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

16. i)Beta’s Internal Rate of Return (IRR) (second decimal; no rounding) is a) 12.44%; b) 14.55%; c) 15.22; d) 15.39%.

ii) Gamma’s Internal Rate of Return (IRR) (second decimal; no rounding) is a) 10.88%; b) 11.17%; c) 12.54%; d) 14.06%.

iii) The incremental Internal Rate of Return (ΔIRR) between Alpha and Gamma (second decimal; no rounding) is a) 8.96%; b) 9.29%; c) 9.68%; d) 9.91%.

17.i) Alpha’s External Rate of Return (ERR) (second decimal; no rounding) is a) 11.98%; b) 12.38%; c) 12.86%; d) 13.17%.

ii) Beta’s External Rate of Return (ERR) (second decimal; no rounding) is a) 11.15%; b) 11.31%; c) 11.58%; d) 12.17%.

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
			ERR =	11.980%	Ans 17. i	a) 11.98%
			Excel Fn	=MIRR(values 0 to 5, 10%, 10%)
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
			IRR =	12.445%	Ans 16.i	a) 12.44%
			Excel Fn	=IRR(Values 0 to 10)
			ERR =	11.158%	Ans 17 ii	a) 11.15%
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
			IRR =	12.544%	Ans 16. ii	c) 12.54%
			Excel Fn	=IRR(Values 0 to 10)
	Alpha and gamma incremental 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
		IRR =	9.914%	Ans 16. iii	d) 9.91%
			=IRR(Values 0 to 10)
Since alpha has only 5 year life its cash flow is repetaed for another 5 years and combined.