Question

A project has a forecasted cash flow of $110 in year 1 and $121 in year 2. Risk free rate is 5%, the estimated risk premium on the market is 10%, and the project has a beta of 0.7.
If you use a constant risk-adjusted discount rate, what is
a)The PV of theproject?
b)The certainty-equivalent cash flow in year 1 and year2?
c)The ratio of the certainty-equivalent cash flows to the expected cash flows in years 1 and2?

Answer 1

From the question we are told that:

$Cash Flow:$

Year 1= \$110

Year 2 = \$121

Risk free rate is $r=5%$

Risk premium  $R=10\%$

$\beta = 0.7.$

a)

Generally, the equation for Equity Return is mathematically given by

$e=r+\beta*R$

$e=0.05+(0.7*0.10)$

$e=0.12$

Therefore Present Value (PV) is

$PV=\frac{110}{1+0.12}+\frac{121}{1+0.12^2}$

b)

Generally, the equation for  certainty-equivalent cash flow is mathematically given by

$CE=(1+r)\frac{Year}{1+e}$

Therefore

For Certainty-equivalent cash flow Year One

$CE__=(1+0.05)\frac{110}{1+0.12}$

$CE_1=103.125$

For Certainty-equivalent cash flow Year Two

$CE_2=(1+0.05)\frac{121}{1+0.12}$

$CE_2=113.4$

c)

The Ratio of the certainty-equivalent cash flows to the expected cash flows in years 1 and 2 could be written as

$R=103.125:113.4$

or

$R=\frac{103.125}{113.4}$