calculating the present value of future cash flows

Question

A financial company advertises on television that they will pay you
$60,000 now in exchange for annual payments of $10,000 that you are expected to receive for a legal settlement over the next 10 years, If you estimate the time value ofmoney at 10 percent, would you accept this offer?

Answer 1

We can view this problem as one of depreciation.

 

You are comparing 60,000 now to 10,000 that depreciates at 10% each year over the next 10 years.

 

We know the value of $60,000 in hand (it's just $60,000, naturally), so now we need to compare it to the $10,000 each year for the next 10 years.

 

At year 1:

 

P₁ = 10,000

 

At year 2:

 

P₂ = P₁ + 10,000 * (0.90)              (the 0.90 is the 10% loss from 100%)

 

At year 3:

 

P₃ = P₂ + 10,000 * (0.90)^2          (the 0.90^2 is a 10% loss from 100% compounded twice)

 

and so on and so forth. We need to add all of these terms to see if they exceed $60,000

 

Written out, we have

 

P_T = 10,000 + 10,000 * (0.90) + 10,000 * (0.90)^2 + ... + 10,000 * (0.90)^9

 

or

 

P_T = 10,000 * (1 + 0.9 + 0.9^2 + 0.9^3 + ... 0.9^9)

 

 

What we have in this case is a finite summation of powers, such that

 

a * sigma (i = 1, n) for r^(i-1) = a * (1 - rⁿ) / (1 - r)

 

where a = 10,000, r = 0.9 and n = 10

 

10,000 * (1 - 0.9^(10)) / (1 - 0.9) = 10,000 * (1 - 0.34) / (0.1) = 65,140

 

So our expected gain from the 10 year plan is $65,140, which exceeds the offering of $60,000.

 

You would decline the offer.