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?