Question

19. Lebleu, Inc, is considering a project that will result in initial aftertax cash savings of $2.9 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 75, a cost of equity of 10 percent, and an aftertax cost of debt of 4.6 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. Under what circumstances should the company take on the project?

Answer 1

To determine whether the company should take on the project, calculate the present value of the aftertax cash savings using the formula for the present value of a growing perpetuity. If the present value is greater than the initial investment, the company should take on the project.

Step-by-step explanation:

To determine whether the company should take on the project, we need to calculate the present value of the aftertax cash savings. The cost of capital is 10% + 3% (adjustment factor) = 13%. Using the formula for the present value of a growing perpetuity, we can calculate the present value of the cash savings as:

PV = C / (r - g)

Where PV is the present value, C is the cash savings, r is the cost of capital, and g is the growth rate. Plugging in the values, we have PV = 2.9 / (0.13 - 0.02) = $29 million.

Since the present value of the cash savings is greater than the initial investment, the company should take on the project.

Answer 2

Lebleu, Inc. should take on the project if the present value of the adjusted after tax cash savings, discounted at an adjusted cost of capital (considering the company's target debt-equity ratio, cost of equity, after tax cost of debt, and an additional risk factor), exceeds the project's cost.

Step-by-step explanation:

Lebleu, Inc. should consider taking on the cost-saving project if the present value of the project's cash flows, discounted back at the adjusted cost of capital, exceeds the initial investment cost. To calculate the adjusted cost of capital, you would consider the firm's target debt-equity ratio, cost of equity, and after tax cost of debt, and make an upward adjustment to the cost of capital by the specified risk factor. For this firm, the cost of capital would be adjusted by an additional 3% above the weighted average cost of capital (WACC) because the project is riskier than usual.

By applying the Gordon Growth Model or a perpetuity growth formula, we can determine the present value of the future cash flows. This model calculates the present value of an infinite series of future cash flows that grow at a constant rate. The formula for the Gordon Growth Model is:

PV = D / (k - g)

where PV is the present value of the cash flows, D is the initial after tax cash savings, k is the adjusted cost of capital, and g is the growth rate of the cash savings. In this case, these are $2.9 million, (cost of capital + 3%), and 2% per year, respectively.

Finally, if the calculated present value is greater than the project's cost, Lebleu, Inc. should undertake the project, as it suggests that the project will add value to the company.