Question

# Wilma is considering opening a widget factory. The unlevered cost of equity for making widgets is...

Wilma is considering opening a widget factory. The unlevered cost of equity for making widgets is 0.13. This factory would cost \$27 million to set up, and would produce EBIT of \$3 million per year for the foreseeable future. She is thinking of applying for a \$3 million subsidized perpetual loan to finance this project. Complying with the auditing requirements of this loan would have a present value of \$2 million. This loan would have a rate of 0.04, while the rate she could get from the bank is 0.08. Her tax rate is 0.42. What is the NPV of this project, using the APV method? Answer should be -13,485,385, how do you get there?

Present value using apv = value of unlevered company + present value of interest tax shields

Value of unlvered company = cash flows each year till per perpetuity / cost of equity

Cash flow eac year = EBIT * ( 1 - Tax rate )

= 3 * ( 1 - 0.42)

= \$1.74 million

Value of unlvered company = 1.74 / 0.13 * 1000000 = \$13384615.38

Interest = value of loan * interest rate = 2 * 0.04 = 0.08

Interest tax shield = interest * tax rate = 0.08* 0.42 = 0.0336

Present value of interest tax shield = Interest tax shield / rate on similar loans

= 0.0336 / 0.08 * 1000000

= 420000

Present value using APV = 13384615.38 + 420000 = 13804615.38

NPV = Present value using APV - cash outflow

= 27000000 - 13804615.38

= \$ 13,195,385

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