Photochronograph Corporation (PC) manufactures time series photographic equipmen
ID: 2726989 • Letter: P
Question
Photochronograph Corporation (PC) manufactures time series photographic equipment. It is currently at its target debtequity ratio of .8. It’s considering building a new $48 million manufacturing facility. This new plant is expected to generate aftertax cash flows of $6 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 7.8 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 5.0 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, e.g. 1,234,567. Do not round intermediate calculations and round your final answer to the nearest whole dollar amount, e.g., 32.)
Explanation / Answer
Computation of NPV of the new plant:
formula for NPV = Cash flows after tax / WACC - initial investment
here, we know the cash flows after tax i.e, $6 million = $6,000,000 and initial investment = $48 million
Now, let us compute the WACC,
formula for WACC = weight of common equity * cost of equity + weight of debt1 * after tax cost of debt1 + weight of debt2 * WACC
here, first we need to collect all the information given in question.
that means given, debt/ equity ratio = 0.8 that means, debt = 0.8equity
value of the firm = equity + debt = 1 equity +0.8equity = 1.8 is the value of the firm
Therefore, weight of common equity = 1 / 1.8 = 0.56 and cost of equity given = 14%
Now we will calculate, weight of debt1 = 1 / 1.15 * 0.8 / 1.8 = 0.87 * 0.44 = 0.3828 and
cost of after tax debt = 8%(1-35%) = 5.2%
Note:
debt1 = debt / value of the firm * debt portion / total debt (given that accounts payable to long-term debt of 0.15)
weight of debt2 = 0.15 / 1.15 * 0.8 / 1.8 = 0.13 * 0.44 = 0.0572
Therefore,
WACC = weight of common equity * cost of equity + weight of debt1 * after tax cost of debt1 + weight of debt2 * WACC
WACC = 0.56 * 14% + 0.3828 * 5.2% + 0.0572 * WACC
WACC = 0.0784 + 0.0199 + 0.0572 * WACC
WACC = 0.0983 + 0.0572 * WACC
WACC - 0.0572 * WACC = 0.0983
0.9428WACC = 0.0983
WACC = 0.0983 / 0.9428
WACC = 0.1043 = 10.43%
NPV = Cash flows after tax / WACC - initial investment
= 6,000,000 / 10.43% - 48,000,000
=57,526,366 - 48,000,000 = $9,526,366 is the NPV of the New plant.