Sommer, Inc., is considering a project that will result in initial aftertax cash savings of $1.89 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 12.9 percent, and an aftertax cost of debt of 5.7 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 1 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?

The maximum initial cost is $2,17,24,138

Explanation:

Solution

From the given question, we are asked to find the maximum initial cost the company would be willing to pay for the project.

Now,

The first step to take is to calculate the weighted Average Cost of Capital (WACC)

Which is:

The weighted Average Cost of Capital (WACC) = [After-tax Cost of Debt x Weight of Debt] + [Cost of Equity x Weight of Equity]

= [5.70% x (0.80/1.80)] + [12.90% x (1/1.80)]

= 2.53% + 7.17%

= 9.70%

Secondly we calculate for the project discount rate which is stated as follows:

The Project Discount Rate = Weighted Average Cost of Capital (WACC) + Risk Adjustment Factor

= 9.70% + 1%

= 10.70%

The third step is to find the maximum initial cost the company would be willing to pay for the project

So,

as regards to the  NPV Method of Capital Budgeting, the Project should be received if the NPV of the present value is  seen as positive,

Hence,

The NPV = Present Value of Annual cash inflows – Present Value of Cash Outflows.

Thus,

The Maximum initial cost the company would be willing to pay for the project is the Present Value of the annual after-tax in-flows which is determined as follows

The Maximum initial cost = Initial After-tax Savings / (Ke – g)

= $18,90,000 / (0.1070 - .02)

= $18,90,000 / 0.0870

= $2,17,24,138

answerup to (3) three years;