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Question (20 Marks) General Motors (GM) is evaluating a maintenance contract for its heavy equipment. One...

Question
General Motors (GM) is evaluating a maintenance contract for its heavy equipment. One company has offered GM a four-year contract for R100,000 to be paid in advance. Another company has offered an eight-year contract for R165,000, also to be paid in advance. GM will be able to save R34,000 per year under either contract because its employees will no longer have to do the work themselves.

Required

1. If GM’s cost of capital is 10%, which project should be selected? Use both the replacement chain and the equivalent annuity (EAA) method to justify your answer. [12]

2. If GM’s cost of capital is 12%, does it change the decision? What about 14%? [8]

Expert Solution

1. Replacement chain method: The two contracts have lives of 4 years and 8 years. Least common life of 4 and 8 years = 8 years

Thus the cycle for the 4 year contract will be repeated.

Contract 1
Year	0	1	2	3	4	5	6	7	8
Cash flows	-100,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00
					-100,000.00
Net cash flows	-100,000.00	34,000.00	34,000.00	34,000.00	-66,000.00	34,000.00	34,000.00	34,000.00	34,000.00
1+r	1.10
PVIF	1.0000	0.9091	0.8264	0.7513	0.6830	0.6209	0.5645	0.5132	0.4665
PV (Net cash flow*PVIF)	-100,000.00	30,909.09	28,099.17	25,544.70	-45,078.89	21,111.32	19,192.11	17,447.38	15,861.25
NPV (sum of all PVs)	13,086.15


Contract 2
Year	0	1	2	3	4	5	6	7	8
Cash flows	-165,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00
Net cash flows	-165,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00
1+r	1.10
PVIF	1.0000	0.9091	0.8264	0.7513	0.6830	0.6209	0.5645	0.5132	0.4665
PV (Net cash flow*PVIF)	-165,000.00	30,909.09	28,099.17	25,544.70	23,222.46	21,111.32	19,192.11	17,447.38	15,861.25
NPV (sum of all PVs)	16,387.49

As we can see that the NPV of contract 2 is higher and so the 2nd contract or project will be selcted.

(ii) EAA method:

EAA = NPV/Annuity discount factor:

Contract 1
Year	0	1	2	3	4
Cash flows	-100,000.00	34,000.00	34,000.00	34,000.00	34,000.00
1+r	1.10
PVIF	1.0000	0.9091	0.8264	0.7513	0.6830
PV (Net cash flow*PVIF)	-100,000.00	30,909.09	28,099.17	25,544.70	23,222.46
NPV (sum of all PVs)	7,775.43

Contract 2
Year	0	1	2	3	4	5	6	7	8
Cash flows	-165,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00

Net cash flows	-165,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00
1+r	1.10
PVIF	1.0000	0.9091	0.8264	0.7513	0.6830	0.6209	0.5645	0.5132	0.4665
PV (Net cash flow*PVIF)	-165,000.00	30,909.09	28,099.17	25,544.70	23,222.46	21,111.32	19,192.11	17,447.38	15,861.25
NPV (sum of all PVs)	16,387.49

Now annuity discount factor for 10% and 4 years = 3.16987. Thus EAA of project 1 = 7775.43/3.16987 = 2452.92

EAA for project 2 = 16387.49/5.33493 = 3071.73

As EAA for project 2 is more it will be selected.

2. if cost of capital = 12% then the project 1 will become more lucrative and attractive.

The replacement chain analysis in case of 12% is provided below:

Contract 1
Year	0	1	2	3	4	5	6	7	8
Cash flows	-100,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00
					-100,000.00
Net cash flows	-100,000.00	34,000.00	34,000.00	34,000.00	-66,000.00	34,000.00	34,000.00	34,000.00	34,000.00
1+r	1.12
PVIF	1.0000	0.8929	0.7972	0.7118	0.6355	0.5674	0.5066	0.4523	0.4039
PV (Net cash flow*PVIF)	-100,000.00	30,357.14	27,104.59	24,200.53	-41,944.19	19,292.51	17,225.46	15,379.87	13,732.03
NPV (sum of all PVs)	5,347.94


Contract 2
Year	0	1	2	3	4	5	6	7	8
Cash flows	-165,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00
Net cash flows	-165,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00
1+r	1.12
PVIF	1.0000	0.8929	0.7972	0.7118	0.6355	0.5674	0.5066	0.4523	0.4039
PV (Net cash flow*PVIF)	-165,000.00	30,357.14	27,104.59	24,200.53	21,607.61	19,292.51	17,225.46	15,379.87	13,732.03
NPV (sum of all PVs)	3,899.75

NPV of project 1 > NPV of project 2

(ii) cost of capital = 14%. In this case the NPV for both the projects becomes negative but project 1 has a lower negative value than project 2 and hence project 1 will be preferred.

Contract 1
Year	0	1	2	3	4	5	6	7	8
Cash flows	-100,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00
					-100,000.00
Net cash flows	-100,000.00	34,000.00	34,000.00	34,000.00	-66,000.00	34,000.00	34,000.00	34,000.00	34,000.00
1+r	1.14
PVIF	1.0000	0.8772	0.7695	0.6750	0.5921	0.5194	0.4556	0.3996	0.3506
PV (Net cash flow*PVIF)	-100,000.00	29,824.56	26,161.90	22,949.03	-39,077.30	17,658.53	15,489.94	13,587.67	11,919.01
NPV (sum of all PVs)	-1,486.66


Contract 2
Year	0	1	2	3	4	5	6	7	8
Cash flows	-165,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00
Net cash flows	-165,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00	34,000.00
1+r	1.14
PVIF	1.0000	0.8772	0.7695	0.6750	0.5921	0.5194	0.4556	0.3996	0.3506
PV (Net cash flow*PVIF)	-165,000.00	29,824.56	26,161.90	22,949.03	20,130.73	17,658.53	15,489.94	13,587.67	11,919.01
NPV (sum of all PVs)	-7,278.63

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