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Math Help - Present value

  1. #1
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    Present value

    I am double-checking my answers because present and future values make me VERY nervous and I can't afford to mess up this grade!

    On January 1, 2006 XYZ Co completed the following transactions (using 8% interest rate)

    a) borrowed $10,0000 for 10 years. Will pay $8,000 interest at end of each year and repay $10,000 at end of tenth year.
    Determine present value of debt.

    I have 100,000*.4632=$46,320
    (10 year period, 8% using present value of $1)

    b)Established a plant addition fund of $400,000 to be available at end of year 5. A single sum that will grow to $400,000 will be deposited on January 1, 2006.
    What is the single sum? What is total amount of interest revenue that'll be earned?

    I have 400,000*.6806=$272,240 as the single sum.
    I have interest as 8% of 272,240=$21,779

    c)Agreed to pay severance to discharged employee. Will pay $50,000 at end of first year, $75,000 at end of second year and $100,000 at end of third year.
    Determine persent value of obligation.

    I have:
    50,000*.9259=46295
    75,000*.8573=64297.5
    100,000*.7938=79380

    46925+64297.5+79380=$189,972.5

    d)Purchase a $180,000 machine Jan. 1, 2006 and paid cash $60,000. Four-year note payable signed for the balance. Note will be paid in 4 equal year-end payments starting Dec 31, 2006.
    What is amount of each of the equal annual payments? What is total amount of interest expense incurred?

    I have:
    180,000-60,000=120,000*3.3121=397,452/4=$99,363 is equal payments

    120,000*8%=9600 int exp year one
    (120,000-89763)*8%=2419 int exp year two
    (120,000-89763-96944)*8%=
    And this is where I run into a problem. Since it can't be negative, I assume I got the payments wrong? Anyone willing to knock some numbers around and help me see my mistake?
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  2. #2
    Senior Member
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    Berkeley, Illinois
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    Answers below in red:

    On January 1, 2006 XYZ Co completed the following transactions (using 8% interest rate)

    a) borrowed $10,0000 for 10 years. Will pay $8,000 interest at end of each year and repay $10,000 at end of tenth year.
    Determine present value of debt.

    I have 100,000*.4632=$46,320
    (10 year period, 8% using present value of $1)

    No. Go here: Annuity Immediate Present Value

    PV of 8k payments are 8,000 for 9 years @ 8% = 49,975.10. Then, you need to discount 10,000/(1.08^10). Add that to the 49,975.10 and you have your answer

    b)Established a plant addition fund of $400,000 to be available at end of year 5. A single sum that will grow to $400,000 will be deposited on January 1, 2006.
    What is the single sum? What is total amount of interest revenue that'll be earned?

    I have 400,000*.6806=$272,240 as the single sum.
    I have interest as 8% of 272,240=$21,779

    I agree with PV. However, interest earned is 400k - PV of 272,240. You made no payments, so it is all interest for 5 years.

    c)Agreed to pay severance to discharged employee. Will pay $50,000 at end of first year, $75,000 at end of second year and $100,000 at end of third year.
    Determine persent value of obligation.

    I have:
    50,000*.9259=46295
    75,000*.8573=64297.5
    100,000*.7938=79380

    46925+64297.5+79380=$189,972.5

    This is correct. This method though will become cumbersome with more than a few payments. There is a formula which accounts for the PV of arithmetic increases. Go here and see the math work that matches your answer, it will make your life easier in the future:

    Arithmetic Annuity Immediate Present Value

    d)Purchase a $180,000 machine Jan. 1, 2006 and paid cash $60,000. Four-year note payable signed for the balance. Note will be paid in 4 equal year-end payments starting Dec 31, 2006.
    What is amount of each of the equal annual payments? What is total amount of interest expense incurred?

    I have:
    180,000-60,000=120,000*3.3121=397,452/4=$99,363 is equal payments

    120,000*8%=9600 int exp year one
    (120,000-89763)*8%=2419 int exp year two
    (120,000-89763-96944)*8%=

    No, this is a 4 year loan, go back here:

    http://www.mathcelebrity.com/annimmpv.php

    120k PV @ 8% per year for 4 years has an annual payment of 36230.50. Interest expense = Total amount of payments - Original Loan Amount. 36230.5*4 - 120,000
    Last edited by mathceleb; July 8th 2008 at 07:41 AM.
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  3. #3
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    I'm sorry; I made an error in transcribing the first problem.
    It should have been:
    a) borrowed $100,000 for 10 years. Will pay $8,000 interest at end of each year and repay the $100,000 at end of tenth year.

    So, the entire amount will be paid off rather than one payment of $10,000 on the tenth year. That was my mistake.
    Is my answer correct with the revised problem?

    Should it be 8,000*0.4632=$3705.6?
    This doesn't look right...that's a really small number.

    As for the rest, I see what you are saying. It is so much easier than it seems when I read how you go through the steps...thank you for your help.
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  4. #4
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    Berkeley, Illinois
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    Quote Originally Posted by Lionne View Post
    I'm sorry; I made an error in transcribing the first problem.
    It should have been:
    a) borrowed $100,000 for 10 years. Will pay $8,000 interest at end of each year and repay the $100,000 at end of tenth year.

    So, the entire amount will be paid off rather than one payment of $10,000 on the tenth year. That was my mistake.
    Is my answer correct with the revised problem?

    Should it be 8,000*0.4632=$3705.6?
    This doesn't look right...that's a really small number.

    As for the rest, I see what you are saying. It is so much easier than it seems when I read how you go through the steps...thank you for your help.
    PV of 8k payments are 8,000 for 9 years @ 8% = 49,975.10. Then, you need to discount 100,000/(1.08^10). Add that to the 49,975.10 and you have your answer. I copied in my answer from above with the revised 100k instead of 10k. You want the present value of your payment obligation. You pay 8k at the end of each year, with an 8% effective rate you could have earned with that money on your own. That's an annuity immediate. The last balloon payment is discounted back 10 years. Add that to the PV of the 8k and you have your answer.

    The payment stream is \frac{8000}{1.08} + \frac{8000}{1.08^2} + \frac{8000}{1.08^3} + .... + \frac{8000}{1.08^9}
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  5. #5
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    OK...believe I've got it all worked out.
    Many thanks again.
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