Question

In: Finance

Suppose that, at age 30, you might wish to leave your job and pursue a master’s...

Suppose that, at age 30, you might wish to leave your job and pursue a master’s degree. If you choose to remain at your job, your employer would pay you $75k per year until retirement, at age 55. If you go back to the university, you would have to sacrifice 2 years of income, but once you graduate, you would receive $113k per year until you retire at age 55. The master’s program you are interested in costs $22k per year.

Note: The term “k” is used to represent thousands (× $1,000).

Required: At an opportunity cost of 9%, determine the percentage difference between your most and least profitable alternatives, with the least profitable option as the basis for your calculation.

Solutions

Expert Solution

Answer - We should go for masters degree

Without Masters - 736,693.47

With Masters - 872,471.49

Percentage increase = (872471.49 - 736693.47) / 736693.47 = 18.43%

Workings

Alternative A - Without Master Degree

Present Value of all the cash flows of 75K for 25 Years (55-30)

N = 25, I/Y = 9, PMT = 75K

CPT PV = 736693.47

Present Value of all the cash flows under alternative 1 = 736,693.47

Alternative B - With Master Degree

In Year 1&2 there will be a cash outflow of 22K

after that from year 3 we will start recieving 113k per year for 23 years (55-32)

Now we will calculate the present value of these cash flows and compare with alternative 1

Following is the cash flow table along with present value

Year Cash Flow Present value factor @ 9% Present Value
1 -22000 0.92 -20,183.49
2 -22000 0.84 -18,516.96
3 113000 0.77 87,256.73
4 113000 0.71 80,052.05
5 113000 0.65 73,442.25
6 113000 0.60 67,378.21
7 113000 0.55 61,814.87
8 113000 0.50 56,710.89
9 113000 0.46 52,028.34
10 113000 0.42 47,732.42
11 113000 0.39 43,791.21
12 113000 0.36 40,175.42
13 113000 0.33 36,858.19
14 113000 0.30 33,814.85
15 113000 0.27 31,022.80
16 113000 0.25 28,461.28
17 113000 0.23 26,111.27
18 113000 0.21 23,955.29
19 113000 0.19 21,977.33
20 113000 0.18 20,162.69
21 113000 0.16 18,497.88
22 113000 0.15 16,970.53
23 113000 0.14 15,569.30
24 113000 0.13 14,283.76
25 113000 0.12 13,104.37
Present value of Alternative 2 872,471.49

Present value under alternative 2 - 872471 which is greater than alternative 1 we should go for Masters degree

jeff jeffy answered 2 years ago
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