1. Anton could take professional development classes this year. The classes will cost him $22,000. If he takes the classes, he will make $1,000 a year more in his salary for the rest of his long career. If the yearly interest rate is 5%, should Anton take the classes? Show your work
To determine if Anton should take the professional development classes, we will calculate the net present value (NPV) of the investment.
The NPV formula is:
NPV = (Cash inflows / (1 + interest rate)^year) - Initial investment
In this case, the initial investment is $22,000, and the cash inflow is an additional $1,000 in salary every year for the rest of Anton's long career. Since Anton's long career is not specified, we will assume it is 25 years.
The interest rate is 5%, so we need to divide it by 100 to convert it to decimal form: 5% / 100 = 0.05
Plugging the numbers into the NPV formula:
NPV = ($1,000 / (1 + 0.05)^25) - $22,000
Calculating the present value of $1,000:
PV = $1,000 / (1 + 0.05)^25 = $397.45 (rounded to the nearest cent)
Calculating the NPV:
NPV = $397.45 - $22,000
NPV = -$21,602.55
The NPV is negative, which means that the investment is not expected to return a positive value. Therefore, Anton should not take the professional development classes.
To determine whether Anton should take the professional development classes, we can compare the cost of the classes with the additional income he would earn over his long career.
First, we calculate the present value of Anton's additional income using the formula for present value of an ordinary annuity:
PV = PMT × (1 - (1 + r)^(-n)) / r
where:
PV = present value
PMT = annual income increase
r = discount rate (interest rate)
n = number of years in the career
Given that the annual income increase is $1,000, the discount rate is 5% (0.05), and Anton has a long career ahead, we can assume n = 30 years.
PV = $1,000 × (1 - (1 + 0.05)^(-30)) / 0.05
≈ $1,000 × (1 - 0.434) / 0.05
≈ $1,000 × 0.566 / 0.05
≈ $11,320
The present value of the additional income Anton would earn over his long career is approximately $11,320.
Next, we compare the present value of the additional income with the cost of the classes. If the present value of the additional income is greater than the cost of the classes, Anton should take the classes.
In this case, the cost of the classes is $22,000, which is greater than the present value of the additional income ($11,320). Therefore, Anton should NOT take the classes, as he would not recover the cost in additional income.