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.

option (A) $69,035

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 ×

on substituting the respective values, we get

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

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

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