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Thread: Investment+Revenue to NPV question using a discount rate of 4%, compounded annually

  1. #1

    Investment+Revenue to NPV question using a discount rate of 4%, compounded annually

    Q. During the next 3 years, a business decides to invest 10,000, at the beginning of each year.

    The revenue at the end of each year is:

    Year 1 = 5,000
    Year 2 = 20,000
    Year 3 = 50,000

    Calculate the NPV using a discount rate of 4%, compounded annually.



    A. My answer was 39,997.85. The textbook answer (Ian Jacques) is 38,887.69.

    I drew out a timeline, like this:

    Year 1 = -10,000 +5,000 = -5,000
    Year 2 = -10,000 + 20,000 = 10,000
    Year 3 = -10,000 + 50,000 = 40,000

    Year 1 = -5,000 x (1.04)^(-1) = -4,807.69
    Year 2 = 10,000 x (1.04)^(-2) = 9,245.56
    Year 3 = 40,000 x (1.04)^(-3) = 35,559.85

    Total = 39,997.72.

    This is higher than the answer, so I was thinking the 10,000 investments who should be increased by 4% compounded annually, and minus them from the future revenues.

    Year 1 = -10,000 +5,000 = -5,000
    Year 2 = -10,400 + 20,000 = 9,600
    Year 3 = -10,816 + 50,000 = 39,184

    Year 1 = -5,000 x (1.04)^(-1) = -4,807.69
    Year 2 = 9,600 x (1.04)^(-2) = 8,875.74
    Year 3 = 39,184 x (1.04)^(-3) = 34,834.43

    Total = 38,902.48

    Where am I going wrong?

    Thanks (as always) for your help.

  2. #2
    Elite Member
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    The 10000's are at "beginning" of each year.

    So you have:
    5000/1.04 + 20000/1.04^2 + 50000/1.04^3

    -10000 - 10000/1.04 - 10000/1.04^2
    I'm just an imagination of your figment !

  3. #3
    Quote Originally Posted by Denis View Post
    The 10000's are at "beginning" of each year.

    So you have:
    5000/1.04 + 20000/1.04^2 + 50000/1.04^3

    -10000 - 10000/1.04 - 10000/1.04^2
    Thanks Dennis. I hate when I thought I had tried every conceivable way, and yet that's one more I didn't try!

    Got it now.

    Thxs.

  4. #4
    Elite Member
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    Quote Originally Posted by radnorgardens View Post
    Thanks Dennis. I hate when I thought I had tried every conceivable way, and yet that's one more I didn't try!
    On the positive side: you'll never forget that way again
    I'm just an imagination of your figment !

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