Problem 14-20 WACC and NPV [LO3, 5] Sommer, Inc., is considering a project that will result in initial aftertax cash savings of $1.86 million at the end of the first year, and these savings will grow at a rate of 2 percent per year indefinitely. The firm has a target debt-equity ratio of .80, a cost of equity of 12.6 percent, and an aftertax cost of debt of 5.4 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? (Do not round intermediate calculations and enter your answer in dollars, not millions, rounded to the nearest whole dollar amount, e.g., 1,234,567.)
Calculation of the Weights of capital components :-
Debt to equity ratio = 0.80
debt/equity = 0.80
debt = 0.80 equity -----------eq 1
here Debt + equity = 1 -----------eq2
substitute eq 1 in eq 2
0.80 equity + equity = 1
equity = 1/ 1.8 = 0.5556
substitute equity value in eq 2
debt +equity = 1
debt + 0.5556 = 1
debt = 0.4444
weight of equity = 0.5556
weight of debt = 0.4444
Calculation of the WACC :-
WACC = cost of debt after tax * weight of equity + cost of equity * weight of equity
= 5.4% * 0.4444 +12.6% * 0.5556 = 0.094003
WACC = 9.4%
Discounting rate for the project = WACC + 3% = 9.4% +3% = 12.4%
maximum initial cost the company would be willing to pay for the project = FCF in First year / ( Discounting rate - g)
= $ 1,860,000 / (0.124 - 0.02)
Maximum initial cost to company would willing to pay = $ 17,884,615.385
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