An expenditure of $20,000 is made to modify a material-handling system in a small job shop. This modification will result in first-year savings of $2,000, a second-year savings of $4,000, and a savings of $5,000 per year thereafter. How many years must the system last if an 18% return on investment

Question

An expenditure of [latex]\$ 20,000[/latex] is made to modify a material-handling system in a small job shop. This modification will result in first-year savings of [latex]\$ 2,000[/latex], a second-year savings of [latex]\$ 4,000[/latex], and a savings of [latex]\$ 5,000[/latex] per year thereafter. How many years must the system last if an [latex]18 \%[/latex] return on investment is required? The system is tailor made for this job shop and has no market (salvage) value at any time. (4.10)

Accepted Answer

Equivalent cash inflows = Equivalent cash outflows

Using time 0 as the equivalence point and [latex]N=[/latex] total life of the system:

[latex]\begin{aligned}&\$ 2,000(P / F, 18 \%, 1)+\$ 4,000(P / F, 18 \%, 2) \&\quad+\$ 5,000(P / A, 18 \%, N-2)(P / F, 18 \%, 2)=\$ 20,000 \&\$ 2,000(0.8475)+\$ 4,000(0.7182)+\$ 5,000(P / A, 18 \%, N-2)(0.7182) \&\quad=\$ 20,000 \&\$ 5,000(P / A, 18 \%, N-2)(0.7182)=\$ 15,432.20 \ &(P / A, 18 \%, N-2)=4.297\end{aligned}[/latex]

From Table [latex]C-17,(P / A, 18 \%, 8)=4.078[/latex] and [latex](P / A, 18 \%, 9)=4.303[/latex]. Thus, [latex](N-2)=9[/latex] and [latex]N=11[/latex] years. Note that if the system lasts for only 10 years, the present equivalent of the cash inflows [latex]<[/latex] present equivalent of the cash outflows.

TABLE C-17 Discrete Compounding; i = 20%
Single Payment			Uniform Series				Uniform Gradient
	Compound Amount Factor	Present Worth Factor	Compound Amount Factor	Present Worth Factor	Sinking Fund Factor	Capital Recovery Factor	Gradient Present Worth Factor	Gradient Uniform Series Factor
N	To Find F Given P F/P	To Find P Given F P/F	To Find F Given A F/A	To Find P Given A P/A	To Find A Given F A/F	To Find A Given P A/P	To Find P Given G P/G	To Find A Given G A/G	N
1	1.2000	0.8333	1.0000	0.8333	1.0000	1.2000	0.000	0.0000	1
2	1.4400	0.6944	2.2000	1.5278	0.4545	0.6545	0.694	0.4545	2
3	1.7280	0.5787	3.6400	2.1065	0.2747	0.4747	1.852	0.8791	3
4	2.0736	0.4823	5.368	2.5887	0.1863	0.3863	3.299	1.2742	4
5	2.4883	0.4019	7.4416	2.9906	0.1344	0.3344	4.906	1.6405	5
6	2.9860	0.3349	9.9299	3.3255	0.1007	0.3007	6.581	1.9788	6
7	3.5832	0.2791	12.9159	3.6046	0.0774	0.2774	8.255	2.2902	7
8	4.2998	0.2326	16.4991	3.8372	0.0606	0.2606	9.883	2.5756	8
9	5.1598	0.1938	20.7989	4.0310	0.0481	0.2481	11.434	2.8364	9
10	6.1917	0.1615	25.9587	4.1925	0.0385	0.2385	12.887	3.0739	10
11	7.4301	0.1346	32.1504	4.3271	0.0311	0.2311	14.233	3.2893	11
12	8.9161	0.1122	39.5805	4.4392	0.0253	0.2253	15.467	3.4841	12
13	10.6993	0.0935	48.4966	4.5327	0.0206	0.2206	16.588	3.6597	13
14	12.8392	0.0779	59.1959	4.6106	0.0169	0.2169	17.601	3.8175	14
15	15.4070	0.0649	72.0351	4.6755	0.0139	0.2139	18.510	3.9588	15
16	18.4884	0.0541	87.4421	4.7296	0.0114	0.2114	19.321	4.0851	16
17	22.1861	0.0451	105.9306	4.7746	0.0094	0.2094	20.042	4.1976	17
18	26.6233	0.0376	128.1167	4.8122	0.0078	0.2078	20.681	4.2975	18
19	31.9480	0.0313	154.7400	4.8435	0.0065	0.2065	21.244	4.3861	19
20	38.3376	0.0261	186.6880	4.8696	0.0054	0.2054	21.740	4.4643	20
21	46.0051	0.0217	225.0256	4.8913	0.0044	0.2044	22.174	4.5334	21
22	55.2061	0.0181	271.0307	4.9094	0.0037	0.2037	22.555	4.5941	22
23	66.2474	0.0151	326.2369	4.9245	0.0031	0.2031	22.887	4.6475	23
24	79.4968	0.0126	392.4842	4.9371	0.0025	0.2025	23.176	4.6943	24
25	95.3962	0.0105	471.9811	4.9476	0.0021	0.2021	23.428	4.7352	25
30	237.3763	0.0042	1181.8816	4.9789	0.0008	0.2008	24.263	4.8731	30
35	590.668.2	0.0017	2948.3411	4.9915	0.0003	0.2003	24.661	4.9406	35
40	1469.7716	0.0007	7343.8578	4.9966	0.0001	0.2001	24.847	4.9728	40
45	3657.2620	0.0003	18281.3099	4.9986	0.0001	0.2001	24.932	4.9877	45
50	9100.4382	0.0001	45497.1908	4.9995	a	0.2000	24.970	4.9945	50
60	56347.5144	a	281732.5718	4.9999	a	0.2000	24.994	4.9989	60
80	2160228.4620	a	10801137.3101	5.0000	a	0.2000	25.000	5.0000	80
∞				5.0000		0.2000			∞
[latex]{ }^{a} [/latex] Less than 0.0001.

Question 4.T-Y-S.Q: An expenditure of $20,000 is made to modify a material-handl...

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