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).