Question

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:    α_t = PVIF(RADR, t)/PVIF(R_F, t)

Answer 1

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%

Please like the solution if satisfied and drop a comment in case of any doubt.

Thankyou