Question

You are considering the following two mutually exclusive projects. The crossover rate between these two projects is ___ percent and Project ___ should be accepted if the required return is greater than the crossover rate.

Year	Project A			Project B
0		−$24,000			−$24,000
1		8,500			16,570
2		8,500			6,500
3		16,500			8,590

Multiple Choice

• 12.17%; B

• 12.17%; A

• 17.82%; A

• 16.49%; A

• 16.49%; B

Answer 1

				12.00%			13.00%
Year	Cash Flow-A	Cash Flow-B	Differential cashflow- Cashflow B less Cashflow A	PV factor = 1/ (1+r)^t	PV		PV factor = 1/ (1+r)^t	PV
0	$             (24,000.00)	$(24,000.00)	$              -	1.000	$            -		1.000	$            -
1	$               16,570.00	$    8,500.00	$ (8,070.00)	0.893	$(7,205.36)		0.885	$(7,141.59)
2	$                 6,500.00	$    8,500.00	$    2,000.00	0.797	$ 1,594.39		0.783	$ 1,566.29
3	$                 8,590.00	$ 16,500.00	$    7,910.00	0.712	$ 5,630.18		0.693	$ 5,482.03
				Total	$       19.21		Total	$     (93.27)
NPV @ 0.12	19.21
NPV @ 0.13	(93.27)
Difference in both	112.49
Cross over-rate	=Lower rate + Difference in rates*(NPV at lower rate)/(Lower rate NPV-Higher rate NPV)
	'=12%+ (13%-12%)*(19.212/(19.212+93.272)
Cross over-rate	12.17%

IRR-project A

		17.00%			18.00%
Year	Cash Flow-A	PV factor = 1/ (1+r)^t	PV		PV factor = 1/ (1+r)^t	PV
0	$             (24,000.00)	1.000	$(24,000.00)		1.000	$(24,000.00)
1	$               16,570.00	0.855	$ 14,162.39		0.847	$ 14,042.37
2	$                 6,500.00	0.731	$    4,748.34		0.718	$    4,668.20
3	$                 8,590.00	0.624	$    5,363.34		0.609	$    5,228.14
		Total	$       274.07		Total	$       (61.29)
NPV @ 0.17	274.07
NPV @ 0.18	(61.29)
Difference in both	335.36
Required rate	=Lower rate + Difference in rates*(NPV at lower rate)/(Lower rate NPV-Higher rate NPV)
	'=17%+ (18%-17%)*(274.07/(274.07+61.289)
Required rate	17.81%

IRR Project-B

		16.00%			17.00%
Year	Cash Flow-B	PV factor = 1/ (1+r)^t	PV		PV factor = 1/ (1+r)^t	PV
0	$             (24,000.00)	1.000	$(24,000.00)		1.000	$(24,000.00)
1	$                 8,500.00	0.862	$    7,327.59		0.855	$    7,264.96
2	$                 8,500.00	0.743	$    6,316.88		0.731	$    6,209.37
3	$               16,500.00	0.641	$ 10,570.85		0.624	$ 10,302.11
		Total	$       215.32		Total	$     (223.56)
NPV @ 0.16	215.32
NPV @ 0.17	(223.56)
Difference in both	438.89
Required rate	=Lower rate + Difference in rates*(NPV at lower rate)/(Lower rate NPV-Higher rate NPV)
	'=16%+ (17%-16%)*(215.32/(215.32+223.56)
Required rate	16.49%

Since, IRR is higher in Project A, Project A should be selected.