Question

Photochronograph Corporation (PC) manufactures time series photographic equipment. It is currently at its target debt−equity ratio of .80. It’s considering building a new $50 million manufacturing facility. This new plant is expected to generate aftertax cash flows of $6.2 million in perpetuity. The company raises all equity from outside financing. There are three financing options: 1. A new issue of common stock: The flotation costs of the new common stock would be 8 percent of the amount raised. The required return on the company’s new equity is 14 percent. 2. A new issue of 20-year bonds: The flotation costs of the new bonds would be 4 percent of the proceeds. If the company issues these new bonds at an annual coupon rate of 8 percent, they will sell at par. 3. Increased use of accounts payable financing: Because this financing is part of the company’s ongoing daily business, it has no flotation costs, and the company assigns it a cost that is the same as the overall firm WACC. Management has a target ratio of accounts payable to long-term debt of .15. (Assume there is no difference between the pretax and aftertax accounts payable cost.) What is the NPV of the new plant? Assume that PC has a 35 percent tax rate. (Enter your answer in dollars, not millions of dollars, i.e. 1,234,567. Do not round intermediate calculations and round your final answer to the nearest whole dollar amount.)

Answer 1

We can use the debt-equity ratio to calculate the weights of equity and debt. The debt of the company has a weight for long-term debt and a weight for accounts payable. We can use the weight given for accounts payable to calculate the weight of accounts payable and the weight of long-term debt. The weight of each will be:

Accounts payable weight = 0.15/(1+0.15) = 0.13

Long term debt weight = 1-0.13 = 0.87

Since the accounts payable has the same cost as the overall WACC, we can write the equation for the WACC as:

RWACC = (1 / 1.80)(.14) + (.80 / 1.80)[(.15 / 1.15)WACC + (1 / 1.15)(.080)(1 – .35)]

Solving for WACC, we find:

RWACC = .0778 + .4444[(.15 / 1.15)RWACC + .0452]

RWACC = .0778 + .05797RWACC + .0201

.9420RWACC = .0979

RWACC = .1039, or 10.39%

We will use basically the same equation to calculate the weighted average flotation cost, except we will use the flotation cost for each form of financing. Doing so, we get:

Flotation costs = (1/1.80)*0.08 + (0.8/1.8)[(0.15/1.15)(0)+(1/1.15)(0.04)] = 5.99%

The total amount we need to raise to fund the new equipment will be: $50,000,000/(1-5.99%) = $53,186,022.61

Since the cash flows go to perpetuity, we can calculate the present value using the equation for the PV of a perpetuity. The NPV is:

NPV = -$53,186,022.61+($6,200,000/0.1039)

= $6,486,739.66 or $6,486,740 (rounded off to nearest whole dollar).