Question

Och, Inc., is considering a project that will result in initial aftertax cash savings of $1.79 million at the end of the first year, and these savings will grow at a rate of 3 percent per year indefinitely. The company has a target debt–equity ratio of .85, a cost of equity of 11.9 percent, and an aftertax cost of debt of 4.7 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.

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, e.g., 1,234,567. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Maximum cost

$

Answer 1

Weighted avg. cost of capital = cost of equity * weight of equity + after tax cost of debt* weight of debt

Debt/equity = 0.85/1;

Debt/ total capital = 0.85/(1+0.85)=45.95%

Equity/ total capital = 1 - (debt/total capital)=1-45.95%=54.05%

Weighted avg. cost of capital WACC = 11.9% * 54.05% + 4.7%* 45.95% = 8.59%

2% is added to account for the riskiness; so cost of capital =8.59%+2%=10.59%

Present value (PV) = sum of present value of all future cash flows

After end of 1 year there is a perpetuity model with constant growth which can be calculated using the formula cash flow* (1+ growth rate)/ (cost of capital - growth rate) which needs to be discounted back from year 1 to year 0 (present value)

PV = $1.79 mn /(1+10.59%)^1 + ($1.79 mn *(1+3%)/(10.59%-3%))/(1+10.59%)^1+= $ 23.58 mn

This will be the max initial cost that the firm would be willing to pay.