# Question

Calculate NPV, present value ratio, and payback. 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 $88,000. In addition, delivery and installation costs will total $6,000. The machine has the capacity to produce 10,000 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:

2013 . . . . . . . . . . . . . . . . . . . . . . . 3,000 dozen

2014 . . . . . . . . . . . . . . . . . . . . . . . 4,700 dozen

2015 . . . . . . . . . . . . . . . . . . . . . . . 7,100 dozen

2016 . . . . . . . . . . . . . . . . . . . . . . . 9,400 dozen

2017 . . . . . . . . . . . . . . . . . . . . . . . 10,000 dozen

The caps have a contribution margin of $4.20 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 8%.

Required:

a. Calculate the net present value of the proposed investment in the new sewing machine.

b. Calculate the present value ratio of the investment.

c. What is the internal rate of return of this investment relative to the cost of capital?

d. Calculate the payback period of the investment.

2013 . . . . . . . . . . . . . . . . . . . . . . . 3,000 dozen

2014 . . . . . . . . . . . . . . . . . . . . . . . 4,700 dozen

2015 . . . . . . . . . . . . . . . . . . . . . . . 7,100 dozen

2016 . . . . . . . . . . . . . . . . . . . . . . . 9,400 dozen

2017 . . . . . . . . . . . . . . . . . . . . . . . 10,000 dozen

The caps have a contribution margin of $4.20 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 8%.

Required:

a. Calculate the net present value of the proposed investment in the new sewing machine.

b. Calculate the present value ratio of the investment.

c. What is the internal rate of return of this investment relative to the cost of capital?

d. Calculate the payback period of the investment.

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