Homework 5: Adjusting for project risk 2 (Q) Kindercare is considering a project

Question

Homework 5: Adjusting for project risk 2 (Q) Kindercare is considering a project that will result in initial aftertax cash savings of $3.5 million at the end of the first year, and these savings will grow at a rate of 4 percent per year indefinitely. The firm has a target debt-equity ratio of .55, a cost of equity of 13 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 percent to the cost of capital for such risky projects. Under what circumstances should Kindercare take on the project?

Explanation / Answer

D/E=0.55

proportion of debt, D/(D+E)=1/(1+1/0.55)=0.354839

proportion of equity=1-proportion of debt=1-0.354839=0.645161

Cost of capital=0.354839*5.5%+0.645161*13%=10.3387%

Project's cost of capital=10.3387%+2%=12.3387%

NPV=-Initial Investment+3.5/1.123387+3.5*1.04/1.123387

=-Initial Investment+3.5/(0.23387-0.04)

=-Initial Investment+18.05333

So, project should be undertaken when NPV>0

Hence, -Initial Investment+18.05333>0

Initial Investment<18.0533

So, the initial inevstment for the project must be less than 18.0533 milion for the project to be undertaken

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