Question

2. You just won a Million Dollar lottery and you can choose one of the following two options to claim your winning. If you choose Option A, you will receive $40,000 every year for 25 years (40,000 x 25 = $1,000,000 hence the name), with the first payment to occur one year from today. But you may also choose Option B, in which case you will receive a single payment of $600,000 today. The applicable tax rate for the annual payment from Option A is 15%, while the applicable tax rate for the single payment from Option B is 18%. The appropriate discount rate for both options is 5%. Which option is better from a strictly financial standpoint?

Answer 1

Option A - receive $40,000 every year for 25 years with tax rate 15 %

It means, after paying tax net amount received will be = 40,000 - 40,000*15%

= 34,000 $ each year

Option B - receive a single payment of $600,000 today with tax rate 18%

After paying tax net amount received will be = 600,000 - 600,000*18%

= $ 492,000

The present value of all the cash flow will be compared in both the options to find out which option is better.

Present value of cash inflow for option B = $ 492,000 (as it is received today)

In option A, Present value of cash inflow will be computed as the discounted cash flow for each year at 5 % discount rate.

The present value of all cash inflow can be calculated with help of factor for present value of future annuity table. When the amount of cash inflow per year and time period of each investment is same , this annuity table can be used to find the present value. Take the present value factor corresponding to the the discount rate and no, of year and multiply with the annual cash inflow.

The present value of future annuity factor at 5 % discount rate for 25 years is 14.094

Present value of cash inflow for option A = annual cash inflow * PVAF(5%,25)

= 34,000 * 14.094

= 479,196 $

---->The present value of cash inflow in case of option B is more than option A, hence option B is better.

Hope it helps !