Question

Ariana, Incorporated, is considering a project that will result in initial aftertax cash savings of $3.8 million at the end of the first year, and these savings will grow at a rate of 1.9 percent per year, indefinitely. The firm has a target debt-equity ratio of .55, a cost of equity of 10.6 percent, and an aftertax cost of debt of 3.2 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.

Calculate the discount rate for the project. Note: Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.9. 32.16.

Answer 1

To calculate the discount rate for Ariana, Incorporated's project, we must find the weighted average cost of capital (WACC) using the target debt-equity ratio, cost of equity, and aftertax cost of debt, then add a 2% risk premium for the project's higher risk level.

Step-by-step explanation:

To calculate the discount rate for the project that Ariana, Incorporated is considering, we must take into account the target debt-equity ratio, cost of equity, aftertax cost of debt, and the subjective risk adjustment. The weighted average cost of capital (WACC) will serve as the base for the discount rate calculation, incorporating the risk adjustment for this specific project. First, we calculate the equity proportion (E) and the debt proportion (D) based on the target debt-equity ratio of 0.55. The equity proportion is calculated as E = 1 / (1 + D/E). Substituting in the debt-equity ratio, we find that E = 1 / (1 + 0.55) = 1 / 1.55. The debt proportion is D = 1 - E.

Now, using these proportions, we calculate the WACC as follows: WACC = (E × cost of equity) + (D × aftertax cost of debt). We apply the cost of equity of 10.6% and the aftertax cost of debt of 3.2%, resulting in the initial WACC calculation. Finally, we add the 2% risk premium to the calculated WACC to get the adjusted discount rate since the project is considered riskier than usual. WACC_adjusted = WACC + 2%. We round this final value to two decimal places to get the discount rate for the project.