Can anyone help me with this question?

Kimberly has just won a $20 million lottery, which will pay her $1 million at the end of each year for 20 years. An investor has offered her $10 million for this annuity. She estimates that she can earn 10 percent interest, compounded annually, on any amounts she invests. She asks your advice on whether to accept or reject the offer. What will you tell her? (Ignore Taxes)

I am using PVA and getting that the ticket is worth 2,349,182.48 and she should reject the offer am I doing this correctly?

iamthetman

If you are getting that the PV of the annuity is about 2 million, why in the world would she reject an offer of 10 million??? If the offer is more than the present value then she should choose to accept the offer.

The way you are calculating the PV is wrong. There are 20 years of payments so you need to find the present value of each of those payments and then add them together to get the total present value. For example the present value of the first payment is 1 million/(1+interest) or 1/1.1 million. The present value of the second payment is 1/(1.1^2) million becuase the second payment is received 2 years later so it needs to be discounted back 2 years (at 10%) to the present time.

morgaine300

No, you don't need to calculate each payment separately. It's an annuity, so you can use annuity factors to do it all at once. However, whatever you are doing is not coming up with the right answer.

Is the PVA on a financial calculator or in Excel? I don't have that in Excel, but then I don't have present value of annuity in Excel at all. (I don't have something someone else mentioned either, so I'm beginning to wonder if I don't have some plugin installed or something.) Without knowing exactly what numbers are wanted and how you are to enter them, I can't really tell you exactly how to do it. (Just for instance, N can stand for total periods, or it can stand for periods per year. Different things use these differently. I use algebraic equations so I am not too familiar with what Excel does.)

In this case, since it's compounding annually, this should not be as difficult to figure out. Because of the annual compounding, periods and years would be the same. It's 20 either way. And you also do not have to adjust your interest rate, again because it's compounding annually and the 10% is annual. And 1,000,000 is your payments. But something is going wrong somewhere.

If I knew exactly what you were doing, I might be able to figure out what was wrong.

iamthetman

Of course you don't NEED to add up each payment separately because in math there are formulas for just about everything. But simply using a formula without understanding what it does is not the right way to go. Yeah, formulas make life easy but unless you understand what that formula is doing you won't be able to make the slight adjusts needed when the questions get a little trickier.

The formula for finding the present value of an annuity immediate without using a scientific calculator is P*(1-v^n)/i where v = 1/(1+i), P is the payment per year, n is the number of years and i is the interest rate per year. The formula is derived from the following series Pv + Pv^2 + ... + Pv^20.