Justin Slugger is about to sign a contract with the Columbus Homers. The professional baseball team has given him two options of joining the team with a lumpsum of $20,000,000 or an annuity of $2,500,000 for 15 years. The lumpsum will be paid one year after the signing day if Paul takes the first option. The first annuity will be paid on the signing day if he instead takes the second option. Which is the better option for Paul if an annual interest rate of 10% is utilized for the annuity? Do not consider taxes.

To decide the better option, we need to calculate the present value of option 1 which is the lumpsum and the present value of option 2 which is an annuity and compare these values.

The present value of option 1 can be calculated as follows,

Option 1 Present value = Future value / (1 + r)^t

Where,

r is the rate of return of interest or discount rate
t is the time in years

Option 1 Present value = 20,000,000 / (1+0.1)^1

Option 1 Present value = $18,181,818.18

The present value of option 2 can be calculate using the formula of present value of annuity due as the payments will be made at the start of the period. The formula for present value of annuity due is attached.

Option2 Present value = 2,500,000 + 2,500,000 * [(1 - (1+0.1)^-14) / 0.1]

Option2 Present value = $20,916,718.64

Option 2 which is an annuity for 15 years is a better option as it has a higher present value than option 1.