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Math Help - Present Value of Ordinary Annuity w/ Tax

  1. #1
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    Present Value of Ordinary Annuity w/ Tax

    Company A promises to pay $1000 to company B at the end of each year, for 8 years. Both companies have an income tax rate of 20% and have savings accounts earning a nominal rate of 10%, compounded monthly. To company B, what is the present value of all the payments it will receive from company A?

    The way I'm seeing it: 800[(1+0.8r)^8 -1]/[(0.8r)(1+0.8r)^8] = $4532.25; where r is the annual effective rate. (r = 0.1047130674)

    The correct answer is given as $4195.69.

    Any ideas?
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  2. #2
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    Re: Present Value of Ordinary Annuity w/ Tax

    could you fix this please so we can read it
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  3. #3
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    Re: Present Value of Ordinary Annuity w/ Tax

    Quote Originally Posted by Convrgx View Post
    Company A promises to pay 1000 to company B at the end of each year, for 8 years. Both companies have an income tax rate of 20% and have savings accounts earning a nominal rate of 10%, compounded monthly. To company B, what is the present value of all the payments it will receive from company A?

    The way I'm seeing it: 800[(1+0.8r)^8 -1]/[(0.8r)(1+0.8r)^8] = 4532.25; where r is the annual effective rate. (r = 0.1047130674)

    The correct answer is given as 4195.69.

    Any ideas?
    Do not use dollar signs. They invoke the LaTeX editor and make a hash of your posts. There is probably some way to deal with it, but I do not know it yet.

    I get the same present value as your book for post-tax present value.

    I have no idea in the world what your formula is supposed to mean. For example, what is 0.8 and why is it there?

    Your value for r is correct.

    What is the formula for the present value of an annuity equal to 1 dollar?
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    Re: Present Value of Ordinary Annuity w/ Tax

    Company A promises to pay 1000 to company B at the end of each year, for 8 years. Both companies have an income tax rate of 20% and have savings accounts earning a nominal rate of 10%, compounded monthly. To company B, what is the present value of all the payments it will receive from company A?

    The way I'm seeing it: 800[(1+0.8r)^8 -1]/[(0.8r)(1+0.8r)^8] = 4532.25; where r is the annual effective rate. (r = 0.1047130674)

    The correct answer is given as 4195.69.

    Any ideas?

    Ok, I see what's wrong here. At first I was thinking that each year company B gets 1,000, then pays taxes on it, then this accumulates interest, and then you pay taxes on the interest. I guess the correct way to look at it is to just find the future value without any taxes, use this to find the present value, and then account for taxes.
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  5. #5
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    Re: Present Value of Ordinary Annuity w/ Tax

    The 0.8r was for the resulting interest taking into account a 20% tax.
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  6. #6
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    Re: Present Value of Ordinary Annuity w/ Tax

    You already took the tax into account when you multiplied by \$800 instead of \$1000.

    You get \$1000 and pay tax of \$200 so the net cash flow is \$800.

    I am more interested in your getting the formula correct. The net payment is correct. The opportunity rate of interest is correct. All you need to do is to set up the formula correctly.
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