Question

TopCap Co. is evaluating the purchase of another sewing machine that will be used to manufacture sport caps. The invoice price of the machine is $121,500. In addition, delivery and installation costs will total $4,500. The machine has the capacity to produce 12,000 dozen caps per year. Sales are forecast to increase gradually, and production volumes for each of the five years of the machine's life are expected to be as follows: Use Table 6-4. (Use appropriate factor(s) from the tables provided. Round the PV factors to 4 decimals.)

2019	3,600	dozen
2020	5,600	dozen
2021	8,500	dozen
2022	11,300	dozen
2023	12,000	dozen

The caps have a contribution margin of $8.00 per dozen. Fixed costs associated with the additional production (other than depreciation expense) will be negligible. Salvage value and the investment in working capital should be ignored. TopCap Co.'s cost of capital for this capacity expansion has been set at 6%.   


Required:

The caps have a contribution margin of $5.00 per dozen. Fixed costs associated with the additional production (other than depreciation expense) will be negligible. Salvage value and the investment in working capital should be ignored. TopCap Co.'s cost of capital for this capacity expansion has been set at 16%.

Required:

1. Calculate the net present value of the proposed investment in the new sewing machine.
2. Calculate the present value ratio of the investment.
3. What is the internal rate of return of this investment relative to the cost of capital?
4. Calculate the payback period of the investment.

Answer 1

years (a)	PV factors @6% (b)	PV factors @16% (c)	SALES AMOUNT AT MARGIN $8 (d)	AMOUNT AT MARGIN $5 (e)	PV AMOUNT AT MARGIN 6%(f=d*b)	PV AMOUNT AT MARGIN $5 (g=e*b)	pv amount at 16% (h=c*e)
2019	0	0			(126000)	(126000)	(126000)
2019	0.9434	0.862	3600*8=28800	3600*5=18000	27170	16981	15516
2020	0.8900	0.743	5600*8=44800	5600*5=28000	39872	24920	20804
2021	0.8396	0.641	8500*8=68000	8500*5=42500	57093	35683	27242
2022	0.7921	0.552	11300*8=90400	11300*5=56500	71606	44754	31188
2023	0.7473	0.476	12000*8=96000	12000*5=60000	71741	44838	28560
TOTAL			328000	205000	267482	167176(a)	123310(b)

A) NPV =PV VALUE OF CASH INFLOWS - PV OF CASH OUT FLOWS

NPV AT contribution $8=267482-126000=141482

NPV AT contribution $5=167176-126000=41176

B) PV RATIO= CONTRIBUTION/SALES=28800/328000=8.7%

C) INTERNAL RATE OF RETURN = a+ NPV_a/NPV_a-NPV_b *(b-a)

IRR = 6%+167176/167176-123310 *(16%-6%)

IRR = 6% + 167176/43866*(10%)=6%+3.8%*10%=6%+0.38%=6.38%

D) pay back period = total cash out flows/total cash inflows = 126000/123310=1.02