Question

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

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)

ertainity equivalent cash flow = \$8.85 million

Uncertain cash flow = (0.3 x 7.5) + (0.4 x 15.5) + (0.3 x 4) = \$9.65 million

certain cash flow = uncertain cash flow / [ 1+ Risk premium ] ^3

8.85 = 9.65 / [ 1+ ( Risk premium)^t]

[ 1+ risk premium ] ^3 = 9.65 / 8.85 = 1.09

1+ risk premium = 1.09^0.33 = 1.029

risk premium = 2.9%

Risk premium = 1 - [ (1+ RART) / (1+RFR)]

0.029 = 1 - (1.06/1+RFR)

1.06/1+RFR = 1.029

1+RFR = 1.06/1.029 = 1.0301 = 1.03

RFR = 1.03 -1 = 3%

Ans - A - 3%

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Thankyou

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