Macroeconomics value over time

[Nickod777]

Homework Statement

Your favorite Aunt, Harriet of Harriet’s Psychic Services has suddenly died and in reading
her will for the disposition of her assets you discover that she has left you a choice as
to which of her assets you can receive. You can choose her stock portfolio which will
pay you a cumulative dividend of $10,000/yr. Payable quarterly but which is also
scheduled for liquidation at the end of the 4th Year for a prearranged amount of
$100,000, Or, you can receive the proceeds of her business which are $6000 every 6
months and which will continue for 5 years at which time the sole employee will
exercise her right to purchase the business for $85,000. Which would you choose
given that they have the same risk of default and that comparable investments
currently return 8%?

Homework Equations

FV=PV(1+r)^n
FV= Future value
PV= Present value
r= rate
n= number of times compounded in a year.

The Attempt at a Solution

I don't know exactly what I'm supposed to do actually. Apparently, we learned this formula in class, and we were supposed to discuss 6 problems today. No one did the 6th problem because it was very different.

I assume the first part is compounded quarterly because it's dispersed quarterly, with 8% return as it says as the end...

Correct me if I'm wrong. Starts at 0, add 2500 and goes 2550 because interest. 5050 because of payment, 5151 because interest. 7651 payment, 7804.02 interest. 10,304.02 payment, 10510.1 interest... etc. etc. until.. $ 47,530.18 +100k from liquidation...

I don't know if I did that right or not. I just plugged in 2500 then did interest, add in 2500 then interest, etc.

 

[Matterwave]

This is a discounted cash flow problem. You can't really just add up what is the total money netted by each investment because if one investment pays out earlier than the other one, then that investment is preferred even if it pays out slightly less. There's no interest payments on either investment specified in the problem. The 8% a year rate is for OTHER similar investments, and so you use that as the discount rate (it is r).

The way to think about this is to use the future value of all the payments to find the present value and then compare the present value.

In your equation FV=PV(1+r)^n, the n is actually the number of years, where r is a yearly rate (8% in this problem). For a compound interest rate the equation is FV=PV(1+r/m)^(n*m) where m is the number of times compounded per year.

So, look at all the payments from both investments. In year 1 investment A gives you $10,000, in year 2 also $10,0000. The present value of those 2 payments for investment A is PV=10,000/(1+.08/4)^(1*4)+10,000/(1+.08/4)^(2*4).

Can you add up all the other future values to give 1 present value for investment A? Then do the same thing for investment B and see which one has greater present value.