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 $124,000. In addition, delivery and installation costs will total $5,500. 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 $9.00 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 10%.   


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

1. Calculate the net present value of the proposed investment in the new sewing machine as follows: B C D E G H A 1 Period 2 Present value factor 3 Cash flow Present value for this 4 cash flow F 41 0.5523 $101,700 0.8621 $32,400 0.7432 $50,400 0.6407 $76,500 0.4761 $108,000 -129500 37455 49010 56168.0047 2 7931 NPV 51420 92,485 S Calculate the net present value of the proposed investment in the new sewing machine using excel spreadsheet as follows: B G 1 Period 2 Present value factor 3 Cash flow C D E F 1 2 3 45 0.862 0.7431 0.6406 0.5522 0.4761 -3600*9 -5600*9 -8500*9 -11300*9 -12000*9 4 Present value for this cash flow =-124000+5500) =C2°C3 =D2 D3 =E2 E3 =F2 F3 NPV =G2 G3 =(C4+D4+E4+F4+G4)+B4 Hence, the net present value of the proposed investment in the new sewing machine is $92,485. Calculate the present value ratio of the investment as follows: Present value ratio = Present value of Cash inflows Present value of Cash outflow $27,929+$37,452 +$49,006 + $56,159 + 51,419 ($129,500) $221,964 $129,500 =1.71 Hence, present value ratio is 1.71.

As the net present value of the investment is positive, the internal rate of return should be lower than the cost of capital of 16%. 4. The projected annual and cumulative cash flow are as follows: Year 2019 2020 20213 20224 2023 5 Cash Flow 1 $32,400 21 $50,400 $76,500 $101,700 $108,000 Cumulative Cash flow $32,400 $82,800 $159,300 $261,000 $369,000 Therefore, the payback period is more than 2 years and less than 3 years. $129,500-$82,800 $76,500 = 0.61 year Therefore, the payback period is 2.61 years that is (2 years + 0.61 year).