Question

Ecoosa Organic Mattresses Manufacturers Limited (EOMML) is planning to purchase a new
material handling machine for its manufacturing unit. The company is considering the
following four mutually exclusive investments. The required payback period is five and a half
years. The financial data regarding the four machines is given below (ignore taxes).

Machine/asset Machine A Machine B Machine C Machine D $ $ $ $ Revenue 66,000 62,500 58,500 47,000 Operational costs 31,000 29,000 26,610 22,100 Depreciation 8,750 10,250 11,600 12,000 Interest 12,600 11,250 10,440 8,850 Cost of the machine 140,000 120,000 116,000 98,000 Machine life (years) 16 12 10 8

The manufacturing department has requested the chief financial offer (CFO) to evaluate the
above investment opportunities using both payback period and internal rate of return methods.
The CFO is seeking your help to calculate each machine's payback period, internal rate of
return and determine appropriate hurdle rates.
Required:
(a) Calculate each machine’s payback period and state which alternative should be accepted
based on this criterion.
(b) Calculate each machine's internal rate of return (IRR), and using a hurdle rate of 25% state
which of the alternatives is acceptable by this criteria.
(c) Explain two probable circumstances in which EOMML is choosing ONE machine from
among the four mutually exclusive investments.

Answer 1

	Machine/asset	Machine A	Machine B	Machine C	Machine D
	Revenue	66,000	62,500	58,500	47,000
	Operational costs	31,000	29,000	26,610	22,100
	Depreciation	8,750	10,250	11,600	12,000
	Interest	12,600	11,250	10,440	8,850
	Cost of the machine	1,40,000	1,20,000	1,16,000	98,000
	Machine life (years)	16	12	10	8
	Annual operational cash inflow from the machine (Revenue-Operational costs. Interest need not be deducted and tax shield on depreciation ignored as directed)	35,000	33,500	31,890	24,900
a)	Payback period in years = Cost of the machine/Annual operational cash flow =	4.00	3.58	3.64	3.94
	Using the payback method, projects having payback period less than the maximum payback period prescribed by the mangement can be accepted. Here, the maximum payback period prescribed by the management is 5.5 years. As such all the four projects are acceptable for their payback period is less than 5.5 years.
b)	IRR:
	IRR is that discount rate for which the NPV = 0. This means that the PV of the cash inflows, when discounted with the IRR of the project, should be equal to the initial investment. Putting in the form of an equation, we have Initial investment = Annual cash inflow*PVIFA(IRR,n). This means that Initial investment/Annual cash inflow = PVIFA(IRR,n). The value of IRR can be interpolated from the Interest factor tables.
	Interest fator for IRR = Initial investment/Annual cash inflow	4.0000	3.5821	3.6375	3.9357
	Interest rates within which the factors lie:
	Lower bound %	24	26	24	19
	Upper bound %	25	27	25	20
	Lower bound interest annuity factor	4.0333	3.6059	3.6059	3.9544
	Upper bound interest annuity factor	3.8874	3.4933	3.4933	3.8372
	IRR = Lower bound interst rate+(Lower bound interest factor-Interest factor for IRR)/(Higher bound interst factor-Lower bound interest factor).
	IRR (%)	24.23	26.21	23.72	19.16
	All projects with IRR>Hurdle rate (of 25%) are acceptable. Hence, only Machine B is acceptable.
c)	The probable circumstances for choosing one machine from the four alternatives are:
	i) The firm technically needs only one of the machines, making the alternatives 'mutually' exclusive.
	ii) The firm has funds to buy only one of the machines.