book 6 exam 2 pm question

An investor wants to receive $10,000 a year for ten years with the first payment starting five years from today. If the investor can earn a 14% annual return, the amount that she will have to invest today is closet to: a. 27,091 b. 30,884 c. 52,161 d. 73,667 The correct answer is b. but I will get the answer A by all means. the following is my calc: N=10, PMT=10,000, FV=0, I/Y=14 ===>> PV5= 52,161===>> PV=52,161/(1.14^5)=27,091 anything wrong in calc? thx

Use N =4 in the second calculation as 4th year’s end= 5th year begining.

I don’t have my HP handy, but if you are buying the annuity at the end of 5 years, and you recieve annuity payment 1 on that day, you need to do an annuity due calculation to come up with that PV in the first part.

oh, that makes sense, thanks for the answer

First you value the annuity as $52,161. That’s the value four years from today. The ordinary annuity discounting formula assumes the first cash flow is one year away (so applying the ordinary annuity formula to cash flows that start in five years gives you a PV as of four years from today). Then you discount by four years at 14% to arrive at the answer of $30,884. There are sure to be some of these timing tricks on the test; drawing a timeline is helpful.