Question

Photochronograph Corporation (PC) manufactures time series photographic equipment. It is currently at its target debt–equity ratio of .66. It’s considering building a new $65.6 million manufacturing facility. This new plant is expected to generate aftertax cash flows of $7.81 million in perpetuity. There are three financing options:

1. A new issue of common stock: The required return on the company’s new equity is 15.2 percent.
2. A new issue of 20-year bonds: If the company issues these new bonds at an annual coupon rate of 7.1 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, 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.)

If the tax rate is 34 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

Answer:

Target debt equity ratio = 0.66

Total liabilities / Equity = 0.66

Hence:

Total liabilities = 0.66 / (1 + 0.66) = 0.66/1.66

Equity = 1 / (1 + 0.66) = 1/1.66

Given that:

Management has a target ratio of accounts payable to long-term debt of .15.

Hence:

Accounts payable = 0.15 / Long-term debt

Weight of long accounts payable = (0.15 / (1 + 0.15)) * 0.66/1.66  = (0.15/1.15) * (0.66/1.66)

Weight of long-term debt = (1 / (1 + 0.15) * 0.66/1.66 = (1/1.15) * (0.66/1.66)

Cost of equity = 15.2%

New bonds are issued at par.

Cost of debt = 7.1%

Given that:

Company assigns accounts payable a cost that is the same as the overall firm WACC.

WACC = 15.2% * (1/1.66) + 7.1% * (1 - 34%) * (1/1.15) * (0.66/1.66) + WACC * (0.15/1.15) * (0.66/1.66)

=> WACC - WACC * (0.15/1.15) * (0.66/1.66) = 15.2% * (1/1.66) + 7.1% * (1 - 34%) * (1/1.15) * (0.66/1.66)

=> WACC * (1 - (0.15/1.15) * (0.66/1.66)) = 10.7767207962284%

=> WACC = 10.7767207962284%/ 94.8140387637507% = 11.3661657458564%

WACC = 11.3661657458564%

NPV =  (Perpetual annual after-tax cash flows / WACC) - Initial investment

= 7810000 / 11.3661657458564% - 65600000

= $3112705.54

Net Present Value = $3,112,705.54