Scrap value of both machines is negligible.

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written 7.8 years ago by

Given cost of money R = 10%: discount factor $V = \bigg(\dfrac{1}{1+R}\bigg)^{1-N}$, where N is the year.

Machine A: Cost price = Rs. 25000

Year	Running Cost	Discount Factor $(V)^{R-1}$	Discounted running cost	Σ Discounted Costs	Total costs (cost price + Σ costs)	$$\sum_{R=1} ^N V^{R-1}$$	Weighted Average annual cost
1	4000	1	4000	4000	29000	1	29000
2	4000	0.9091	3636.36	7636.36	32636.36	1.9091	17095.16
3	4000	0.8264	3305.8	10942.14	35942.15	2.7355	13139.15
4	4000	0.7513	3005.26	13947.14	38947.4	3.4868	11170
5	4000	0.6830	2732.05	16679.2	41679.2	4.1698	9995.5
6	5000	0.6209	3104.6	19783.8	44783.8	4.7907	9348
7	6000	0.5645	3386.84	23170.64	48170.64	5.3552	8995.11
8	7000	0.5131	3592.1	26762.75	51762.75	5.8683	8820.74
9	8000	0.4665	3732.06	30494.81	55494.81	6.3348	8760.31
10	9000	0.4241	3816.88	34311.7	59311.7	6.7589	8775.34

Machine B: Cost prince = Rs. 12500

Year	Running Cost	Discount Factor $(V)^{R-1}$	Discounted running cost	Σ Discounted Costs	Total costs (cost price + Σ costs)	$$\sum_{R=1} ^N V^{R-1}$$	Weighted Average annual cost
1	6000	1	6000	6000	18500	1	18500
2	6000	0.9091	5454.6	11454.6	23654.6	1.9091	12547.6
3	6000	0.8264	4958.4	16413	28913	2.7355	10569.55
4	6000	0.7513	4507.8	20920.8	33420.8	3.4868	9584.95
5	6000	0.6830	4098	25018.8	37518.8	4.1698	8997.75
6	6000	0.6209	3275.4	28744.2	41244.2	4.7907	8608.86
7	7000	0.5645	3951.5	32695.7	45195.7	5.3552	8439.6
8	8000	0.5131	4104.8	36800.5	49300.5	5.8683	8401.16
9	9000	0.4665	4198.5	40999	53499	6.3348	8445.25

Machine B has a lower weighted average annual cost, and hence it should be purchased.

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