In: Finance
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.
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