Question

Garrett Boone, Ayayai Enterprises’ vice president of operations, needs to replace an automatic lathe on the production line. The model he is considering has a sales price of $395,900 and will last for 12 years. It will have no salvage value at the end of its useful life. Garrett estimates the new lathe will reduce raw materials scrap by $42,500 per year. He also believes the lathe will reduce energy costs by $23,500 per year. If he purchases the new lathe, he will be able to sell the old lathe for $5,338. A )Calculate the lathe’s internal rate of return.

Answer 1

Internal Rate of Return (IRR) is the discount rate that makes the net present value (NPV) of a project zero. In other words, it is the expected rate of return that will be earned on a project or investment.

Here, initial investment is 395,900 - 5,338 =390,562

Cash Inflows every year = Savings from new investment

= 42,500 + 23,500

= 66,000

Let us calculate NPV using 10% discount rate:

Period	Cash Flows	Discounting Factor @ 10%	NPV
0.00	-390562.00	1.00	-390562.00
1.00	66000.00	0.91	60000.00
2.00	66000.00	0.83	54545.45
3.00	66000.00	0.75	49586.78
4.00	66000.00	0.68	45078.89
5.00	66000.00	0.62	40980.81
6.00	66000.00	0.56	37255.28
7.00	66000.00	0.51	33868.44
8.00	66000.00	0.47	30789.49
9.00	66000.00	0.42	27990.44
10.00	66000.00	0.39	25445.86
11.00	66000.00	0.35	23132.60
12.00	66000.00	0.32	21029.63
		Total	59141.66

Here NPV is coming positive at 10%. Let us take higher rate say 15% and compute NPV again:

Period	Cash Flows	Discounting Factor @ 15%	NPV
0.00	-390562.00	1.00	-390562.00
1.00	66000.00	0.87	57391.30
2.00	66000.00	0.76	49905.48
3.00	66000.00	0.66	43396.07
4.00	66000.00	0.57	37735.71
5.00	66000.00	0.50	32813.66
6.00	66000.00	0.43	28533.62
7.00	66000.00	0.38	24811.84
8.00	66000.00	0.33	21575.52
9.00	66000.00	0.28	18761.32
10.00	66000.00	0.25	16314.19
11.00	66000.00	0.21	14186.25
12.00	66000.00	0.19	12335.87
		Total	-32801.15

Since NPV is positive at 10% and negative at 15%, therefore IRR is somewhere between 10% and 15%. It will be calculated as follows:

NPV difference = 59,141 - (-32,801)

= 91,941

Rate Difference = 15 - 10 = 5%

For a rate difference of 91,941, rate difference is 5%

so eliminate difference of 59,141, rate difference required = 5 / 91,941 x 59,141

= Aprox. 3

So IRR = 10 + 3 = 13%. At this rate, NPV will be calculated as follows:

Period	Cash Flows	Discounting Factor @ 13%	NPV
0.00	-390562.00	1.00	-390562.00
1.00	66000.00	0.88	58407.08
2.00	66000.00	0.78	51687.68
3.00	66000.00	0.69	45741.31
4.00	66000.00	0.61	40479.04
5.00	66000.00	0.54	35822.16
6.00	66000.00	0.48	31701.02
7.00	66000.00	0.43	28054.00
8.00	66000.00	0.38	24826.55
9.00	66000.00	0.33	21970.40
10.00	66000.00	0.29	19442.83
11.00	66000.00	0.26	17206.05
12.00	66000.00	0.23	15226.59
		Total	2.70

Which is almost equal to zero. Hence we can say that IRR for the project is 13%.