Question

The millionaire lottery winner won the $ 175,000,000 jackpot and has the option of receiving payments of $ 7,000,000 annually for 25 years beginning in year 1 or taking $ 109,355,000 today. At what interest rate? Are the two options equivalent?

Answer 1

Basically the idea behind solving this question is we have to find the rate of interst using which present value of annual cash flows of 7,000,000 is equal to 109,355,000

the rate of interest is 4%

which can be calculated using IRR function in excel of using a financial calculator as shown below

We can use a financial calculator to calculate the desired return

PV = -109,355,000

N = 25

PMT = 7,000,000

CPT I/Y = 4%

OR we can use IRR formulae

Step 1 - Concept of IRR

To solve this question we need to understand concept of IRR

IRR is the rate at which NPV of the project is zero (ie cash flow of the projects are equal to the initial investment)

We have to consider option 1 on recieving 7,000,000 annually for 25 years as inflows from a project

and will have to consider 109,355,000 as initial investment made in project today

Step 2 - Cash Flows

Therefore we have the following cash flows

Year	Cash Flow
0	-109,355,000
1	7,000,000
2	7,000,000
3	7,000,000
4	7,000,000
5	7,000,000
6	7,000,000
7	7,000,000
8	7,000,000
9	7,000,000
10	7,000,000
11	7,000,000
12	7,000,000
13	7,000,000
14	7,000,000
15	7,000,000
16	7,000,000
17	7,000,000
18	7,000,000
19	7,000,000
20	7,000,000
21	7,000,000
22	7,000,000
23	7,000,000
24	7,000,000
25	7,000,000

Step 3 - Calculation of IRR / Required interest rate

We will get the answer as 4%