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?

The net present value of this project = -7.32 million

Explanation:

Calculate the net present value of this project

Cost of equity KE = 0.13

Cost of debt KD = 0.08

Tax rate tC = 0.42

Weight of debt WD = Value of debt / Project cost

= 3 / 27

= 0.1111

Weight of Equity WE = 1 - WD

= 1 - 0.1111

= 0.8888

WACC = WE * KE + WD * KD * (1 - tC)

= 0.8888 * 0.13 + 0..1111* 0.08* (1 - 0.42)

= 0.1207

PV of cash inflow = EBIT * (1 - tC) / WACC

= 3 * (1 - 0.42) / 0.1207

= 14,415,907.2

Base case NPV = PV of cash inflow + PV on auditing - Project cost

= 14,415,907.2 + 2,000,000 - \$25,000,000

= -8,584,093

Annual Tax shield on interest on bonds:

= \$3M × 4/100) × .42

=.0504

Pesent value of Annual tax shield on interest on bonds = .0504/.04

=1.26M

Adjusted Present VAlue - Base case NPV + present value of Annual tax shield on interest on bonds

= -8,584,093 + 1,260,000

= -7,324,093

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