap some additional gains from reduced costs of financial distress. Thus, the true benefit
would be higher than $131,215.8.
It would be appropriate to use the after-tax discount rate if the firm plans to adjust its
borrowing to reflect its increased debt capacity. In order for this calculation to be correct,
the firm must borrow $138,229.5, and use the cash flows from the grant to exactly pay
this off over three years. Specifically, we would have to adjust borrowing as follows:
Interest Tax A-T Reduction in
Year CF gained Beg. Bal paid shield Pmt Borrowing
1 50000.0 138229.5 9676.1 3870.4 5805.6 44194.4
2 50000.0 94035.2 6582.5 2633.0 3949.5 46050.5
3 50000.0 47984.6 3358.9 1343.6 2015.4 47984.6
Then, the PV(tax shields) at 7% = $7,014, the difference in PV between the values of the
grant using pre-tax and after-tax discount rates. Note that we have a temporary increase
in debt capacity because the grant is only for 3 years, and so we temporarily increase our
Part B. Your firm is now hit with a judgment by Revenue Canada. They determine that
you owe back taxes, and you will be required to make annual payments of $50,000 per
year for three years, starting one year from today. The judgment will not reduce your
taxable income, therefore it must be paid for from your firm’s after-tax cash flow.
You have the same argument with your colleague about whether it is appropriate to use a
pre-tax or after-tax discount rate. Answer the same questions from Par A, under these
W/ pre-tax disc. rate, PV=
W/ aft-tax disc. rate, PV== 50,000 * 2.7646 = $ -138,229.5 ?50,000*A(3yrs,0.6x7%)
It would be appropriate to use the pre-tax discount rate if the firm does not plan to reduce
its borrowing to reflect its decreased debt capacity. Even in this case, the firm will still
suffer some additional losses from increased costs of financial distress. Thus, the true
cost would be higher than $131,215.8.
It would be appropriate to use the after-tax discount rate if the firm plans to reduce its
borrowing to reflect its decreased debt capacity. In order for this calculation to be correct,
the firm must reduce its borrowing by $138,229.5, equivalent to the amount of debt that
the cash flow lost would have supported. Specifically, we would have to reduce
borrowing as follows:
Beginning Interest Tax shield A-T Pmt Increase in
Year CF lost Balance Saved lost Saved Borrowing
1 50000.0 -138229.5 9676.1 3870.4 5805.6 44194.4
2 50000.0 -94035.2 6582.5 2633.0 3949.5 46050.5
3 50000.0 -47984.6 3358.9 1343.6 2015.4 47984.6
Then, the PV(tax shields lost) at 7% = $7,013.7, the difference in PV between the values
of the grant using pre-tax and after-tax discount rates.
Note that in the first year, you reduce your borrowing by 138,229.5, so you save interest
(both pre and after tax) on that amount at the same time that you lose tax shields. After
taxes you save 5,805.6 in interest, but your CF decreases by 50,000, so you now need to
increase your borrowing to cover the difference 50,000-5,805.6 = 44,194.4. Thus, for the
beginning of year two, the balance is less negative: -138,229.5+44,194.4 = -94,035.2. In
year two, you save 3,949.5 after taxes and your CF is -50,0000, so you increase your
borrowing to cover the difference 50,000 – 3,949.5 = 46,050.5. Thus, for the beginning of
year 3, the balance is less negative: -94,035.2+46,050.5 = -47,984.6. At the end of year 3
you increase your borrowing by that same amount, and so starting in year 4 your
borrowing goes back to its original level (balance =0). Note that here you temporarily
reduce your borrowing, because you have a temporary reduction in debt capacity.
Question 4 (15 points). Air Canada has decided to begin the construction of a new
hangar for its recently acquired airplanes that will cost $10 million. The firm has no cash
available to fund the project, so it needs to raise the full amount, and faces a marginal tax
rate of 30%. AC’s management can choose among different financing alternatives. First,
the firm could finance all the cost with an equity issue. Second, the firm could issue a 5
year bond with a bullet maturity structure at an interest rate of 5% per year. Third, the
firm could issue a 4 year bond with an amortizing maturity structure and level payments
at an interest rate of 3% per year. Which financing strategy should AC choose? Carefully explain why and show your all details of your work. Note that detailed calculations for
each financing option are required here. For simplicity, assume that the firm will not
optimally adjust its borrowing due to changes in its debt capacity. Use two decimal places.
The all-equity financing does not generate tax shields, so NPVF = 0
5 year bond with bullet structure at 5% per year
Year interest principal payment tax shield
1 0.5 0.5 0.15
2 0.5 0.5 0.15
3 0.5 0.5 0.15
4 0.5 0.5 0.15
5 0.5 10 10.5 0.15
PV at 5% 10.0 0.65
So NPVF = $0.65M = $10M x .05 x .3 x [1-1/(1.05)
5]/.05 (simplest way to calculate)
4 year bond with amortizing structure at 3% per year
beg. end total tax
Year Balance interest principal balance payment shield
1 10.00 0.30 2.39 7.61 2.69 0.09
2 7.61 0.23 2.46 5.15 2.69 0.07
3 5.15 0.15 2.54 2.61 2.69 0.05
4 2.61 0.08 2.61 0.00 2.69 0.02
PV at 3% 10.0 0.22
The level payment solves: LP x [1-1/(1.03)4]/0.03 = 10 , so LP = 2.69
So NPVF = $0.22M
So AC should use the bullet loan!