FINC 101 HW #1 – Due Tuesday, January 24th Suppose that you

FINC 101 HW #1 – Due Tuesday, January 24th
Suppose that you just won the lottery and they give you three different options to collect your winnings:
Option #1: $50,000/yr for the next 20 years
Option #2: $500,000 today + $500,000 in 10 years
Option #3: $25,000/yr for the next 35 years
If the interest rate is 10% per year, then which option is more valuable to you today? Be sure to show
your work.
Need to figure out the PV of all of these options, and choose the one with the highest value.
Option #1 – this is an annuity of $50,000/yr for 20 years, so I need to use the PVIFA table, or exhibit 1-D
in chapter 1.
PVIFA (10%, 20yrs) = 8.514
So, I take the annuity amount and multiply it by that factor: 50,000 x 8.514 = $425,700
Option #2 – this has two parts: a lump sum today and another lump sum in 10 years. Since I’m looking
for the PV, I don’t need to do anything to the lump sum that happens today because it’s already in PV
terms. But, I need to find the PV of the $500,000 that occurs in 10 years. This is a lump sum, so I’d want
to use the PVIF table, or exhibit 1-C in chapter 1.
PVIF (10%, 10yrs) = 0.386
So, the PV of the $500,000 in 10 years is 500,000 x 0.386 = 193,000
Add to that the $500,000 from today and you have $693,000
Option #3 – Similar to option #1, I’d use the PVIFA table, but I see that 35 years is not on the table. To
handle this, you’d find the PVIFA for 30 years and the PVIFA for 40 years, and take their midpoint:
PVIFA (10%, 30yrs) = 9.427
PVIFA (10%, 40yrs) = 9.779
Therefore, 9.603 is a good estimate of the PVIFA (10%, 35yrs):
25,000 x 9.603 = $240,075
So, option #2 is the most valuable.
Midpoint = 9.603