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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.