After a sterling year, your boss has decided to reward you. She has offered you three alternatives:
Take $28,000 right now.
Take $2,500 bonus per month for the next 12 months, starting next month. Take $16,000 at the end of six months and another $15,000 at the end of the year. If your discount rate is 6% per year on a monthly compounded basis, how much is the present value of your bonus?
- $29,656
- $29,047
- $28,000
- $30,176
Answer(s): A
Explanation:
The discount rate per period (1 month) = 6%/12 = 0.5%. The present value of alternative B is (using the annuity formula) 2,500/0.005*[1 - 1/1.005^12] = $29,047. The present value of alternative C is trickier, since the rate you have been given is compounded monthly. Therefore, the PV of C is 16,000/1.005^6 + 15,000/1.005^12 = $29,656. So you should take alternative C and your bonus is worth $29,656.