Question

Sisters Ltd is planning to invest in a capital project, which will generate cash inflows of $15,000 in the 1st year, $22,000 in the 2nd year, and $25,000 in the 3rd year. The project ends after year 3. The company’s current debt to equity ratio is 0.8 with the cost of debt of 8% p.a. compounded annually. Sisters Ltd stock has a beta of 1.2. The risk-free rate is 3% p.a. compounded annually and the expected market return is 10.5% p.a. compounded annually. The new debt to equity ratio as a result of financing the project is 1. What is the total present value of the project’s cash inflows? Show your working.

Answer #1

Unlevered Beta = (Levered Beta) / (1 + (1 - tax)(D/E))

Unlevered Beta = (1.20) / (1 + (1 - 0)(0.80))

Unlevered Beta = (1.20) / 1.80

**Unlevered Beta = 0.67**

Levered Beta at DE ratio is 1 = Unlevered Beta * (1 + (1 - tax)(D/E))

Levered Beta at DE ratio is 1 = 0.67 * (1 + (1 - 0.00)(D/E))

**Levered Beta at DE ratio is 1 = 1.33**

**Expected Rate of Return = Risk Free + Beta * (Market
Rate - Risk Free) = 3% + 1.33 * (10.50%-3%) = 13%**

Present value of the project’s cash inflows = Yr1 / (1 + Expected Return) + Yr2 / (1 + Expected Return)^2 + Yr3 / (1 + Expected Return)^3

Present value of the project’s cash inflows = 15000 / (1 + 0.13) + 22000 / (1 + 0.13)^2 + 25000 / (1 + 0.13)^3

**Present value of the project’s cash inflows =
$47829.82**

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