Question

You are considering taking a 1-year certificate in stock trading or a 1-year certificate in financial analytics. The certificate in trading will cost you $25,000 and will increase your salary by $8,000 a year for the next 5 years. The certificate in analytics will cost $40,000, and will increase your salary by $12,000 a year for the next 5 years. Based on your calculation of NPV and IRR and MIRR, which certificate will you choose? Use 10% as your discount rate.

Answer 1

NPV = PV of Cash Inflows - PV of Cash Outflows

Certificate 1:

Year	CF	PVF @10%	Disc CF
0	$ -25,000.00	1.0000	$ -25,000.00
1	$    8,000.00	0.9091	$    7,272.73
2	$    8,000.00	0.8264	$    6,611.57
3	$    8,000.00	0.7513	$    6,010.52
4	$    8,000.00	0.6830	$    5,464.11
5	$    8,000.00	0.6209	$    4,967.37
NPV	$    5,326.29

Certificate 2:

Year	CF	PVF @10%	Disc CF
0	$ -40,000.00	1.0000	$ -40,000.00
1	$ 12,000.00	0.9091	$ 10,909.09
2	$ 12,000.00	0.8264	$    9,917.36
3	$ 12,000.00	0.7513	$    9,015.78
4	$ 12,000.00	0.6830	$    8,196.16
5	$ 12,000.00	0.6209	$    7,451.06
NPV	$    5,489.44

IRR is The Rate at which PV of Cash Inflows are equal to PV of Cash Outflows

Certificate 1:

Year	CF	PVF @18%	Disc CF	PVF @19%	Disc CF
0	$ -25,000.00	1.0000	$ -25,000.00	1.0000	$ -25,000.00
1	$    8,000.00	0.8475	$    6,779.66	0.8403	$    6,722.69
2	$    8,000.00	0.7182	$    5,745.48	0.7062	$    5,649.32
3	$    8,000.00	0.6086	$    4,869.05	0.5934	$    4,747.33
4	$    8,000.00	0.5158	$    4,126.31	0.4987	$    3,989.35
5	$    8,000.00	0.4371	$    3,496.87	0.4190	$    3,352.39
NPV	$          17.37		$      -538.92

IRR = Rate at which least +ve NPV + [ NPV at that Rate / Change in NPV due to 1% inc in Rate ] * 1%

= 18% + [ 17.37 / 556.29 ] * 1%

= 18% + 0.03%

= 18.03%

Certificate 2:

Year	CF	PVF @15%	Disc CF	PVF @16%	Disc CF
0	$ -40,000.00	1.0000	$ -40,000.00	1.0000	$ -40,000.00
1	$ 12,000.00	0.8696	$ 10,434.78	0.8621	$ 10,344.83
2	$ 12,000.00	0.7561	$    9,073.72	0.7432	$    8,917.95
3	$ 12,000.00	0.6575	$    7,890.19	0.6407	$    7,687.89
4	$ 12,000.00	0.5718	$    6,861.04	0.5523	$    6,627.49
5	$ 12,000.00	0.4972	$    5,966.12	0.4761	$    5,713.36
NPV	$        225.86		$      -708.48

IRR = Rate at which least +ve NPV + [ NPV at that Rate / Change in NPV due to 1% inc in Rate ] * 1%

= 15% + [ 225.86 / 934.34] * 1%

= 15% + 0.24%

= 15.24%

Part 3:

MIRR is similar to IRR, Here intermediary CFs are reinvested at COC, where as in IRR, Intermediary CFs are reinvested at IRR.

Certificate 1:

Year	CF	FVF@10%	FV of CF
1	$    8,000.00	1.4641	$ 11,712.80
2	$    8,000.00	1.3310	$ 10,648.00
3	$    8,000.00	1.2100	$    9,680.00
4	$    8,000.00	1.1000	$    8,800.00
5	$    8,000.00	1.0000	$    8,000.00
FV of CFs	$ 48,840.80

Thus 25000 has become 48840.80 over a period of 5 Years.

48840.80 = 25000 ( 1 + r) ^5

(1+r)^5 = 48840.80 / 25000

= 1.9536

1+r = 1.9536 ^ ( 1/5)

= 1.1433

r = 1.1433 - 1

= 0.1433 i.e 14.33%

Certificate 2:

Year	CF	FVF@10%	FV of CF
1	$ 12,000.00	1.4641	$ 17,569.20
2	$ 12,000.00	1.3310	$ 15,972.00
3	$ 12,000.00	1.2100	$ 14,520.00
4	$ 12,000.00	1.1000	$ 13,200.00
5	$ 12,000.00	1.0000	$ 12,000.00
FV of CFs	$ 73,261.20

Thus 40000 has become 73261.20over a period of 5 Years.

73261.20 = 40000 ( 1 + r) ^5

(1+r)^5 = 73261.20 / 40000

= 1.8315

1+r = 1.8315 ^ ( 1/5)

= 1.1287

r = 1.1287 - 1

= 0.1287 i.e 12.87%

Selection:

Particulars	Certificate 1	Certificate 2	Selected
NPV	$    5,326.29	5,489.44	Certificate 2
IRR	18.03%	15.24%	Certificate 1
MIRR	14.33%	12.87%	Certificate 1