A start-up company is in need of an industrial engineer and they want to hire yo

Question

A start-up company is in need of an industrial engineer and they want to hire you on a 3 year contract. They will pay you a base salary of $50,000 each year. In addition they will pay you bonuses, and the company is evaluating the following options from which you could choose:

Option 1: $5,000 at the end of year 1, $7,000 at the end of year 2, $15,000 at the end of year 3

Option 2: a one-time signing bonus of $X paid at the beginning of your employment (i.e. at time 0)

          Assuming that you will put all this money in a secure investment that pays 5% compounded annually, at what value of $X in Option 2 will you be economically indifferent in choosing between these options?

Explanation / Answer

Option 1:

Amount after 1 year = $5,000

Amount after 2 year = $7,000 + $5,000 × 105% = $12,250

Amount after 3 year = $15,000 + $12,250 × 105% = $27,862.5

Option 2:

Amount = Principal (1 + interest rate)^3

$27,862.5 = Principal (1 + 0.05)^3

Principal = $27,862.5 / 1.157625

               = $24,068.68

Answer: The value of $X in option 2 would be $24,068.68.

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