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Capital structure, taxes and firm value Firm M will operate from time 0 to time

ID: 2722589 • Letter: C

Question

Capital structure, taxes and firm value

Firm M will operate from time 0 to time 1, then shut down. At time 1, its EBIT will be 250. The tax rate on firm profits is 20%. The cost of capital is 25% for all cash flows regardless of risk.

a. First, assume that the firm is all equity financed. What is the firm value at time 0?

b. Next, assume that the firm repurchases 100 worth of stock. To finance this deal, the firm borrows 100 at time 0 and promises to pay back principal plus interest at time 1. The interest rate is equal to the required cost of capital. What is the total payoff (principal + interest) to the debt holders at time 1?

c. What is the payoff to the equity holders at time 1? What is the value of equity at time 0?

d. What is the present value of the tax shield of debt? Why is it not equal to the amount of debt times the tax rate as usual?

Explanation / Answer

a) firm value at time 0=250*(1-20%)/(1+25%)=250*(1-0.20)/(1+0.25)=250*0.80/1.25=200/1.25=160

b) value of equity=160-100=60(after repurchase)

value of debt=100

cost of capital=(60/160)*25%+(100/160)*interest rate of debt*(1-20%) (cost of capital initially 25% was cost of equity only,as all was equity financed)

cost of capital=(60/160)*25%+(100/160)*cost of capital*(1-20%) (as the interest rate =cost of capital given)

cost of capital=(15/160)+(80/160)*cost of capital

=> cost of capital=(15/160)+0.50*cost of capital

=> cost of capital-0.50*cost of capital=(15/160)+0.50*cost of capital-0.50*cost of capital

=>0.50*cost of capital= (15/160)

=>cost of capital=(15/160)*2=30/160=18.75%=interest rate of debt

total payoff (principal + interest) to the debt holders at time 1

=100+100*interest rate of debt

=100+100*18.75%

=100+18.75

=118.75

c)payoff to the equity holders at time 1

=250*(1-20%) - 118.75

=200 - 118.75

=82.25

value of equity at time 0=82.25/1.25=65.80

d) value of firm levered(debt)=value of equity at time 0+100=65.80+100=165.80

value of unlevered firm(w/o debt)=160

present value of the tax shield of debt=value of firm levered(debt)-value of unlevered firm(w/o debt)

present value of the tax shield of debt=165.80-160=5.80

its not equal to 100*0.20=20 because value of equity is affected by the payoff to debt holders.

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