Your grandfather would like to share some of his fortune with you. He offers to
ID: 2590704 • Letter: Y
Question
Your grandfather would like to share some of his fortune with you. He offers to give you money under one of the following scenarios (you get to choose):
1. $7,550 a year at the end of each of the next eight years
2. $48,350 (lump sum) now
3. $100,000 (lump sum) eight years from now
Requirement
Calculate the present value of each scenario using an 8% discount rate. Which scenario yields the highest present value? Would your preference change if you used a 10% discount rate?
1. $7,550 a year at the end of each of the next eight years
2. $48,350 (lump sum) now
3. $100,000 (lump sum) eight years from now
Explanation / Answer
Solution:
1.
i. PV = A (PVIFA @ I, n)
PV = 7,500 (PVIFA @ 8%, 8)
PV = 7,500 [(1.08^8-1)/ (0.08*1.08^8)]
PV = 7,500 (5.7466)
PV = $43,099.79
ii. PV = $48,350
iii. PV = $100,000/1.08^8
PV = $54,026.89
Scenario iii yield the highest present value.
When the discount rate is 10%,
i. PV = A (PVIFA @ I, n)
PV = 7,500 (PVIFA @ 10%, 8)
PV = 7,500 [(1.08^10-1)/ (0.08*1.08^10)]
PV = 7,500 (6.7101)
PV = $50,325.61
ii. PV = $48,350
iii. PV = $100,000/1.10^8
PV = $46,650.74
Scenario i has the highest present value.
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