Scanlin, Inc., is considering a project that will result in initial aftertax cas

Question

Scanlin, Inc., is considering a project that will result in initial aftertax cash savings of $1.84 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 0.75, a cost of equity of 12.4 percent, and an aftertax cost of debt of 5.2 percent. The cost-saving proposal is somewhat riskier than the usual project the firm undertakes; management uses the subjective approach and applies an adjustment factor of 3 percent to the cost of capital for such risky projects.

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

Scanlin, Inc., is considering a project that will result in initial aftertax cash savings of $1.84 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 0.75, a cost of equity of 12.4 percent, and an aftertax cost of debt of 5.2 percent. The cost-saving proposal is somewhat riskier than the usual project the firm undertakes; management uses the subjective approach and applies an adjustment factor of 3 percent to the cost of capital for such risky projects.

Explanation / Answer

cost of capital= Wt of debt*cost of debt+wt of equity*cost of equity+adjustment factor

Weight of debt= debt/(debt +equity) = 1/(1+equity/debt)=1/(1+(1/0.75))= 0.429

Weight of equity=1-0.429=0.571

weight of debt* after tax cost of debt =0.429*5.2%=2.23%

wt of equity*cost of equity=0.571*12.4%=7.09%

Cost of capital=2.23%+7.09%+3%=12.31%

The max initial cost is when NPV=0

=1.84/(1+12.31%)+1.84*1.01/(1+12.31%)^2+ 1.84*1.01^2/(1+12.31%)^3......

It is a geometric progression and sum to infintiy of an GP =a/(1-r)

a=first term r= common ratio

a=1.84/(1+12.31%) =1.638*10^6

r=1.01/(1+12.31%)=0.899

=1.638*10^6/(1-0.899)

=$16,262,626

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