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I've looked for a question that hits on something similar without success. The problem is this: at time 10, an asset pays 1000. Then the teacher gave us a bunch of random interest rates for times 0 to 2, 2 to 5, 5 to 8, and 8 and beyond. I'm positive I converted them all properly to an annual effective rate (used a financial calculator and Wolfram Alpha both and my answers each way matched). We're supposed to find the PV of this asset. I tried discounting from time 10 back to 8 with the discount rate based on the interest rate for 8 and beyond, etc., then the discount rate from 8 to 5, from 5 to 2, and then 2 back to time 0. I also tried starting at time 0 and advancing by the interest rate all the way to 10 and then discounting back to 2 and so on. I get the same answer both ways, but it's NOT one of the multiple choice answers.

If anyone knows of a YouTube channel that uses really complex financial math problems, I'd die grateful to you. He's the worst teacher I've ever had -- teaches concepts and then gives us very complex problems, and when I ask for an example problem of similar complexity, he gets mad and implies I'm stupid. Which I probably am, but I don't think needing an example problem is why. Blech.

Edit: for times 0 to 2, annual interest rate of 8%. For 2 to 5, force of interest of 0.015t. For 5 to 8, d of 6%. For 8 and beyond, i^(4) of 10%. I got annual interest rates of .08, .0151130646, .0638298, and .10381289 respectively, and calculated the discount factor by using 1/1+i for each. PV=1000*(1/1.08)^2 * (1/1.0151130646)^3 * (1/1.0638298)^3 * (1/1.10381289)^2. I get $558.73 on both a calculator and wolfram alpha. Not one of the choices available.

ravenclawmathboy
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  • Your approach - treating each period separately and then "daisy chaining" them together - sounds correct. If you can share the details of the problem and your attempt at answering then I (or someone else here) can check your calculations. Ideally, your teacher should be able to show you how the "correct" answer was obtained, and identify where you went wrong - but it sounds as if that might not be possible. – gandalf61 Feb 22 '19 at 12:41
  • Thanks--I will edit my post per the suggestion it made when I clicked to "add comment." – ravenclawmathboy Feb 22 '19 at 12:52
  • I can replicate all of your annual interest rates apart from $.0638298$. What does "For 5 to 8, d of 6%" mean ? Is $d$ a daily rate ? – gandalf61 Feb 22 '19 at 13:49
  • From the nomenclature he told us to use, d is discount rate, which I translated to an interest rate by d=1-v, .06-1=-v, .94=v, .94=1/1+i, i=.0638298. – ravenclawmathboy Feb 22 '19 at 13:54
  • The only thing I can possibly think of that might have been misunderstood on my part is the exact wording, so I'll copy it out here. "Find the present value of an asset which will payout a single cash-flow amount of 1000 at time t=10." Does that change anything? – ravenclawmathboy Feb 22 '19 at 14:36
  • I don't think that changes anything - it just tells us that $PV(10)=1000$ and there are no other cash flows in the period. What answer do other students get ? If several of you go to your teacher with the same solution, might he/she be more responsive ? – gandalf61 Feb 22 '19 at 15:07
  • Thank you so much!! – ravenclawmathboy Feb 22 '19 at 16:58

1 Answers1

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I agree with your present value at time $0$ of $558.73$ to $2$ decimal places. In detail, my calculations are as follows:

$PV(10) = 1000 \\ PV(8) = \frac{PV(10)}{1.025^8} = 820.746571 \\ PV(5) = PV(8) \times 0.94^3 = 681.698970 \\ PV(2) = PV(5) \times e^{-0.015 \times 3} = 651.702498 \\ PV(0) = \frac{PV(2)}{1.08^2} = 558.729851$

where $PV(n)$ is the present value at time $n$.

So either we have both misunderstood something about the conditions of the problem, or the "official" answer is incorrect.

gandalf61
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