Question

A metal plating company is considering three different methods for recovering byproduct heavy metals from a manufacturing site’s liquid waste. The investment costs and incomes associated with each method have been estimated. All methods have a 10-year life. The MARR is 12% per year. Using internal rate of return method, determine which method should be selected.

Method                         A                  B                    C
Initial cost          ($) -15,000          -18,000          -25,000

Annual income  ($) 4,000                5,000             6,000

Salvage value   ($) 1000                  2000              -500

Life, years                10                     10                   10

Answer 1

Internal rate of return

First we must understand what Internal Rate of Return means. Internal rate of return is a rate of return in which total present value of future cash inflows is equal to the the total present value of cash outflows(investment). It means, at Internal Rate of Return, the Net Present Value is Zero.

Steps to calculate Internal Rate of Return(IRR)

1. To calculate IRR, guess any rate of return (for example 12%) and calculate total present value of cash inflows and calculate Net Present Value.

(Present Value of Cash flow = Rn/(1+i)^n   where Rn= Cash flow, n = the year (first, second …), I = rate of return)

2. If Net Present Value is closer to Zero, the selected rate of return is Internal Rate of Return.

3. If Net Present Value is Greater than Zero, increase the rate and calculate Net Present value as in the first step.

4. If Net Present Value is still greater than Zero, increase the rate till the Net Present Value is equal to or closer to zero.

5. If Net Present Value is less than zero, decrease the rate of return and calculate Net Present value and see whether it is equal to or closer to Zero. if it is still less than zero, decrease the rate of return till Net Present Value becomes equal to closer or to Zero.

Calculation of Internal Rate of Return

Method A

Initial cost $15000

Annual income $4000

Salvage value $1000

Life 10 years

Year	Cash inflow	PV @12%	PV @15%	PV @20%	PV @23%
1	4000	3571.43	3478.26	3333.33	3252.03
2	4000	3188.78	3024.57	2777.78	2643.93
3	4000	2847.12	2630.06	2314.81	2149.54
4	4000	2542.07	2287.01	1929.01	1747.59
5	4000	2269.71	1988.71	1607.51	1420.80
6	4000	2026.52	1729.31	1339.59	1155.13
7	4000	1809.40	1503.75	1116.33	939.13
8	4000	1615.53	1307.61	930.27	763.52
9	4000	1442.44	1137.05	775.23	620.75
10	4000	1287.89	988.74	646.02	504.67
10	1000 (salvage value)	321.97	247.18	161.51	126.17
	Total	22922.87	20322.26	16931.39	15323.25

At 23%, total present value of cash inflows = Total present value of cash outflows(investment)

That is, 15323 = 15000 approximately.

Hence, The internal rate of return for Machine A is 23%

Method B

Initial cost $18000

Annual income $5000

Salvage value $2000

Life 10 years

Year	Cash inflow	PV @15%	PV @20%	PV @23%	PV @25%
1	5000	4347.83	4166.67	4065.04	4000
2	5000	3780.72	3472.22	3304.91	3200
3	5000	3287.58	2893.52	2686.92	2560
4	5000	2858.77	2411.27	2184.49	2048
5	5000	2485.88	2009.39	1776.01	1638.4
6	5000	2161.64	1674.49	1443.91	1310.72
7	5000	1879.69	1395.41	1173.91	1048.576
8	5000	1634.51	1162.84	954.40	838.8608
9	5000	1421.31	969.03	775.93	671.0886
10	5000	1235.92	807.53	630.84	536.8709
10	2000 (salvage value)	494.37	323.01	252.34	214.7484
	Total	25588.21	21285.37	19248.69	18067.26

At 25%, total present value of cash inflows = Total present value of cash outflows(investment)

That is, 18067 = 18000 approximately.

Hence, The internal rate of return for Machine A is 25%

Method C

Initial cost $25000

Annual income $6000

Salvage value $500

Life 10 years

Year	Cash inflow	PV @12%	PV @15%	PV @20%
1	6000	5357.14	5217.39	5000.00
2	6000	4783.16	4536.86	4166.67
3	6000	4270.68	3945.10	3472.22
4	6000	3813.11	3430.52	2893.52
5	6000	3404.56	2983.06	2411.27
6	6000	3039.79	2593.97	2009.39
7	6000	2714.10	2255.62	1674.49
8	6000	2423.30	1961.41	1395.41
9	6000	2163.66	1705.57	1162.84
10	6000	1931.84	1483.11	969.03
10	500 (salvage value)	160.99	123.59	80.75
	Total	34062.32	30236.20	25235.59

At 20%, total present value of cash inflows = Total present value of cash outflows(investment)

That is, 25235 = 25000 approximately.

Hence, The internal rate of return for Machine A is 20%

From the above calculation, we come to know all these three methods give different Internal Rate of Return each as follows:

Method A	Method B	Method C
IRR 23%	IRR 25%	IRR 20%

Comparatively Method B gives highest rate of return 25%. Hence, Method B should be selected.