Capital Formation – Only Problem Set 7

Ramapo College of New Jersey

Anisfield School of Business

Capital Formation Spring 2021

Finance 406-02

Capital Structure Theory with

corporate and personal taxes

Round 1

Problem Set 7

16. Assume that all of the facts from the prior problem set hold, except that both

corporate and personal income taxes apply. Assume as in Problem Set 6 that both

firms face a corporate income tax rate (T) of 30%; however, also assume that:

(1) investors of both firms face a marginal personal tax rate on debt income (TPD)

of 35% and a marginal personal tax rate on stock income (TPS) of 25%;

(2) the firms must put all after- tax equity and debt cash flows out to bid by

investors in order to determine their market values;

(3) firm U will put a $10,000 before-tax cash flow to bid, and firm L will put a

before-tax $7,000 equity cash flow and a $3,000 before-tax debt cash

flow to bid;

(3) the equilibrium required rate of return on equity (ke*) for firm U is 15% and

for firm L is 19.091%, and that these rates are the appropriate equity

capitalization rates to use on equity earnings after corporate and personal

income taxes are paid (or the rate that equity investors will use to determine EU

and EL);

(4) the equilibrium required rate of return on debt for firm L (ki*) is 10%, and that

this is the rate that debt investors will use to determine the market value

of the debt after personal taxes are paid;

a. What is the value of the unlevered firm?

b. What is the value of the levered firm?

c. What is the gain from leverage in this situation? (Hint: this can be determined by

VL – VU)

d. Use the Miller model as well as the market value of the debt you calculated in (b) to

determine the present value of the debt tax shield and to check your answer in (c).

e. What if the marginal tax rate on stock income and the marginal tax rate on debt

income are both equal to 35% (TPS = TPD = 35%). Now, what are the values of the

unlevered firm, the levered firm and the gain from leverage?

f. Use the Miller model as well as the market value of the debt you calculated in (b) to

determine the present value of the debt tax shield and to check your answer in (e).

RamapoCollege of New Jersey

Anisfield School of Business

Capital Formation Spring 2021

Finance 406

Capital Structure and MM Arbitrage Round 1

Problem Set 6

Two firms have expected annual net operating income of $10,000 in perpetuity with

identical operating conditions and business risk. Both firms are no-growth firms that pay

out all earnings in common dividends. One firm is considering issuing $30,000 of long-

term debt at a 10% interest rate. Assume perfect capital markets and, for now, no taxes.

Also assume that all investors can borrow at 10%. If investors are capitalizing the

unlevered firm’s common dividends at 15% and the levered firm’s common dividends at

16%:

1. What is the value of the unlevered firm?
2. What is the value of the levered firm’s equity?
3. What is the WACC for the unlevered firm?
4. What is the WACC for the levered firm?
5. What is the debt-to-equity ratio for the levered firm?
6. If you hold 1% of the stock of the levered firm, how can you capture higher

returns through the use of homemade leverage?

7. What is the return-on-invested funds (ROI) using arbitrage? Take your answer
out to at least five decimal places.

8. In theory, how will investors respond once they realize the returns through
arbitrage?

9. Assuming that all adjustments occur to the levered firm’s stock, what is the
(i) equilibrium equity capitalization rate, (ii) equilibrium equity value and (iii)

equilibrium debt-equity ratio for the levered firm?

10. Use the equilibrium debt-equity ratio of the levered firm from (9) along with MM

proposition II (equation 9-6 in VH9) to check that the equilibrium cost of equity

for the levered firm that you calculated in (9).

Now assume a corporate tax rate of 30%. Also assume that investors are capitalizing the

unlevered firm’s common dividends at the equilibrium rate of 15% and are investors are

capitalizing the levered firm’s common dividends at the equilibrium rate obtained in (9).

11. Calculate EACS for the unlevered and levered firms

12. How much total after-tax income can each firm generate?

13. Using equation 9-2 from VH9, what is the gain from financial leverage?

14. What is the value of firm U (VU)? What is the value of firm L (VL)?

15. What is VL – VU? Does this match your answer in (13)?