Question

In: Economics

Suppose you are looking forward to the future and trying to decide what to do. Suppose...

Suppose you are looking forward to the future and trying to decide what to do. Suppose that you have a job that is offering you $30, 000 for the first three years, $40,000 for the next 3 years, and $60,000 per year every year until you retire after 20 years. Alternatively, if you get your masters degree you pay $20,000 for the next two years. Then, you will be hired for $65,000 per year for every year after that for 18 years.
When is it optimal to get your masters degree? (Explain using different rates)

Expert Solution

We will find out the net present worth of cash flows in both the options given at different rates.

I randomly select 10% as rate of interest and look at the net present worth in both the cases as given

Rate of interest=	10%
	Case 1, Accept Job		Case 2, Go for Master's Degree
Year, n	Cash Flow, Cf1	PV1, Cf/(1+i)^n	Cash Flow, Cf2	PV2, Cf/(1+i)^n
1	30000	27272.73	-20000	-18181.82
2	30000	24793.39	-20000	-16528.93
3	30000	22539.44	65000	48835.46
4	40000	27320.54	65000	44395.87
5	40000	24836.85	65000	40359.89
6	40000	22578.96	65000	36690.81
7	60000	30789.49	65000	33355.28
8	60000	27990.44	65000	30322.98
9	60000	25445.86	65000	27566.35
10	60000	23132.60	65000	25060.31
11	60000	21029.63	65000	22782.10
12	60000	19117.85	65000	20711.00
13	60000	17379.86	65000	18828.18
14	60000	15799.88	65000	17116.53
15	60000	14363.52	65000	15560.48
16	60000	13057.75	65000	14145.89
17	60000	11870.68	65000	12859.90
18	60000	10791.53	65000	11690.82
19	60000	9810.48	65000	10628.02
20	60000	8918.62	65000	9661.84
Net Present worth		398840.09		405860.98

NPW is higher in case of choosing masters degree. We find that choosing master's degree is preferable at 10% interest rate.

Let us see the scenario at 11%

Rate of interest=	11%
	Case 1, Accept Job		Case 2, Go for Master's Degree
Year, n	Cash Flow, Cf1	PV1, Cf/(1+i)^n	Cash Flow, Cf2	PV2, Cf/(1+i)^n
1	30000	27027.03	-20000	-18018.02
2	30000	24348.67	-20000	-16232.45
3	30000	21935.74	65000	47527.44
4	40000	26349.24	65000	42817.51
5	40000	23738.05	65000	38574.34
6	40000	21385.63	65000	34751.65
7	60000	28899.50	65000	31307.80
8	60000	26035.59	65000	28205.22
9	60000	23455.49	65000	25410.11
10	60000	21131.07	65000	22891.99
11	60000	19037.00	65000	20623.42
12	60000	17150.45	65000	18579.65
13	60000	15450.86	65000	16738.43
14	60000	13919.69	65000	15079.66
15	60000	12540.26	65000	13585.28
16	60000	11297.53	65000	12238.99
17	60000	10177.96	65000	11026.12
18	60000	9169.33	65000	9933.44
19	60000	8260.66	65000	8949.05
20	60000	7442.03	65000	8062.20
Net Present worth		368751.78		372051.84

NPW is higher in case of choosing masters degree. We find that choosing master's degree is preferable at 11% interest rate.

Let us see the scenario at 12%

Rate of interest=	12%
	Case 1, Accept Job		Case 2, Go for Master's Degree
Year, n	Cash Flow, Cf1	PV1, Cf/(1+i)^n	Cash Flow, Cf2	PV2, Cf/(1+i)^n
1	30000	26785.71	-20000	-17857.14
2	30000	23915.82	-20000	-15943.88
3	30000	21353.41	65000	46265.72
4	40000	25420.72	65000	41308.68
5	40000	22697.07	65000	36882.75
6	40000	20265.24	65000	32931.02
7	60000	27140.95	65000	29402.70
8	60000	24232.99	65000	26252.41
9	60000	21636.60	65000	23439.65
10	60000	19318.39	65000	20928.26
11	60000	17248.57	65000	18685.95
12	60000	15400.51	65000	16683.88
13	60000	13750.45	65000	14896.32
14	60000	12277.19	65000	13300.29
15	60000	10961.78	65000	11875.26
16	60000	9787.30	65000	10602.91
17	60000	8738.66	65000	9466.88
18	60000	7802.38	65000	8452.57
19	60000	6966.41	65000	7546.94
20	60000	6220.01	65000	6738.34
Net Present worth		341920.16		341859.50

NPW is higher in case of choosing current job offer. We find that choosing current job offer is preferable in this case of 12% interest rate.

Now we have seen that going for masters was preferable at 11% interest rate but becomes unattractive at 12% interest rate.

Now let us consider a case of 11.9%

Rate of interest=	11.90%
	Case 1, Accept Job		Case 2, Go for Master's Degree
Year, n	Cash Flow, Cf1	PV1, Cf/(1+i)^n	Cash Flow, Cf2	PV2, Cf/(1+i)^n
1	30000	26809.65	-20000	-17873.10
2	30000	23958.58	-20000	-15972.39
3	30000	21410.71	65000	46389.86
4	40000	25511.71	65000	41456.54
5	40000	22798.67	65000	37047.84
6	40000	20374.15	65000	33107.99
7	60000	27311.19	65000	29587.12
8	60000	24406.78	65000	26440.68
9	60000	21811.25	65000	23628.85
10	60000	19491.73	65000	21116.04
11	60000	17418.88	65000	18870.46
12	60000	15566.47	65000	16863.68
13	60000	13911.06	65000	15070.31
14	60000	12431.69	65000	13467.66
15	60000	11109.64	65000	12035.44
16	60000	9928.19	65000	10755.53
17	60000	8872.37	65000	9611.74
18	60000	7928.84	65000	8589.58
19	60000	7085.65	65000	7676.12
20	60000	6332.13	65000	6859.80
Net Present worth		344469.34		344729.76

NPW is higher in case of choosing masters degree. We find that choosing master's degree is preferable at 11.9% interest rate.

We can say at choosing a maters is preferable option till the interest rate is 11.9%. At 12% option becomes unattractive.

It is optimal to go for masters degree till the interest rate is 11.9%

Note : More accuracy we can go for interest rates like 11.91% or 11.92% and see the pattern. We can use Excel functions like NPV and make full sensitivity report.

Rahul Sunny answered 1 year ago

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