An engineering student has just finished the freshman year and has received an offer of $20,000 per year in a full-time job. with prospects of salary increasing 3 % per year until retirement after 33 years. If employment is taken, the student will likely not finish his engineering degree. Tuition and other costs are $10,000 next year, increasing at 7% per year. A starting salary of $45.000 could be expected upon graduation from the fouryear program. Salary increases in the engineering job are estimated at 4% per year until retirement after 30 years. Required:
On the basis of economics alone, should the student take the job now or finish college? Analyze as two mutually exclusive alternatives and solve with present worth analysis. Interest rate is 7%.

Since the $860,886.33 which is the present worth of net salary if he finishes his engineering degree is greater than the $357,788.81 which is the present worth of net salary if he does NOT finish his engineering degree, the student should finish college.

Explanation:

This can be dermined based on the following 3 steps:

Step 1: Calculation of present worth of net salary if he does NOT finish his engineering degree

This can be calculated using the formula for calculating the present worth (PW) of a growing annuity as follows:

PWN = (P / (r - g)) * (1 - ((1 + g) / (1 + r))^n) (1)

Where;

PWN = present worth of net salary if he does NOT finish his engineering degree = ?

P = Annual salary = $20,000

r = interest rate per year = 7%, or 0.07

g = growth rate of salary = 3% or 0.03

n = number of years = 33

Substituting the values into equation (1), we have:

PWN = ($20,000 / (0.07 - 0.03)) * (1 - ((1 + 0.03) / (1 + 0.07))^33)

PWN = $357,788.81

Step 2: Calculation of present worth net salary if he finishes his engineering degree

Calculation of the present worth of tuition and other costs

This can be calculated using the formula for calculating the present worth (PW) of a growing annuity as follows:

PWT = (P / (r - g)) * (1 - ((1 + g) / (1 + r))^n) (2)

Where;

PWT = present worth tuition and other costs = ?

P = Tuition and other costs next year = $10,000

r = interest rate per year = 7%, or 0.07

g = growth rate of tuition and other costs = 7% or 0.07

n = number of years = Number of years for engineering degree - One year already spent = 4 - 1 = 3

Substituting the values into equation (2), we have:

PWT = (10,000 / (0.07 - 0.07)) * (1 - ((1 + 0.07) / (1 + 0.07))^3)

PWT = undefined or 0

Note: The PWT is undefined because r = g here. Therefore, it should not be considered in the further analysis.

Calculation of the present worth of salary after graduation

This can be calculated using the formula for calculating the present worth (PW) of a growing annuity as follows:

PWG = (P / (r - g)) * (1 - ((1 + g) / (1 + r))^n) (3)

Where;

PWG = present worth of salary after graduation = ?

P = Starting salary = $45,000

r = interest rate per year = 7%, or 0.07

g = growth rate of salary = 4% or 0.04

n = number of years = 30

Substituting the values into equation (3), we have:

PWG = ($45,000 / (0.07 - 0.04)) * (1 - ((1 + 0.04) / (1 + 0.07))^30)

PWG = $860,886.33

Step 3: Decision

Present worth of net salary if he does NOT finish his engineering degree = $357,788.81

Present worth of net salary if he finishes his engineering degree = present worth of salary after graduation = $860,886.33

Since the $860,886.33 which is the present worth of net salary if he finishes his engineering degree is greater than the $357,788.81 which is the present worth of net salary if he does NOT finish his engineering degree, the student should finish college.