Question

Consider an all-equity project with the following characteristics:

·         Cash inflows = $18,000 per year in perpetuity

·         Cash outflows (costs) =50% of cash inflows

·         Corporate tax rate = 35%

·         Cost of capital of all-equity project = 12%

Now suppose that the management issues debt to finance a share repurchase program. The new cost of capital of the levered project is 10%. (Hint: Solve part a. first).

a) Using this information, determine the present value of the tax shield of debt.

CF in perpetuity

$ 9,000.00

b) Assuming that the debt is static, perpetual, and risk free, what is the current level of debt in the firm?

Tax Shield = Debt * Tax Rate

Answer 1

Cash Flow details:

Inflow = 18000

outflow = 50% = 50% 0f 18000 = 9000

Net inflow before tax = 18000 - 9000 = 9000

Tax rate = 35% = 35% * 9000 = 3150

Net cash flow after tax = 9000 - 3150 = 5850

Since the cash flows are in perpetuity

Present value =

Σ int ci/(1 + y)

where Ci is the annual cash flow

y is the WACC (weighted average cost of capital)

Formula for infinite GP = a/(1-r)

PV =

(1 - 1 +)

PV = C/y

(a) When the project is all equity financed

y = 12%

PV = 5850/12% = 48750

(b) When the project is financed by debt

Let the amount of debt = d

Interest cost = 10% of d = 0.1d

Inflow = 18000

outflow = 50% = 50% 0f 18000 = 9000

Net inflow before interest tax = 18000 - 9000 = 9000

Net inflow before tax = 9000 - 0.1d

Tax rate = 35%

Net cash flow after tax = 0.65*(9000 - 0.1d)

y = 10%

PV = C/y = 0.65*(9000 - 0.1d)/0.1

0.65*(9000 - 0.1d)/0.1 = 48750

d = 15000

(b) Present level of debt in company = 15000

(a) Tax benefit per year due to debt

Interest expense = 10% of debt = 10% * 15000 = 1500

tax on interest expense = 35%*1500 = 525

Present value = c/y = 525/10% = 5250