The present value of the annuity can be solved with a calculator as
PMT = 29,000
n = 10
i% = ?
PV = ?
This is easily solved by trial and error. Start with say 10 percent. and you get
$210,000 for the perpetuity
$178,192 for the annuity. Therefore 10 percent is too low
at 12% the perpetuity is $175,000 and the annuity is $163,856, still too low.
at 14% the annuity exceeds the perpetuity. So it is between 12 and 14%
at 13.5%: P = 155,555; A = 154,266
at 13.7% they are only $150 apart so I would consider that close enough as the indifference point. You could try further to be precise to a hundredth of a percent, but it seems pointless.
You can, of course set 21,000 / i% = PV of annuity formula and try to solve for i%. It's complicated but you should get about 13.7%
The only way I know how is by trial and error.
Divide 21,000 by X%, change sign to negative, enter N at 10, and R at X% to get PMT, or Annuity of 29,000.
The answer I get is 13.745%.
A - 21,000 / .13745 = 152,782.83
B - PV 152,782.83, N 10, R 13.745% computes to an Annuity of 28,999.61.
At 13.7444%, Annuity = 29,000.20
Your financial planner offers you two different investment plans. Plan A is a $21,000 annual perpetuity. Plan B is a 10-year, $29,000 annual annuity. Both plans will make their first payment one year from today.
At what discount rate would you be indifferent between these two plans?
I have tried setting equal the annual perpetuity formula to the annual annuity formula and still cannot get the right answer.
