Question

Garland Inc. offers a new employee a single-sum signing bonus at the date of employment, June 1, 2018.

Alternatively, the employee can receive $39,000 at the date of employment plus $10,000 each June 1 for five years, beginning in 2022.

Assuming the employee's time value of money is 9% annually, what single amount at the employment date would make the options equally desirable?(A) $69,035. (B) $65,855.(C) $40,855.(D) $44,035.

Answer 1

option (A) $69,035

Step-by-step explanation:

Data provided in the question:

Amount received at the time of joining = $39,000

Amount received each year = $10,000

Duration, n = 5 years

Time value of money, r = 9% = 0.09

Now,

The single-sum equivalent

= $39,000 + Present value of a $10,000 deferred annuity

also,

Present value of the deferred annuity = $10,000 ×
`[(1-(1)/((1+r)^n))/(r)]*(1+r)`

on substituting the respective values, we get

Present value of the deferred annuity = $10,000 ×
`[(1-(1)/((1+0.09)^5))/(0.09)]*(1+0.09)`

or

Present value of the deferred annuity = $10,000 × 4.23972

= $42,397

Equivalent amount at the time of joining of the differed annuity i.e n = 4 years before

= $42,397 × [ 1 ÷ (1 + r )ⁿ]

= $42,397 × [ 1 ÷ (1 + 0.09 )⁴]

= $42,397 × 0.70843

= $30,035

Hence,

The single-sum equivalent = $39,000 + $30,035

= $69,035

Hence,

The answer is option (A) $69,035