Question

suzanne is a recent chemical engineering graduate who has been offered a 5-year contract at a remote location. she has been offered two choices. the first is a fixed salary of $80,000 per year. the second has a starting salary of $70,000 with annual raises of 8% starting in year 2. (for simplicity, assume that her salary is paid at the end of the year, just before her annual vacation.) if her interest rate is 10%, which should she take? plus

Answer 1

• $70,000 with raises

Step-by-step explanation:

You want to know if a series of 5 fixed annual payments of $80,000 is a better offer than a series of 5 payments beginning with $70,000 and increasing at 8% per year. The interest rate is assumed to be 10%.

Present value

We can compare the present values of the two offers by discounting each series of payments to its equivalent present value at an interest rate of 10%. The attached spreadsheet makes those calculations.

The sum of discounted values of the series starting with $70,000 is greater, so that offer is the better offer.

__

Additional comment

The salary value is discounted by the factor 1.10^n, where n is the year number. Effectively, a 10% discount is applied to the first payment in each series—equivalent to it being made at the end of the year.

The increasing series is the better deal, because its discounted value effectively decreases about 2% per year, where the discounted value of the fixed payments decreases at 10% per year. The fixed series already has a lower value payment in the 3rd year. After 5 years, the difference is not great, but it is increasing.

<95141404393>