Sommer, Inc., is considering a project that will result in initial aftertax cash savings of $1.85 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 12.5 percent, and an aftertax cost of debt of 5.3 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 2 percent to the cost of capital for such risky projects. What is the maximum initial cost the c

$22,583,305.84

Explanation:

The computation of the maximum initial cost is as follows

But before that following calculations need to be done

WACC = wd × rd + we × re

Where,

Weight of debt wd = 0.85 ÷  (1 +0.85) = 0.85 ÷1.85

Weight of equity we = 1 ÷ (1 + 0.85) = 1 ÷ 1.85

After-tax cost of debt, rd = 5.3%

And the cost of equity, re = 12.5%

Now  

WACC = (0.85 ÷ 1.85) ×  5.3% + (1 ÷ 1.85) × 12.5%

= 9.19%

The discount rate would be

= WACC + adjustment factor of +2%

= 9.19% + 2%

= 11.19%

Now

PV of future Cash Flows is

= After-tax cash savings  ÷ (k –g)

Where,

After-tax cash savings = $1.85 million

k = 11.19% per year

 g = 3% per year

Therefore,

= $1,850,000 ÷ (0.1119 - 0.03)

= $22,583,305.84

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