Question

Norwich Tool, a large machine shop, is considering replacing one of its lathes with either of two new lathes - lathe A or lathe B. Lathe A is highly automated, computer-controlled lathe; lathe B is a less expensive lathe that uses standard technology. To analyze these alternatives, Mario Jackson, a financial analyst, prepared estimates of the initial investment and incremental (relevant) cash inflows associated with each lathe. These are shown in the following table. Initial investment (at Year 0) Year (t) Lathe A Lathe B $660,000 $360,000 Cash inflows 128,000 88,000 182,000 120,000 166,000 96,000 168,000 86,000 450,000 207,000 Note that Mario plans to analyze both lathes over a 5-year period. At the end of that time, the lathes would be sold, thus accounting for the large fifth-year cash inflows. Mario believe that the two lathes are equally risky and that the acceptance of either of them will not change the firm's overall risk. He therefore decides to apply the firm's 13% cost of capital when analyzing the lathes. Norwich Tool requires all projects to have a maximum payback period of 4.0 years. What is the payback period of each lathe? Which lathe should Norwich Tool choose? Why? What is the profitability index of each lathe? Which lathe should Norwich Tool choose? Why? 3. What is the internal rate of return (IRR) of each lathe? Which lathe should Norwich Tool choose? Why? What is the net present value (NPV) of each lathe? Which lathe should Norwich Tool choose? Why? Which lathe should Mario recommend the company to buy? Why?

Answer 1

Answer 1:- Calculating Payback Period for both the Lathe Machines.

	Lathe A		Lathe B
Year	Cash Flows	Cumulative Cash inflow	Cash Flows	Cumulative Cash Flow
0	-$660,000	-	-$360,000	-
1	128000	128000	88000	88000
2	182000	310000	120000	208000
3	166000	476000	96000	304000
4	168000	644000	86000	390000
5	450000	1094000	207000	597000

Payback period For each Lathe

Lathe A

Payback Period = 4 Years + [(660000 - 644000) / 450000]

Payback Period = 4 Years + (16000 / 450000)

Payback Period = 4 Years + 0.035 years

Payback Period = 4.035 Years

Lathe B

Payback Period = 3 Years + [(360000 - 304000) / 86000]

Payback Period = 3 Years + (56000/86000)

Payback Period = 3 Years + 0.65 years

Payback Period = 3.65 Years

Advice- As the Payback period of Lathe B is Less than Payback period of Lathe A, Norwich tools should select Lathe B.

.

Answer 2 and 4 : -

NPV and Profitability Index
	Lathe A			Lathe B
Year	Cash Flows	Disc Factor @ 13%	PV of Cash Flows	Cash Flows	Disc Factor @ 13%	PV of Cash Flows
1	128000	0.8850	$113,274	88000	0.8850	$77,876
2	182000	0.7831	$142,533	120000	0.7831	$93,978
3	166000	0.6931	$115,046	96000	0.6931	$66,533
4	168000	0.6133	$103,038	86000	0.6133	$52,745
5	450000	0.5428	$244,242	207000	0.5428	$112,351
PV Of Cash Inflows (1-5 years)			$718,133			$403,483
Less :- Initial Investments			($660,000)			($360,000)
Net Present Value			$58,133			$43,483

.

Profitability Index = Present Value of Cash Inflows/ Initial Investment

Profitability Index (Lathe A) = 718133 / 660000

Profitability Index (Lathe A) = 1.088

Profitability Index (Lathe B) = 403483/360000

Profitability Index (Lathe B) = 1.121

.Advice:- Since Profitability index of Lathe B is higher than Profitability index of Lathe A, Norwich tools should select Lathe B.

NPV OF Lathe A = $58133

NPV OF Lathe B = $43483

Advice:- NPV of Lathe A is Highest, hence Lathe A is selected.

.Answer 3 :-Internal Rate of Return (IRR)

IRR (Using Extrapolation Formula) = Lower Rate + [Desired Value - Value At Lower Rate] / (Value at Lower Rate - Value at Higher Rate) x (Higher Rate - Lower Rate)]

Lathe A
	Project A	Discounted cash flows
Year	Cash flows	Rate @ 12%	Rate @ 15%
0	-660000	-660000.00	-660000.00
1	128000	114285.71	111304.35
2	182000	145089.29	137618.15
3	166000	118155.52	109147.69
4	168000	106767.04	96054.55
5	450000	255342.09	223729.53
Net Present Value		$79,639.65	$17,854.27

IRR for Lathe A

= 12% + [(79639.65 - 0) / (79639.65- 17854.27) x (15% - 12%)]

= 12% + (79639.65) / (61785.38) x (3%)

= 12% + 3.90%

= 15.90% (Approx)

.

Lathe B
	Project A	Discounted cash flows
Year	Cash flows	Rate @ 12%	Rate @ 15%
0	-360000	-360000.00	-360000.00
1	88000	78571.43	76521.74
2	120000	95663.27	90737.24
3	96000	68330.90	63121.56
4	86000	54654.55	49170.78
5	207000	117457.36	102915.58
Net Present Value		$54,677.51	$22,466.90

IRR for Lathe B

= 12% + [(54677.51 - 0) / (54677.51 - 22466.9) x (15% - 12%)]

= 12% + (54677.51) / (32211) x (3%)

= 12% + 5.10%

= 17.10% (Approx)

Advise :-Considering the highest Internal rate of return, Norwich tools should select Lathe B (17.10%).

Answer 5:- Considering all the factors ,

Payback period of Lathe A is 4.035 Years as compared to Lathe B which is 3.65 Years, but the maximum acceptable payback period should be 4 years,

Required rate of return is 13%, whereas IRR for Lathe A is 15.90% and IRR for Lathe B is 17.10%, .

Net present Value(NPV) of Lathe A is $17854 higher than Lathe B.$22867.

Conclusion :- As the acceptance criteria of maximum payback period should be 4 years is not met by Lathe A. Hence, only Lathe B will accepted.