Question

A project has the following forecasted cash flows: Cash Flows ($ thousands) C1 С2 Се Сз -145 +95 +85 +105 The estimated project beta is 1.59. The market return rm is 17%, and the risk-free rate rf is 4%. a. Estimate the opportunity cost of capital and the project's PV (using the same rate to discount each cash flow). (Do not round intermediate calculations. Enter your cost of capital answer as a percent and enter your PV answer in thousands. Round your answers to 2 decimal places.) Cost of capital PV b. What are the certainty-equivalent cash flows in each year? (Do not round intermediate calculations. Enter your answers in thousands rounded to 2 decimal places.) Certainty-Equivalent Cash Flow Year 1 2

Answer 1

a.) First of all we need to calculate the expected rate of return for project. which can be calculated from below formula

ER_i​=R_f​+β_i​(ER_m​−R_f​)

where:ER_i​=expected return of investment

R_f​=risk-free rate

β_i​=beta of the investment

(ER_m​−R_f​)=market risk premium​

After putting the value

ER_i = 4% + 1.59 ( 17% - 4%) = 24.67%

Net present value of the project will be as under :-

Cash Flows	Amount In Thousand	Discount Factor @ 24.67%	Present Value in thousand
C0	-145	1	-145
C1	85	0.80211759	68.17999519
C2	105	0.643392629	67.55622603
C3	95	0.516076545	49.02727179
Total Present Value of the Project			39.76349301

So the present value of the project will be $39.76 Thousand

b) For certainty equivalent cash flow, we need to calculate first risk premium. which is calculated as under

Risk premium = Expected rate of return of project - Risk Free Return

= 24.67% - 4% = 20.67%

Now the formula for Certainty equivalent cash flow is as under

Certainty equivalent cash flow=Expected cash flow ​/ (1+risk premium)

using above formula certainty equivalent cash flow will be as under

YEAR	Cash Flow Amount ($ Thousand)	(1+ Risk Premium)	Certainty Equivalent cash flow
YEAR 1	85	1.2067	70.44
YEAR 2	105	1.2067	87.01
YEAR 3	95	1.2067	78.72

c) Ratio between certainty equivalent cash flow and expected cash flow will be as under

Cash Flows	Certainty Equivalent cash flow ($ Thosuand)	Expected Cash Flow ($ Thousand)	Ratio
Year 1	70.44	85	0.83
Year 2	87.01	105	0.83
Year 3	78.73	95	0.83