Question

Photochronograph Corporation (PC) manufactures time series photographic equipment. It is currently at its target debt–equity ratio of .62. It’s considering building a new $65.2 million manufacturing facility. This new plant is expected to generate aftertax cash flows of $7.77 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 7.2 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 .13. (Assume there is no difference between the pretax and aftertax accounts payable cost.)

If the tax rate is 30 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

Solution:

We can use the debt-equity ratio to calculate equity and debt weights.

Weight of debt = Debt to equity ratio / (1+ Debt to equity ratio) = 0.62/1.62 = 0.3827

Weight of equity = 1/(1+ Debt to equity ratio) = 1/1.60 = 0.6173

The company's debt has a weight for long-term debt and a weight for accounts payable.

We can use the weight given to accounts payable to calculate the weight of accounts payable and the weight of long-term debt in total debt.

The weight of each will be: Accounts payable weight = .13/1.13 = 0.1150

Long-term debt weight = 1/1.13 = 0.8850

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

WACC = Weight of equity * Cost of equity + Weight of debt * [ (Weight of accounts payables * WACC) + (Weight of long term debt * Cost of debt * (1-tax) ) ]

WACC = (0.6173)*(.152) + (0.3827)*[(0.1150)*WACC + ((0.8850)*(0.072)*(1 - .30))]

Solving for WACC:

WACC = 0.0938296 + (0.3827)*[(0.1150*WACC + .044604]

WACC = 0.0938296 + (0.0440105)*WACC + 0.01706995

(0.9559895)*WACC = 0.11089955

WACC = .116005 or 11.60%

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

NPV = -$65200000 + ($7770000/.116005)

NPV = -$65200000 + 66979871.56

= $1,779,871.557

The NPV of the new plant = $1,779,871.56