Question

istina just won the lottery, and she must choose among three award options. She can elect to receive a lump sum today of $64 million, to receive 10 end-of-year payments of $9.9 million, or to receive 30 end-of-year payments of $5.9 million. If she thinks she can earn 7% percent annually, which should she choose? -Select- If she expects to earn 8% annually, which is the best choice? -Select- If she expects to earn 9% annually, which option would you recommend? -Select- Explain how interest rates influence her choice.

Answer 1

We need to compare present values of all 3 options to choose the best option.

She should choose to receive 30 end-of-year payments of $5.9 million if she can earn 7% percent annually because this option has the highest present value.

Option 1	Option 2	Option 3
		Annual payments	$9.90	Annual payments	$5.90
		No. of years	10	No. of years	30
		Future value	$0	Future value	$0
		Interest rate	7%	Interest rate	7%
Present value	$64	Present value	$69.53	Present value	$73.21

Calculation

If she expects to earn 8% annually then she should choose to receive 10 end-of-year payments of $9.9 million because this option has the highest present value.

Option 1	Option 2	Option 3
		Annual payments	$9.90	Annual payments	$5.90
		No. of years	10	No. of years	30
		Future value	$0	Future value	$0
		Interest rate	8%	Interest rate	8%
Present value	$64	Present value	$66.43	Present value	$66.42

Calculation

If she expects to earn 9% annually then she should choose to receive 10 end-of-year payments of $9.9 million because this option has the highest present value.

Option 1	Option 2	Option 3
		Annual payments	$9.90	Annual payments	$5.90
		No. of years	10	No. of years	30
		Future value	$0	Future value	$0
		Interest rate	9%	Interest rate	9%
Present value	$64	Present value	$63.53	Present value	$60.61

Calculation

Higher interest of 8% and 9% accumulated higher return on higher annual cash flow of $9.9 million. so, its present value is also higher than lower annual cash flow of $5.9 million.

If interest rates were lower than 7% for example say 5% or 6% than lower annual cash flow of $5.9 million would have accumulated more value due to its higher duration or no. of years of cash flows.