Question

Your required rate of return is 20% and your income tax is 0%. You have job offers from two different companies, say A and B. Company A offers a 5-year contract, with a signing bonus of $100 and an annual wage of $80 in the first year, which will grow 10% a year over the duration of the contract. Company B offers a 5-year contract, with a constant annual wage and a severance pay of $100 at the termination of the contract. Everything else equal (e.g., perks, location, co-workers), what is the minimum annual wage offered by Company B for which you should accept their offer over Company A’s offer?

Group of answer choices

$114.39

$120.03

$91.75

$136.89

$108.61

Answer 1

Present Value of Job A = Signing Bonus + PV of wage

                                 = $ 100 + [ 80 / 1.20 + ( 80 * 1.1 ) / 1.20² + ( 80 * 1.1² ) / 1.20³ + ( 80 * 1.1³ ) / 1.20⁴ + ( 80 * 1.1⁴ ) / 1.20⁵ ]

                                 = $ 100 + [ { (80/1.20) * (1 - ( 1.1 / 1.20 )⁵) } / ( 1 - ( 1.1 / 1.20 ) ) ]    Sum of GP = a * ( 1 - rⁿ ) / ( 1 - r ) where a = first term and r = common ratio

   = $ 100 + [ { 66.6667 * ( 1 - 0.64723 ) } / 0.083333

                                 = $ 100 + $ 282.22

                                 = $ 382.22

Present Value of Job A = Present value of Job 2

Let us assume company B pays X amount every year

382.22 = X * PVAF(r, n) + Severance pay * PVIF(r, n)

382.22 = X * PVAF(20%, 5) + 100 * PVIF(20%, 5)

382.22 = X * 2.9906 + 100 * 0.4019

382.22 = X * 2.9906 + 40.19

X * 2.9906 = 382.22 - 40.19

X = $ 114.37

Company B should pay $ 114.37 per year to cope with company A.