Question

A project has the following forecasted cash flows:

Cash Flows ($ thousands)
C0	C1	C2	C3
−155	+95	+115	+105

The estimated project beta is 1.51. The market return r_m is 15%, and the risk-free rate r_f is 3%.

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.)

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.)

c. What is the ratio of the certainty-equivalent cash flow to the expected cash flow in each year? (Do not round intermediate calculations. Round your answers to 4 decimal places.)

Answer 1

a)

The opportunity costof capital is equal to the cost of equity calculated by CAPM model.

r = rf + beta* (rm - rf)

= 3 + 1.51*(15-3)

= 21.12%

Present value is equal to the sum of discounted cashflows, ie, cashflow at time t divided by (1+r)^t, where r is the opportunity cost of capital and t is the in years.

PV = -155 + 95/(1+21.12/100) + 115/(1+21.12/100)^2 + 105/(1+21.12/100)^3

= $60.9193

b)

Certainty equivalent cashflows, CEQ, is found by below formula,

CEQ/(1+risk free rate)^t = cashflow/(1+opportunity cost of capital)^t

So, CEQ for year 1,

CEQ1/(1+3/100) = = 95/(1+21.12/100)

CEQ 1 = 80.7876

For year 2,

CEQ 2/(1+3/100)^2 = 115/(1+21.12/100)^2

CEQ 2 = 83.164

For year 3,

CEQ 3/(1+3/100)^3 = 105/(1+21.12/100)^3

CEQ 3 = 64.573

c)

Ratio of CEQ to the expected cashflows in each year is,

Year 1,

Ratio 1 = CEQ 1/ 95

= 80.7876/95

= 0.8503

For year 2,

Ratio 2 = CEQ 2/115

= 83.164/115

= 0.7231

For year 3,

Ratio 3 = CEQ 3/105

= 64.574/105

= 0.6149