Question

1. Netphone Inc expects the following:

unlevered CF before tax =$ 1million in perpetuity from the beginning of year 3 There is no income prior to that. Ignore loss carryovers for taxes.

Tax rate is 50%, amount of debt=0

R₀ =10%

a. Find the value of Netphones today.

In the above example, netphone decides buyback some shares using 1 million dollars of perpetual debt. This is done today.

R_b =5%.

b. Find the Netphones equity value today.

                       

Answer 1

a) Unlevered Cash Flow before tax at the end of year 3= $1 million

Tax rate = 50%

Tax expense = Tax rate% * Cash Flow

Tax expense = 50%*1 million = $0.5 million

After-tax cash flows = Before-tax cash flow - Tax expense

= $1 million - $0.5 million = $0.5 million

Present value of perpetuity = Cash Flow/Required Rate

Required Rate = 10% or 0.10

Present value of perpetuity starting year 3 (at t=2) = 0.5/10% = 5 million

Value of firm at t=2 , V2 = 5 million

Current Present Value of equity = V2/(1+r)^2 = 5/(1+10%)^2

= 5/(1.1)^2 = 4.132231 million

b) Value of debt = 1 million

Rate of interest on debt = 5%

Interest expense = Value of debt * Rate of interest on debt

= 1 million * 5% = 50000

Cash flow at t=1 = Interest expense = -50000

Levered before tax cash flow at end of year 3 = Unlevered before tax cash flow – Interest expense

= 1 million – 0.05 million = 0.95 million

After tax cash flow at end of year 3 = Levered before tax cash flow at end of year 2 * (1 – tax rate)

= 0.95 million * (1 – 50%) = 0.475 million

Present value of perpetuity at year 2= After tax cash flow at end of year 2/ Required Rate

= 475000/0.10 = 4.75 million

Value of firm at t=2 = Present value of perpetuity at year 2 – Interest expense

=4.75 million – 0.05 million = 4.7 million

Present value of cash flow at t=0

= Cash flow at t=1/(1 + Required rate) + Value of firm at t=2/ (1 + Required rate)^2

= -50000/(1+0.10) + 4700000/(1+0.10)^2

= 3.84 million