In: Accounting
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?
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Hint: αt = PVIF(RADR, t)/PVIF(RF, t)
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.)