Question

Quvon is using some of the skills in his manufacturing decision class to determine the value of his college education. He figures that he is going to spend $18,136 per year for four years to obtain his education. For ease of calculation he assumes $18,136 on day one and the rest at the end of each year. Well, then Quvon will graduate and he figures, on the conservative side, that he will earn $20,000 more in salary with his degree for the next twenty years. Allow year 4, to have "zero extra" while you graduate and get settled. For year 5 and beyond, up until 20 years, plus $20,000 at the end of year will be present. Of course, he may work more than 20 years but this is all that he wants to project. Also, with his degree he will obtain raises more readily, but that is also not in the model. At a personal hurdle rate of 15%, what is his net present value? (whole number in dollars will be fine] Is he actually earning 15% or more on his investment (yes or no)? What is his actual internal rate of return? (xx.x% will work. Only one decimal is needed) Given that he will be working more than 20 years is his return more or less, than you just calculated?

Answer 1

Solution:-

At a personal hurdle rate of 15%, what is his net present value? (whole number in dollars will be fine] Is he actually earning 15% or more on his investment (yes or no)? What is his actual internal rate of return? (xx.x% will work. Only one decimal is needed) Given that he will be working more than 20 years is his return more or less, than you just calculated?

Calculation of net present value for Quvon:-

Present value of outflow considering discounting factor using 15%:-

Year	Outflow	Discounting Factor	Present Value
1	18136	1	18136
2	18136	0.87	15778.32
3	18136	0.76	13783.36
4	18136	0.66	11969.76
Present Value of outflow	$59667.44

Present value of inflow considering discounting factor using 15% from year 5 to year 24 ie 20years:-

Year	Outflow	Discounting Factor	Present Value
5	20000	0.57	11400
6	20000	0.5	10000
7	20000	0.43	8600
8	20000	0.38	7600
9	20000	0.33	6600
10	20000	0.29	5800
11	20000	0.25	5000
12	20000	0.22	4400
13	20000	0.19	3800
14	20000	0.16	3200
15	20000	0.14	2800
16	20000	0.12	2400
17	20000	0.11	2200
18	20000	0.09	1800
19	20000	0.08	1600
20	20000	0.07	1400
21	20000	0.06	1200
22	20000	0.05	1000
23	20000	0.05	1000
24	20000	0.04	800
			$82600

Thus, Net Presesnt value= Total inflow- TOtal outflow

=$82600-$59667.44
=$22,933

Calculation of IRR:-

IRR is the rate at which the present value of cash outflow will be equal to present value of cash inflow.

Thus we would use the IRR formula for which we need to calculate NPV at 2 different discounting rates and thus 17% and 20% are taken here at a random basis:-

Year	Value	Discounting Factor 20%	Present value		Discounting Factor 17%	Present value
1	18136	1.00	-18136		1.00	-18136
2	18136	0.83	-15113.33		0.85	-15500.855
3	18136	0.69	-12594.44		0.73	-13248.594
4	18136	0.58	-10495.37		0.62	-11323.584
5	20000	0.40	8037.55		0.46	9122.22
6	20000	0.33	6697.96		0.39	7796.77
7	20000	0.28	5581.63		0.33	6663.91
8	20000	0.23	4651.36		0.28	5695.65
9	20000	0.19	3876.13		0.24	4868.07
10	20000	0.16	3230.11		0.21	4160.75
11	20000	0.13	2691.76		0.18	3556.19
12	20000	0.11	2243.13		0.15	3039.48
13	20000	0.09	1869.28		0.13	2597.85
14	20000	0.08	1557.73		0.11	2220.38
15	20000	0.06	1298.11		0.09	1897.76
16	20000	0.05	1081.76		0.08	1622.02
17	20000	0.05	901.46		0.07	1386.34
18	20000	0.04	751.22		0.06	1184.91
19	20000	0.03	626.02		0.05	1012.74
20	20000	0.03	521.68		0.04	865.59
21	20000	0.02	434.73		0.04	739.82
22	20000	0.02	362.28		0.03	632.33
23	20000	0.02	301.90		0.03	540.45
24	20000	0.01	251.58		0.02	461.92
		NPV	-9371.75			1856.13

IRR= Lower rate + { NPV at lower rate / (NPV at lower rate- NPV at higher rate) X (higher rate- lower rate)}

IRR= 17+ {(1856/(1856+9371) X (20-17)}

IRR=17+ 0.50

IRR=17.50%

Thus it can be concluded that the actual earning rate is 17.5% and is more than 15%