Question

In year​ 1, AMC will earn

​$2,700

before interest and taxes. The market expects these earnings to grow at a rate of

3.1%

per year. The firm will make no net investments​ (i.e., capital expenditures will equal​ depreciation) or changes to net working capital. Assume that the corporate tax rate equals

35​%.

Right​ now, the firm has

​$6,750

in​ risk-free debt. It plans to keep a constant ratio of debt to equity every​ year, so that on average the debt will also grow by

3.1​%

per year. Suppose the​ risk-free rate equals

5.17​%,

and the expected return on the market equals

11.37​%.

The asset beta for this industry is

1.84.

a. If AMC were an​ all-equity (unlevered)​ firm, what would its market value​ be?

b. Assuming the debt is fairly​ priced, what is the amount of interest AMC will pay next​ year? If​ AMC's debt is expected to grow by

3.1​%

per​ year, at what rate are its interest payments expected to​ grow?

c. Even though​ AMC's debt is riskless​ (the firm will not​ default), the future growth of​ AMC's debt is​ uncertain, so the exact amount of the future interest payments is risky. Assuming the future interest payments have the same beta as​ AMC's assets, what is the present value of​ AMC's interest tax​ shield?

d. Using the APV​ method, what is​ AMC's total market​ value,

VL​?

What is the market value of​ AMC's equity?

e. What is​ AMC's WACC?

​(Hint​:

Work backward from the FCF and

VL​.)

f. Using the​ WACC, what is the expected return for AMC​ equity?

g. Show that the following holds for​ AMC:

βA=ED+EβE+DD+EβD.

                                                    

h. Assuming that the proceeds from any increases in debt are paid out to equity​ holders, what cash flows do the equity holders expect to receive in one​ year? At what rate are those cash flows expected to​ grow? Use that information plus your answer to part

​(f​)

to derive the market value of equity using the FTE method.

Answer 1

Since, the question has multiple parts, I have answered the first four parts.

_____

Part a)

The market value​, If AMC were an​ all-equity (unlevered)​ firm is calculated as below:

Market Value = Unlevered Free Cash Flow/(Unlevered Cost of Capital - Growth Rate)

Here, Unlevered Free Cash Flow = EBIT*(1-Tax Rate) = 2,700*(1-35%) = $1,755, Unlevered Cost of Capital = Risk Free Rate + Beta*(Expected Return on the Market - Risk Free Rate) = 5.17​% + 1.84*(11.37​% - 5.17%) = 16.578% and Growth Rate = 3.1%

Using these values in the above formula, we get,

Market Value = 1,755/(16.578%-3.1%) = $13,021.22 or $13021 (if rounded off to zero decimal places)

_____

Part b)

The amount of interest AMC will pay next​ year is arrived as below:

Amount of Interest Payment = Value of Debt*Interest Rate = 6,750*5.17% = $348.98 or $349 (if rounded off to zero decimal places) [we take risk-free rate as the interest rate because debt is risk free]

If​ AMC's debt is expected to grow by 3.1% per year, the interest payments would also grow by the same rate of 3.1%. The same is demonstarted with the use of following calculations:

Year	Value of Debt (A)	Interest Rate (B)	Interest Payment (A*B)
1	6750.00	5.17%	348.98
2	6959.25	5.17%	359.79
3	7174.99	5.17%	370.95
4	7397.41	5.17%	382.45

Interest Payment Growth Rate (Year 2) = (Year 2 Interest Payment - Year 1 Interest Payment)/Year 1 Interest Payment)*100 = (359.79 - 348.98)/348.98*100 = 3.1%

Interest Payment Growth Rate (Year 3) = (Year 3 Interest Payment - Year 2 Interest Payment)/Year 2 Interest Payment)*100 = (370.95 - 359.79)/359.79*100 = 3.1%

Interest Payment Growth Rate (Year 4) = (Year 4 Interest Payment - Year 3 Interest Payment)/Year 3 Interest Payment)*100 = (382.45 - 370.95)/370.95*100 = 3.1%

_____

Part c)

The present value of AMC's interest tax shields is determined as follows:

Present Value of Interest Tax Shields = After-Tax Interest Payment/(Discount Rate - Growth Rate)

Herem After-Tax Interest Payment = Interest Payment*(Tax Rate) = 348.98*35% = $122.14 [as future growth of AMC's debt is uncertain, the interest tax shield is also uncertain], Discount Rate = 16.578% (as future interest payments have the same beta as​ AMC's assets) and Growth Rate = 3.1%

Using these values in the above formula, we get,

Present Value of Interest Tax Shields = 122.14/(16.578%-3.1%) = $906.23 or $906 (if rounded off to zero decimal places)

_____

Part d)

The AMC's total market​ value with the use of APV method and market value of equity is calculated as below:

Total Market Value (APV Method) = Market Value of Unlevered Firm + Present Value of Interest Tax Shields = 13,021.22 + 906.23 = $13,927.45 or $13,927 (if rounded off to zero decimal places)

Market Value of Equity = Total Market Value (APV Method) - Value of Debt = 13,927.45 - 6,750 = $7,177.45 or $7,177 (if rounded off to zero decimal places)