Och, Inc., is considering a project that will result in initial aftertax cash sa

Question

Och, Inc., is considering a project that will result in initial aftertax cash savings of $1.87 million at the end of the first year, and these savings will grow at a rate of 1 percent per year indefinitely. The firm has a target debt–equity ratio of .75, a cost of equity of 12.7 percent, and an aftertax cost of debt of 5.5 percent. The cost-saving proposal is somewhat riskier than the usual projects the firm undertakes; management uses the subjective approach and applies an adjustment factor of +2 per cent to the cost of capital for such risky projects.

What is the maximum initial cost of company would be willing to pay for the project? (Do not round intermediate calculations. Enter your answer in dollars, not millions of dollars, i.e. 1,234,567.)

Och, Inc., is considering a project that will result in initial aftertax cash savings of $1.87 million at the end of the first year, and these savings will grow at a rate of 1 percent per year indefinitely. The firm has a target debt–equity ratio of .75, a cost of equity of 12.7 percent, and an aftertax cost of debt of 5.5 percent. The cost-saving proposal is somewhat riskier than the usual projects the firm undertakes; management uses the subjective approach and applies an adjustment factor of +2 per cent to the cost of capital for such risky projects.

Explanation / Answer

First, we need to find the project discount rate. The project discount rate is the company’s cost of capital plus a risk adjustment factor. A debt-equity ratio of 0.59 implies a weight of debt of 0.75/1.75 and a weight of equity of 1/1.75, so the company’s WACC is

WACC = (0.75/1.75)(0.055) + (1/1.75)(0.127)

WACC = 0.096143 or 9.61%

Adjusting for risk, the project discount rate is:

Project discount rate = 0.0961 + 0.02

Project discount rate = 0.1161 or 11.61%

2:

The company should only accept the project if the NPV is zero (hopefully greater than zero.) The cash flows are a growing annuity. The present value of a growing annuity can be found with the dividend discount equation. So, the present value of the savings is:

PV = [$1,870,000/(0.1161 – 0.010)]

PV = $17,624,882.19

The project should only be undertaken if its cost is less than $17,624,882.19. = the maximum initial cost of company would be willing to pay for the project

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