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Problem

An investor will receive $365 at the end of each year for thirteen years. The first payment will be received four years from now. Given that the interest rate is 3%, the present value of this cash flow stream is closest to:

  • $3,552 (Correct solution)

  • $3,882

  • $3,449 (I answered this)


Solution

  • N = 13
  • PMT = 365
  • I/Y = 3
    • Compute PV: PV = $3881.76

This is the value of the cash flow stream three years from now. We must discount this value back to t = 0 to compute its present value.

  • N = 3
  • I/Y = 3
  • FV = -3,881.76.

    • Compute PV: PV = 3552.36

Question

Why is N = 3 in the bottom half of the solution? I used N = 4 because the initial payment is 4 years from now, resulting in answer C instead. Any clarification on this? Thank you very much!

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Summing the PVs of the cash flows, I get 3552. I'm going to guess that your equation assumes the first payment comes at the end of the first period, not at the start of it. For this setup, that would put the "start" date of the instrument at t=3.

Personally, I would just discount all the cash flows back to today, rather than once to a forward date and then again to today, to eliminate these kinds of issues.

Edit to show how to count:

t    y
0         spot
1
2
3   0   start for purposes of eqn
4   1   first payment
5   2
...
16 13  last payment

In computer science there are 2 hard problems: cache invalidation, naming things and off by one errors. (Forgotten the source for that)

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  • $\begingroup$ Hi, thank you! I'd like to do it your way in a single step, but the problem for me is knowing whether it's N = 16 or N = 17. Given the wording of the problem, I thought it was as simple as 4 + 13 = 17, but apparently it's supposed to be 16, which means I'm double-counting a year. It seems that if I use N = 13 to discount back to the first payment, then I've actually already discounted the 4th year. This means there are only 3 years left to discount. That would be 3 + 13 = 16, which gives the right answer. Is that the correct way to look at it? $\endgroup$ – Blaisem May 22 '16 at 14:07
  • $\begingroup$ I've drawn you a table. $\endgroup$ – Phil H May 22 '16 at 15:45

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