Question

Garland Inc. offers a new employee a single-sum signing bonus at the date of employment, June 1, 2021. Alternatively, the employee can receive $39,000 at the date of employment plus $10,000 each June 1 for five years, beginning in 2025. Assuming the employee's time value of money is 9% annually, what single amount at the employment date would make the options equally desirable?

Answer 1

Answer:$69,030

The employee can decide to receive a single amount of $69,030 at the employment date.

Explanation:

The time value of money is the idea that money is worth more now, than the same amount a year or five years from now. You can buy more with $10,000 today than you will be able to in 2021 or 2025.

The formula for calculating the present value of money is  

$PV =FV \frac{1 }{(1+r)^{n} }$

or

$PV = \frac{FV }{(1+r)^{n} }$

Where PV is the present value

FV is the future value ($10,000)

r is the time value of money (9% or 0.09) and

n is the number of periods   (2025 to 2029).

In this question,

2021 is period 0. In 2021, the employee receives 39,000. This is the present value = 39000

2022 is period 1

2023 is period 2

2024 is period 3

2025 is period 4. In 2025, the employee will receive 10,000 so the present value, PV = $10000\frac{1}{(1+0.09)^{4} }$

PV=10000 * 0.708 = 7080

2026 is period 5. In 2026, the employee will receive 10,000 so the present value, PV = $10000\frac{1}{(1+0.09)^{5} }$

PV=10000 * 0.650 = 6500

2027 is period 6. In 2027, the employee will receive 10,000 so the present value, PV = $10000\frac{1}{(1+0.09)^{6} }$

PV=10000 * 0.596 = 5960

2028 is period 7. In 2028, the employee will receive 10,000 so the present value, PV = $10000\frac{1}{(1+0.09)^{7} }$

PV=10000 * 0.547 = 5470

2029 is period 8. In 2029, the employee will receive 10,000 so the present value, PV = $10000\frac{1}{(1+0.09)^{8} }$

PV=10000 * 0.502 = 5020

In total, the present value = (39000 + 7080 + 6500  + 5960 + 5470 + 5020)

=69,030

The employee can decide to receive a single amount of $69030 at the employment date.

(You can also look up the values in a discount table and multiply them by the present value. Note that the first payment of $10,000 is in period 4, not 5. This is because 2021 is period 0)