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.

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. Question is, how to get Lower bound%? Upper bound%? Lower bound interest annuity factor? Upper bound interest annuity factor? Is there any other answer to this question b) for IRR? How could it use financial calcultor for IRR?

Answer 1

Search 4.0000 in Present Value Annuity Table for 16 period. Exact 4.0000 value will not found. Therefore two nearest value will be choosen; First greater than 4.0000 (i.e. 4.0333) and second less than 4.0000 (i.e. 3.8874) which are at 24% and 25% respectively. Lower Rate i.e. 24% is called Lower bound and Higher Rate i.e. 25% is called Higher bound.

Similarly search 3.5128 for 12 period, 3.6375 for 10 period and 3.9357 for 8 period.

For Machine-A:

Note 1: Depreciation is non-cash item and there is no tax rate therefore no tax saving due to depreciation.

Note 2: Interest is actual cash outflow every year hence it should consider for cashfow computation.

ANNUAL CASH INFLOW = 66,000-31,000-12600

= 22,400

Interest fator for IRR = Initial investment/Annual cash inflow

= 1,40,000/22,400

= 6.25

Using Present Value Annuity Table for 16 years (periods):

search two nearest value to 6.25

At 14% value is 6.2651 and At 15% value is 5.9542

IRR = Lower bound interst rate+(Lower bound interest factor-Interest factor for IRR)/(Lower bound interst factor-Higher bound interest factor).

IRR = 14 + (6.2651-6.2500)/(6.2651-5.9542)

= 14.05%

For Machine-B:

ANNUAL CASH INFLOW = 62,500-29,000-11,250

= 22,250

Interest fator for IRR = Initial investment/Annual cash inflow

= 1,20,000/22,250

= 5.3933

Using Present Value Annuity Table for 12 years (periods):

search two nearest value to 5.3933

At 15% value is 5.4206 and At 16% value is 5.1971

IRR = Lower bound interst rate+(Lower bound interest factor-Interest factor for IRR)/(Lower bound interst factor-Higher bound interest factor).

IRR = 15 + (5.4206-5.3933)/(5.4206-5.1971)

= 15.12%

For Machine-C:

ANNUAL CASH INFLOW = 58,500-26,610-10,440

= 21,450

Interest fator for IRR = Initial investment/Annual cash inflow

= 1,16,000/21,450

= 5.4079

Using Present Value Annuity Table for 10 years (periods):

search two nearest value to 5.4079

At 13% value is 5.4262 and At 14% value is 5.2161

IRR = Lower bound interst rate+(Lower bound interest factor-Interest factor for IRR)/(Lower bound interst factor-Higher bound interest factor).

IRR = 13 + (5.4262-5.4079)/(5.4262-5.2161)

= 13.09%

For Machine-D:

ANNUAL CASH INFLOW = 47,000-22,100-8,850

= 16,050

Interest fator for IRR = Initial investment/Annual cash inflow

= 98,000/16,050

= 6.1059

Using Present Value Annuity Table for 8 years (periods):

search two nearest value to 6.1059

At 6% value is 6.2098 and At 7% value is 5.9713

IRR = Lower bound interst rate+(Lower bound interest factor-Interest factor for IRR)/(Lower bound interst factor-Higher bound interest factor).

IRR = 13 + (6.2098-6.1059)/(6.2098-5.9713)

= 6.44%

All projects with IRR>Hurdle rate (of 25%) are acceptable. Hence, No machine is acceptable.

All machines have negative NPV at this hurdle rate therefore no machine is acceptable.