Evaluating lump sums and annuities Crissie just won the lottery, and she must ch
ID: 2427491 • Letter: E
Question
Evaluating lump sums and annuities
Crissie just won the lottery, and she must choose between three award options. She can elect to receive a lump sum today of $63 million, to receive 10 end-of-year payments of $9.6 million, or 30 end-of-year payments of $5.6 million.
If she thinks she can earn 7% percent annually, which should she choose?
-Select-She should accept the 30-year payment option as it carries the highest present valueShe should accept the lump-sum payment option as it carries the highest present valueShe should accept the 10-year payment option as it carries the highest present valueShe should accept the lump-sum payment option as it carries the highest future valueItem 1
If she expects to earn 8% annually, which is the best choice?
-Select-She should accept the lump-sum payment option as it carries the highest present valueShe should accept the 30-year payment option as it carries the highest present valueShe should accept the 10-year payment option as it carries the highest present valueShe should accept the lump-sum payment option as it carries the highest future valueItem 2
If she expects to earn 9% annually, which would you recommend?
-Select-She should accept the lump-sum payment option as it produces the highest present valueShe should accept the 30-year payment option as it produces the highest present value.She should accept the 10-year payment option as it produces the highest present valueShe should accept the 30-year payment option as it produces the highest future valueItem 3
Explain how interest rates influence the optimal choice.
-Select-The higher the interest rate, the more valuable it is to get money rapidlyThe lower the interest rate, the more valuable it is to get money rapidlyThe higher the discount rate, the higher the more distant cash flows are valuedInterest rates do not influence the optimal choice in any wayInterest rates and the present value of cash flows are positively related
Explanation / Answer
Alternative 1: Receive 63M today
Present value of ALt 1 = 63 Million
Alternative 2 : 10 end of year payments of 9.6 million
Present value of Alt 2 ( When i =7%) = 9.6 Million * PVIFA( 10 yr , 7%) = 9.6 * 7.0236 = 67.43 Million
Present value of Alt 2 ( When i =8%) = 9.6 Million * PVIFA( 10 yr , 8%) = 9.6 * 6.7101 = 64.42 Million
Present value of Alt 2 ( When i =9%) = 9.6 Million * PVIFA( 10 yr , 9%) = 9.6 * 6.4177 = 61.61 Million
Alternative 3 : 30 end of year payments of 5.6 million
Present value of Alt 3 ( When i =7%) = 5.6 Million * PVIFA( 30 yr , 7%) = 5.6 * 12.409 = 69.49 Million
Present value of Alt 3 ( When i =8%) = 5.6 Million * PVIFA( 30 yr , 8%) = 5.6 * 11.2578 = 63.04 Million
Present value of Alt 3 ( When i =9%) = 5.6 Million * PVIFA( 30 yr , 9%) = 5.6 * 10.2737= 57.53 Million
When Interest rate = 7 % ; it is advisable to take 30 end of year payments of 5.6 Million
When interest rate = 8% ; it is advisable to take 10 end of year payments of 9.6 Million
When interest rate = 9% ; it is advisable to take the lump sum today
The higher the interest rate, the more valuable it is to get money rapidly because more cah flow in the earlier years leaves you with an opportunity to reinvest the proceeds at higher rates today and thereby earn more interest. This can be proved by seeing that in Case 3: when i = 9% ; 30 end of year payment scenario has the least present value.
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