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9. With uncertain future cash inflows, the manager decides to adjust them with the appropriate certainty...

9. With uncertain future cash inflows, the manager decides to adjust them with the appropriate certainty equivalent factor. The certainty cash flow at year 3 is $8.85 million derived from an investment project with 30% of $7.5 million, 40% of $15.5 million and 30% of $4 million. Given a cost of capital of 6%, what is the underlying risk-free rate?

____

  1. 3.0%
  2. 2.5%
  3. 2.0%
  4. Undetermined

Hint: αt = PVIF(RADR, t)/PVIF(RF, t)

Solutions

Expert Solution

Answer to question

A)3%

Reason:

Certainty Equivalent Cash Flow = expected cash flow /(1+risk premium)

Based on these probabilities, the expected cash flow of this scenario is:

Expected cash flow = 0.3*$7.5 million+0.4*$15.5million+0.3*$4million

                                    = $9.65 million

Certain equivalent cash flow at year 3= $8.85 million

Cost of capital = 6%

using above formula

                                    8.85=9.65/(1+risk premium)

                                    (1+risk premium)=9.65/8.85

                                    Risk premium=1.0903-1

                              Risk premium=9.03%

           

Risk premium=Risk Adjusted Rate of Return − Risk Free Rate

Risk free rate = 9.03%-6%

                        =3% (approx.)

                                   

ekkarill92 answered 2 years ago
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