Question

Travis Daniels has just graduated from Matchbook State University and is deciding whether to pursue his master's degree. Travis is now 20 years old.  He has just been offered a job with Schmultz, Inc. at an annual salary of $45,000 with anticipated annual increases (for inflation), of 3%. Travis anticipates working only through to his planned retirement, on his 65th birthday. Were Travis to defer the job acceptance and attend graduate school at Matchbook State, the tuition would cost $45,000 annually (paid at the beginning of each of the next three years), with a moderate 5% increase in tuition for the 2^ndand 3^rdyears. Once he completes his three year Master’s program, he could be reasonably assured of a better position with Schmultz, Inc. starting at $60,000 per year (including an anticipated annual increase of the same 3%). Assuming that the salaries are paid at the end of each year, is the pursuit of Travis's master's degree a worthwhile investment, when factoring an interest rate of 6%, or should he start now.

Answer 1

This formula will be used for PV calculation. At the end, table is also given for better understanding

Option 1 - If Travis Danies Select not to pursue his master's degree and start job now.

Calculation of Present value of net inflow

PMT	45000
i	6%
g	3%
n	45
PV	=45000*(1-((1+3%)^45*(1+6%)^-45))/(6%-3%)
	1,087,900.17

Option 2 - If Travis Danies Select to pursue his master's degree by defering the Job Opportunity.

Calculation of Present value of net inflow Considering the tuition fees outflow

PV of Tuition fees outflow -
PMT	45000
i	6%
g	5%
n	3
Therefore PV of Tuition fees =	=45000*(1-((1+5%)^3*(1+6%)^-3))/(6%-5%)
	126,160.77
PV of Salary Inflow at 0
PMT	60000
i	6%
g	3%
n	42
PV at end of 3 year	=60000*(1-((1+3%)^42*(1+6%)^-42))/(6%-3%)
	1,401,109.96
PV at year 0	=1401109.96/(1.06)^3
	1,176,398.94
There for net Inflow = PV of Salary Inflow - Pv of tuition fees outflow
	=1176398.94-126160.77
	1,050,238.17
Comparison	PV
Option 1	1,087,900.17
Option 2	1,050,238.17

Its better to take Option 1(start job now) as Present Value is higher. Pursuit of Travis's master's degree is not a worthwhile investment

Table for understanding

Option 1 - If Travis Danies Select not to pursue his master's degree and start job now.

Year	Cash Flow	PVF @ 6%p.a	PV (PVF*Cash Flow)
1	45,000.00	0.943396226	42,452.83
2	46,350.00	0.88999644	41,251.33
3	47,740.50	0.839619283	40,083.84
4	49,172.72	0.792093663	38,949.40
5	50,647.90	0.747258173	37,847.05
6	52,167.33	0.70496054	36,775.91
7	53,732.35	0.665057114	35,735.08
8	55,344.32	0.627412371	34,723.71
9	57,004.65	0.591898464	33,740.97
10	58,714.79	0.558394777	32,786.03
11	60,476.24	0.526787525	31,858.13
12	62,290.52	0.496969364	30,956.48
13	64,159.24	0.468839022	30,080.36
14	66,084.02	0.442300964	29,229.02
15	68,066.54	0.417265061	28,401.79
16	70,108.53	0.393646284	27,597.96
17	72,211.79	0.371364419	26,816.89
18	74,378.14	0.350343791	26,057.92
19	76,609.49	0.33051301	25,320.43
20	78,907.77	0.311804727	24,603.82
21	81,275.01	0.294155403	23,907.48
22	83,713.26	0.277505097	23,230.86
23	86,224.65	0.261797261	22,573.38
24	88,811.39	0.246978548	21,934.51
25	91,475.73	0.232998631	21,313.72
26	94,220.01	0.219810029	20,710.50
27	97,046.61	0.207367952	20,124.36
28	99,958.01	0.195630143	19,554.80
29	102,956.75	0.184556739	19,001.36
30	106,045.45	0.174110131	18,463.59
31	109,226.81	0.16425484	17,941.03
32	112,503.62	0.154957397	17,433.27
33	115,878.72	0.146186223	16,939.87
34	119,355.09	0.137911531	16,460.44
35	122,935.74	0.130105218	15,994.58
36	126,623.81	0.122740772	15,541.90
37	130,422.52	0.115793181	15,102.04
38	134,335.20	0.10923885	14,674.62
39	138,365.26	0.103055519	14,259.30
40	142,516.21	0.097222188	13,855.74
41	146,791.70	0.091719045	13,463.59
42	151,195.45	0.086527401	13,082.55
43	155,731.32	0.081629624	12,712.29
44	160,403.25	0.077009079	12,352.51
45	165,215.35	0.072650074	12,002.91
Total			1,087,900.17

Option 2 - If Travis Danies Select to pursue his master's degree by defering the Job Opportunity.

Year	Cash Flow	PVF @ 6%p.a	PV (PVF*Cash Flow)
1	(45,000.00)	0.943396226	(42,452.83)
2	(47,250.00)	0.88999644	(42,052.33)
3	(49,612.50)	0.839619283	(41,655.61)
4	60,000.00	0.792093663	47,525.62
5	61,800.00	0.747258173	46,180.56
6	63,654.00	0.70496054	44,873.56
7	65,563.62	0.665057114	43,603.55
8	67,530.53	0.627412371	42,369.49
9	69,556.44	0.591898464	41,170.35
10	71,643.14	0.558394777	40,005.15
11	73,792.43	0.526787525	38,872.93
12	76,006.20	0.496969364	37,772.76
13	78,286.39	0.468839022	36,703.72
14	80,634.98	0.442300964	35,664.93
15	83,054.03	0.417265061	34,655.55
16	85,545.65	0.393646284	33,674.73
17	88,112.02	0.371364419	32,721.67
18	90,755.38	0.350343791	31,795.59
19	93,478.04	0.33051301	30,895.71
20	96,282.39	0.311804727	30,021.30
21	99,170.86	0.294155403	29,171.64
22	102,145.98	0.277505097	28,346.03
23	105,210.36	0.261797261	27,543.78
24	108,366.67	0.246978548	26,764.24
25	111,617.67	0.232998631	26,006.77
26	114,966.20	0.219810029	25,270.72
27	118,415.19	0.207367952	24,555.52
28	121,967.65	0.195630143	23,860.55
29	125,626.68	0.184556739	23,185.25
30	129,395.48	0.174110131	22,529.06
31	133,277.34	0.16425484	21,891.45
32	137,275.66	0.154957397	21,271.88
33	141,393.93	0.146186223	20,669.84
34	145,635.75	0.137911531	20,084.85
35	150,004.82	0.130105218	19,516.41
36	154,504.97	0.122740772	18,964.06
37	159,140.11	0.115793181	18,427.34
38	163,914.32	0.10923885	17,905.81
39	168,831.75	0.103055519	17,399.04
40	173,896.70	0.097222188	16,906.62
41	179,113.60	0.091719045	16,428.13
42	184,487.01	0.086527401	15,963.18
43	190,021.62	0.081629624	15,511.39
44	195,722.27	0.077009079	15,072.39
45	201,593.94	0.072650074	14,645.81
Total			1,050,238.16