#### Suzanne Evans

##### Well-Known Member

*AIMs: Describe how the value of a risky asset or project can be estimated through the development of a risk-adjusted discount rate, how such a risk-adjusted discount rate can be created, and strengths and weaknesses of this approach. Describe problems which arise when using historical betas and equity risk premiums as inputs into a valuation model. Construct a risk-adjusted discount rate for an asset or project and apply that rate to estimate the value of the asset or project. Describe the certainty equivalent approach to estimating value and contrast it with the use of a risk-adjusted discount rate.*

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**Questions:**

302.1. The Walt Disney Company is considering building a hypothetical theme part in Rio De Janeiro, Brazil. In order to determine the net present value (NPV) of the project, a discount rate is computed, which is the company's cost of capital. Here are the assumptions:

- Risk-free rate (US Treasury bond): 1.0%
- Beta for the theme park business: 0.80
- Equity risk premium: 6.0% + 3.0% country risk premium (Brazil) = 9.0%
- Pre-tax cost of debt: 1.0% risk-free rate + 2.0% default spread = 3.0%
- Marginal tax rate: 40.0%
- Funding mix: 40% debt and 60% equity

a. 5.64%

b. 6.12%

c. 7.00%

d. 8.92%

302.2. Bob the analyst is computing cost of capital for a public company's project. His cost of equity component is the risk-free rate plus the project's beta multiplied by the equity risk premium. Which of the following is the MOST appropriate input; i.e., the others are not appropriate or not really correct?

a. An historical, regression-based equity risk premium of +3.0% with a standard error of 9.0%

b. A forward-looking equity risk premium that uses current stock prices and expected future cash flows

c. An historical beta which is the y-intercept of a regression of company returns against the market index

d. An un-levered beta multiplied by the equity risk premium

302.3. Mary estimates the present value of a risky asset by estimating the asset's expected cash flows over its life and discounting this future series at a risk-adjusted discount rate; e.g., weighted average cost of capital. In this way, Mary accounts for the asset's risk in the denominator ("In this approach, the numerator is the expected cash flow, with no adjustment paid for risk, whereas the discount rate bears the burden of risk adjustments"). In Mary's analysis the expected cash flow in the 5th year (year 5) is $300.0 million, which she discounts at 6.0% because 6.0% is the risk-adjusted discount rate (the after-tax weighted average cost of capital). The 6.0% includes an assumption that the risk-free rate is 2.0%.

What is the certainty-equivalent cash flow in the fifth year (assume annual compounding)?

a. $190.15

b. $206.83

c. $247.51

d. $300.00

**Answers:**