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11 January, 17:39

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

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  1. 11 January, 19:10
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    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
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