Question

Congratulations, you won a lottery of $10 million! You are offered three options to receive your windfall:

A) A lump sum of $10 million received immediately

B) An annual payment of $500,000 for 30 years

C) A monthly payment of $50,000 for 30 years

a. If the discount rate is 7%, which option would you choose? Show your work.

b. Calculate the effective annual rate for option C.

Answer 1

Solution a:

For option A:
Present value of the lump sum amount is $10 million or $10000000

For option B:
Discount rate is 7%
Annual payment amount is $500000
Time period is 30 years
As the amount will be paid completely, the future value will be zero.
We can determine the present value of the cash flows using excel as follows:

So, the present value of the cash flows is $6,204,520.59

Н 1 Future value 2 Payment 500000 3 Discount rate 7% 4 Time period 30 5 Present value= ($6,204,520.59) 6 Formula used: PV(13,14,12,11)

For option C:
Monthly payment amount is $50000
Monthly discount rate=7%/12=0.005833333
Time period is 30 years
As the payment is made monthly, the number of periods is 30*12=360
As the amount will be paid completely, the future value will be zero.
We can determine the present value of the cash flows using excel as follows:

So, the present value of the cash flows is $7,515,378.70

1 Future value 2 Payment 50000 3 Discount rate 0.005833333 4 Time period 360 5 Present value= ($7,515,378.70) 6 Formula used: PV(L3,L4,L2,L1)

Answer: We see that, in the three options, we will get higher amount in option A. Hence, we would choose option A.

Solution b:
Given that;
Present value is $10 million or $1000000
Monthly payment is $50,000
Number of periods is 360
We can calculate the monthly rate using excel as:

AN 1 Present value 10000000 2 Future value 3 Payment -50000 4 Number of periods 360 5 Monthly rate= 0.003655928 6 Formula used: RATE(04,03,01,02)

So, we get the monthly rate as 0.003655928
Effective annual rate (EAR)=(1+Monthly rate)^12 -1
=(1+0.003655928)^12 -1
=(1.003655928)^12 -1
=1.044764119 -1
=0.044764119 or 4.48%

Answer: Hence, the effective annual rate for option C is 4.48%