Question

Photochronograph Corporation (PC) manufactures time series photographic equipment. It is currently at its target debt–equity ratio of .68. It’s considering building a new $65.8 million manufacturing facility. This new plant is expected to generate aftertax cash flows of $7.83 million in perpetuity. There are three financing options:

A new issue of common stock: The required return on the company’s new equity is 15 percent.

A new issue of 20-year bonds: If the company issues these new bonds at an annual coupon rate of 7.3 percent, they will sell at par.

Increased use of accounts payable financing: Because this financing is part of the company’s ongoing daily business, 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 .13. (Assume there is no difference between the pretax and aftertax accounts payable cost.)

If the tax rate is 38 percent, what is the NPV of the new plant? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answer in dollars, not millions of dollars, e.g., 1,234,567. Round your answer to 2 decimal places, e.g., 32.16.)

Net present value

Answer 1

Step 1: Calculate Weights of Debt and Equity

The weights of debt and equity are calculated as below:

Accounts Payable Weight = .13/1.13

Long-Term Debt Weight = 1/1.13

Overall Weight of Equity = 1/1.68

Overall Weight of Debt = .68/1.68

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Step 2: Calculate WACC

The WACC can be derived with the use of following equation:

WACC = Overall Weight of Equity*Cost of Equity + Overall Weight of Debt*(Weight of Accounts Payable*WACC + Weight of Long-Term Debt*After-Tax Cost of Debt)

Substituting values in the above formula, we get,

WACC = 1/1.68*15% + .68/1.68(.13/1.13*WACC + 1/1.13*7.3%*(1-38%))

Solving Further, we get,

WACC = .0893 + .4048*(.1150*WACC + .0401)

WACC = .0893 + .0466WACC + .0162

Rearranging values, we get,

WACC - .0466WACC = .1055

WACC = .1055/(1-.0466) = 11.07%

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Step 3: Calculate NPV

The NPV is determined as below:

NPV = Cost of Building + After-Tax Cash Flows/WACC = -65,800,000 + 7,830,000/11.07% = $4,961,004.79