Question

Piedmont Hotels is an all-equity company. Its stock has a beta of .87. The market risk premium is 7.4 percent and the risk-free rate is 4.0 percent. The company is considering a project that it considers riskier than its current operations so it wants to apply an adjustment of 2.2 percent to the project's discount rate. What should the firm set as the required rate of return for the project

Answer 1

The required rate of return for the riskier project by Piedmont Hotels, factoring in its beta, market risk premium, risk-free rate, and additional risk adjustment, should be set at 12.638%.

Step-by-step explanation:

The firm should set the required rate of return for the riskier project by first calculating the expected rate of return using the Capital Asset Pricing Model (CAPM) and then adjusting it for additional risk. Using the CAPM, the formula is as follows: Required Return = Risk-Free Rate + (Beta × Market Risk Premium). Since Piedmont Hotels is an all-equity company with a stock beta of 0.87, the market risk premium is 7.4 percent, and the risk-free rate is 4.0 percent, the initial expected rate of return would be:

Required Return = 4.0% + (0.87 × 7.4%) = 4.0% + 6.438% = 10.438%.

However, since the company considers the project riskier than its current operations, we add the adjustment of 2.2 percent to the project's discount rate:

Adjusted Required Return = Initial Required Return + Risk Adjustment = 10.438% + 2.2% = 12.638%.

Therefore, the adjusted required rate of return for the project would be 12.638%.

Answer 2

12.64%

Step-by-step explanation:

In this question, we apply the Capital Asset Pricing Model (CAPM) formula which is shown below

Expected rate of return = Risk-free rate of return + Beta × (Market rate of return - Risk-free rate of return)

= 4% + 0.87 × 7.4%

= 4% + 6.438%

= 10.438%

The Market rate of return - Risk-free rate of return) is also known as the market risk premium and the same is applied.

Now the required rate of return would be

= 10.438% + 2.2%

= 12.64%