Question

You are a consultant to a large manufacturing corporation considering a project with the following net after-tax cash flows (in millions of dollars): Years from Now After-Tax CF 0 –30 1–9 15 10 30 The project's beta is 1.9. Assuming rf = 4% and E(rM) = 14% a. What is the net

Answer 1

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