Hi
Been a while since I’ve used the good old BAII.
How can I solve this problem the fastest way possible on the calculator. I am looking to get PV of a series of CFs.
CF1 = $100k. Increases by 3% per year.
Discount rate 2.2%.
Time Horizon= 10years.
thanks for the help
although you could use a finance calculator, by adjusting the PMT (it is not 100,000 in this case),
N = 10 and I (even if you convert discount to interest rate, that is not the value you want to use), unless you pay very, very close attention to what you are doing, you are very likely to make a mistake in the calculation. it is far better imo to just do the summation manually, which is fairly trivial anyway.
You could use the CF worksheet to enter individual CFs, but that would be time consuming and error prone.
You could aslo use the TVM worksheet with I = (0.022 - 0.03) / 1.03 = -0.007769
You can be clever about this if you want to: you know how to get the answer if the payments continue forever (Gordon growth); a perpetuity.
So, figure out the present value of the perpetuity starting at time t = 1, figure out the present value of the perpetuity starting at time t = 11, and subtract the latter from the former.
Voilà!
To get you started, I’ll do the hard one: the PV of the perpetuity starting at time t = 1:
PV1 = 100,000 / (0.022 − 0.03) = −12,500,000
(Don’t worry about the fact that it’s negative; the final answer will be correct.)
Gordon growth assumes that the “dividends” ($100k in this case) grow at a slower pace relative to the discount rate. this is not the case for this problem.
the payments increase faster than the interest rate, which means if you tried to evaluate a perpetuity for this problem, you would find that the PV does not reach a limiting number, and is in fact unbounded. intuitively, one would expect that, because the rate of growth (3%) is slightly higher than the rate of interest (which is actually slightly above 2.2%), you would expect that an annuity that lasts for 10 years would be worth at least 10 x 100k = 1 million (and worth strictly more), while an annuity that lasts for 100 years would be worth at least 10 million (and strictly more) (in fact, a 10 year annuity-immediate would be worth 1,010,943.82 while a 100-year annuity would be worth 14,361,145.22). by taking the limit n -> infinity in the summation, one would find, as was already argued, that the summation does not reach a finite value and instead becomes infinity.
I’m aware of all of that.
Now . . . use the Gordon growth formula as I suggested and marvel at the sight of the correct answer; it works.