What is the net present value of the project? (Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places.)
Answer:
Present Value = $22.47 million
Explanation:
Given
After-tax cash flows (in millions of dollars):
Years from Now || After-Tax CF
0 || 30
1–9 || 15
10 || 30
Project Beta = β = 1.9
Risk free rate = rf = 4%
Market Return = E(rM) = 14%
First, we calculate the expected return
Expected return is calculated as
Expected Return = Risk free rate + Project Beta * (market return - risk free rate)
Expected Return = rf + β (E(rM) - rf)
Expected return = 4% + 1.9 * (14% - 4%)
Expected Return = 4% + 1.9(10%)
Expected Return = 0.04 + 1.9(0.1)
Expected Return = 0.04 + 0.19
Expected Return = 0.23
Expected Return = 23%
I = 23%
The Present Value of Annuity is calculated as
PV = - Payment for year 0 + Payment for year 1 - 9 + Payment for year 10
For Year 0, Payment Value = 29
For Year 1 - 9;
PV = Payment per period + [ 1 - (1+i)^-n ]/i
Where n = 9 and I = 24%
Payment per period = 15
PV = 15 + [ 1 - (1 + 23%)^-9]/23%
PV = 18.67
For Year 10
PV = Payment per period + [ 1 - (1+i)^-n ]/i
Where n = 10 and I = 24%
Payment per period = 15
PV = 30 + [ 1 - (1 + 23%)^-10]/23%
PV = 33.80
PV = - Payment for year 0 + Payment for year 1 - 9 + Payment for year 10
Becomes
PV = -30 + 18.67 + 33.80
PV = 22.47
Present Value = $22.47 million
