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 $1.88 million at the end of the first year, and these savings will grow at a rate of 3 percent per year indefinitely. The firm has a target debt–equity ratio of .85, a cost of equity of 12.8 percent, and an aftertax cost of debt of 5.6 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?

Maximum cost:

Explanation / Answer

The debt to equity ratio = D/E = 0.85

D = 0.85E

If E =1, D = 0.85

Weight of equity = 1/1.85 = 0.5405

Weight of debt = 1-0.5405 = 0.4595

Cost of equity = 12.8%

After tax cost of debt = 5.6%

Cost of capital = 0.5405*12.8 + 0.4595*5.6 = 9.4916 %

Risk adjusted cost of capital = 9.4916 +2 = 11.4916%

Now the PV of the growing annuity = C1/(r-g)

C1 = Cash flow next year = 1,880,000 *1.03 = 1,936,400

r = 0.114916

g = 0.03

So PV of the growing annuity = 1,936,400/(0.114916-0.03) = 22,803,712

The maximum initial cost, company is willing to pay is $22,803,712 (22.8 million)

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