Pretty stupid question, but I have yet to find a straightforward answer through my google searches.
Can someone please tell me how to calculated the net present value of a transaction where the first value (61425) is discounted back over 7 months, the second value (165375) is discounted back at 1 year 7 months, etc. So, basically the question is what formula should I use. I am pretty sure the discount rate needs to be adjusted. And for the year would I use (7/12), 1+(7/12), etc, considering the first value is after 7 months, and all subsequent periods are 1 year after the first 7 months.
Thanks.
First, you probably want to convert the discount rate from an annual one to a monthly one. Let d(x) be the discount rate for x years. Thus, d(1/12) = (1 + d(1))^(1/12) - 1. Then, the NPV = 61425 / [1+d(1/12)]^(7/12) + 165375 / [1 + d(1/12)]^(19/12). Hopefully, someone else will check over this and make sure I'm correct (I'm relatively inexperienced with this sort of thing as well).
P.S. I used this for a little help: http://www.experiglot.com/2006/06/07/how-to-convert-from-an-annual-rate…
[quote=econ]First, you probably want to convert the discount rate from an annual one to a monthly one. Let d(x) be the discount rate for x years. Thus, d(1/12) = (1 + d(1))^(1/12) - 1. Then, the NPV = 61425 / [1+d(1/12)]^(7/12) + 165375 / [1 + d(1/12)]^(19/12). Hopefully, someone else will check over this and make sure I'm correct (I'm relatively inexperienced with this sort of thing as well).
P.S. I used this for a little help: http://www.experiglot.com/2006/06/07/how-to-convert-from-an-annual-rate…]
Try calculating "d(1/12) = (1 + d(1))^(1/12) - 1. Then, the NPV = 61425 / [1+d(1/12)]^(7/12) + 165375 / [1 + d(1/12)]^(19/12)" in a calculator or excel. Doesnt work. What does work though is if you change the formula by not subtracting that 1 while converting the discount rate to a monthly rate. Not sure why. So, if anyone can comment on whether the follow formula is correct:
61425 @ 10% discount rate for 7 months:
NPV = 61425/((1+.1)^(1/12))^7 = 58103.
Thanks.
Should be:
NPV = 61,425/(1+(.1/12))^7 = 57,958.39
for those two values it should be as simple as:
= 61,425 / (1+r/12)^7 + 165,375 / (1+r/12)^19 etc etc
I think this is wrong. I don't think d(1/12) equals (1/12)d(1), i.e. I don't think the discount rate for one month is just (1/12) times the discount rate for one year.
Well, if you are converting the annual rate to a monthly rate, i.e. 5% ann --> 5%/12 = 0.004167 monthly, this rate should remain constant throughout the course (unless you expect to use a different discount rate at time 19 then you do at time 7). That being said, giving an annual rate of 5% the equation filled in should be:
= 61,425 / (1+0.004167)^7 + 165,375 / (1+0.004167)^19 NPV = 59,662.93 + 152,812.80 respectively
Who knows, maybe I'm missing something
I believe you're forgetting about compounding. If you invest $100 at a 5% annual rate, you'll receive $105. That's not the same as investing $100 for 12 months, at a monthly rate of 5%/12.
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