Question

ABC Company is considering the purchase of a new forklift for its flourishing roofing business. The key parameters of the three forklifts under scrutiny (Alpha, Beta and Gamma) are provided below.

Parameters	Alpha	Beta	Gamma
Initial Cost($)	400,000	500,000	550,000
Revenues ($)	230,000 at EOY1 Decreasing by 1% annually thereafter	300,000 at EOY1 increasing by 1000 annually thereafter	330,000 at EOY1 decreasing by 1500 annually thereafter
Operating Costs ($)	105,000 at EOY1 increasing by 2% annually thereafter	214,000 annually	223,000 at EOY1 increasing by 1000 annually thereafter
End-of life salvage value	-10,000	10,000	25,000
Useful life (years)	5	10	10
Industry Standard = 4 years	MARR = 10%	EOY = End of year

21.i) The incremental External Rate of Return (ΔERR) between Alpha and Gamma (second decimal; no rounding) is a) 9.40%; b) 9.97%; c) 10.25%; d) 10.62%.

ii) The incremental External Rate of Return (ΔERR) between Beta and Gamma (second decimal; no rounding) is a) 8.19%; b) 9.30%; c) 9.88%; d) 10.91%.

Answer 1

Alpha
Year	Cash flows/revenues	Op. Costs	salvage Value/cost	Net Cash flows
	A	B	C	D = A+B+C
0	-400000			(400,000.00)
1	230000	-105000		125,000.00
2	227700	-107100		120,600.00
3	225423	-109242		116,181.00
4	223168.77	-111426.84		111,741.93
5	220937.0823	-113655.377	-10000	97,281.71
Beta
Year	Cash flows/revenues	Op. Costs	salvage Value/cost	Net Cash flows
	A	B	C	D = A+B+C
0	-500000			-500000
1	300000	-214000		86000
2	301000	-214000		87000
3	302000	-214000		88000
4	303000	-214000		89000
5	304000	-214000		90000
6	305000	-214000		91000
7	306000	-214000		92000
8	307000	-214000		93000
9	308000	-214000		94000
10	309000	-214000	10000	105000
Gamma
Year	Cash flows/revenues	Op. Costs	salvage Value/cost	Net Cash flows
	A	B	C	D = A+B+C
0	-550000			-550000
1	330000	-223000		107000
2	328500	-224000		104500
3	327000	-225000		102000
4	325500	-226000		99500
5	324000	-227000		97000
6	322500	-228000		94500
7	321000	-229000		92000
8	319500	-230000		89500
9	318000	-231000		87000
10	316500	-232000	25000	109500
	Alpha and gamma incremental external rate of return
Year	alpha	Gamma	Incremental cash flows
0	(400,000.00)	(550,000.00)	(150,000.00)
1	125,000.00	107,000.00	(18,000.00)
2	120,600.00	104,500.00	(16,100.00)
3	116,181.00	102,000.00	(14,181.00)
4	111,741.93	99,500.00	(12,241.93)
5	(302,718.29)	97,000.00	399,718.29
6	125,000.00	94,500.00	(30,500.00)
7	120,600.00	92,000.00	(28,600.00)
8	116,181.00	89,500.00	(26,681.00)
9	111,741.93	87,000.00	(24,741.93)
10	97,281.71	109,500.00	12,218.29
		ERR =	9.973%	Ans 21. i	b) 9.97%
		Excel Fn	=MIRR(Values0 to 10,10%,10%)
Since alpha has only 5 year life its cash flow is repetaed for another 5 years and combined.
	Beta and gamma incremental external rate of return
Year	alpha	Gamma	Incremental cash flows
0	-500000	(550,000.00)	(50,000.00)
1	86000	107,000.00	21,000.00
2	87000	104,500.00	17,500.00
3	88000	102,000.00	14,000.00
4	89000	99,500.00	10,500.00
5	90000	97,000.00	7,000.00
6	91000	94,500.00	3,500.00
7	92000	92,000.00	-
8	93000	89,500.00	(3,500.00)
9	94000	87,000.00	(7,000.00)
10	105000	109,500.00	4,500.00
		ERR =	10.912%	Ans 21. iI	d) 10.91%
		Excel Fn	=MIRR(Values0 to 10,10%,10%)