Question

I am having some trouble visualizing this present value question and have already put it on a timeline, but it's still not clear. I think I may be making it more complex than it really is, but here is the question and then I will explain why I am having problems.

At an annual interest rate of 6%, which would you prefer - three annual year-end cash flows of $250 each with the first cash flow one year from today or $668.25 today?

What is confusing me is how to treat the first cash flow since it is at the end of year 1. Do I bring the 3 year annuity back to the beginning of year 1 and then use the sum to do another present value calculation to bring the value of that sum back to year 0 or did I already bring it back to present value with the first calculation? Its confusing since the Present Value calculation is considered to be one period prior to the first annuity cash flow. Can you help explain? (Hopefully I am making sense).

So, my first PV calculation would look like this:

Rate 6%; Nper 3; Pmt -250. This would equal 668.25

Now, would I then need to bring this sum back to year zero by then doing another Present Value Calculation as follows?

Rate 6%, Nper 1, fvm -668.25

Answer 1

The formula for PV =PV(6%,3,-250,0)

It is used correctly to bring the future cash flows to PV at t=0

There is no need to do another level of calculation as the cash flow PV are already at    Year 0 level.

In the PV formula we are mentioning nper as 3 , that means it is taking all three period's cash flow to year 0 with discount rate 6%. So the correct amswer is $668.25 is the PV of the cash flows today.

I have used the PV of annuity formula as well that gives the same result:

Formula for present value of an anuuity = PV= A [ {(1+k)n-1}/k(1+k)n]
PV = Present value of Annuity
A = periodical Payment =$250
k=interest rate=6% pa
n=periods=3
PV =250*[(1.06^3-1)/6%*1.06^3]
PV =668.25

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