Quaker State Inc.offers a new employee a lump-sum signing bonus at the date of employment.Alternatively,the employee can take $8,000 at the date of employment plus $20,000 at the end of each of his first three years of service.Assuming the employee's time value of money is 10% annually,what lump sum at employment date would make him indifferent between the two options?
A)$23,026.
B)$57,737.
C)$62,711.
D)None of these answer choices is correct.

Question

Quizplus · Accepted Answer

We need to find out the Present Value (PV) of the second option and compare it with the lump-sum option. Let x be the lump-sum amount at employment date.

PV of $8,000 at year 1 = $8,000/(1+10%)^1 = $7,272.73
PV of $20,000 at year 2 = $20,000/(1+10%)^2 = $16,528.93
PV of $20,000 at year 3 = $20,000/(1+10%)^3 = $13,537.19

Total PV of the second option = $7,272.73 + $16,528.93 + $13,537.19 = $37,338.85

Now, we need to find out the lump-sum amount (x) that has the same PV as $37,338.85.

x = $37,338.85/(1+10%)^1 = $33,944.41

Therefore, the employee would be indifferent between the two options if Quaker State Inc. offers a lump-sum amount of $33,944.41 at the date of employment. Since this option is not one of the answer choices, the closest option is B, which is $57,737. This option is higher than the actual amount needed to make the employee indifferent because Quaker State Inc. wants to incentivize the employee to choose the lump-sum option.