Question from Schweser:
What is the maximum an investor should be willing to pay for an annuity that will pay out $10,000 at the beginning of each of the next 10 years, given the investor wants to earn 12.5%, compounded annually?
a) $52,285
b) $62,285
c) $55,364
Why is the answer b)? I used the TVM function on my calculator and for I/Y=12.5%, N=10, FV=0 and PMT=10,000 and got $55,364.
You need to put your calculator in to BEG mode to get the correct answer.
Note the wording in the question “… will pay out $10,000 at the beginning of each”
Alternately, since you’re off by one period (END mode instead of BEGIN mode), multiply your answer by 1.125 (i.e. increase it by one year’s interest rate).
If the first cash flow occurs at the beginning of period 1 then surely that should be discounted at 12.5%? I don’t understand how I’m off by one period. Can anyone please explain?
You can post the following figures into your BAII financial calculator to get the ans.
PV = Compute
FV = 0
PMT = 10000
I/Y = 12.5
P/Y = 1
N= 10
You will get the desired ans.
I doubt it.
That’s what I did but I got the wrong answer. Doing it this way gives you option c which is incorrect.
If you’re ever in doubt about a TVM question, draw a timeline.
In regards to your question, the cash flow is already at the beginning of period 1 (ie. It is now, time 0). We don’t need to discount this because it is already the present value.
So for example, let’s say the investor puts in a lump sum on January 1st, 2014. In an annuity-due, he also gets back PMT on that very same day, January 1st, 2014 (If he gets this back right away it is not discounted). In a regular annuity, he would get his first PMT on December 31, 2014 (This gets discounted one year at 12.5%).
It is discounted at 12.5%, but for zero years.
This is a weird one: you’re buying the annuity today, and as soon as you buy it, the seller says, “Oh, and here’s $10,000 of your money back!” Immediately. You’re left asking yourself, “Why didn’t I just buy a 9-year annuity with the first payment starting one year from today? It amounts to the same thing, and I wouldn’t be walking around with $10,000 in cash right now, risking getting mugged.”
How can it be discounted for 0 years? If we are at the beginning of t = 0 and the payment is at the beginning of t = 1, then 1 full year will pass before I get the payment hence it should be discounted by one year.
There is no “beginning of t = 1”; t represents a _ point in time _, not a span of time. The first payment is at the beginning of year 1, and the beginning of year 1 is t = 0. (The end of year 1 is t = 1.) The point is that the first payment is made immediately, at time t = 0.