Net Present Value Method and Present Value Index Diamond & Turf Inc. is consider

Question

Net Present Value Method and Present Value Index

Diamond & Turf Inc. is considering an investment in one of two machines. The sewing machine will increase productivity from sewing 150 baseballs per hour to sewing 290 per hour. The contribution margin per unit is $0.32 per baseball. Assume that any increased production of baseballs can be sold. The second machine is an automatic packing machine for the golf ball line. The packing machine will reduce packing labor cost. The labor cost saved is equivalent to $21 per hour. The sewing machine will cost $260,000, have an eight-year life, and will operate for 1,800 hours per year. The packing machine will cost $85,000, have an eight-year life, and will operate for 1,400 hours per year. Diamond & Turf seeks a minimum rate of return of 15% on its investments.

a. Determine the net present value for the two machines. Use the table of present values of an annuity of $1 above. Round to the nearest dollar.

b. Determine the present value index for the two machines. Round to two decimal places.

Present Value of an Annuity of $1 at Compound Interest Year 6% 10% 12% 15% 20% 1 0.943 0.909 0.893 0.870 0.833 2 1.833 1.736 1.690 1.626 1.528 3 2.673 2.487 2.402 2.283 2.106 4 3.465 3.170 3.037 2.855 2.589 5 4.212 3.791 3.605 3.352 2.991 6 4.917 4.355 4.111 3.784 3.326 7 5.582 4.868 4.564 4.160 3.605 8 6.210 5.335 4.968 4.487 3.837 9 6.802 5.759 5.328 4.772 4.031 10 7.360 6.145 5.650 5.019 4.192

Explanation / Answer

a.

Investment in sewing machine

Life (n) = 8 years

Yearly operations of hours = 1800 hrs.

Cash inflows per hour = increase in production per hour*contribution margin = (290-150)*.32 = $44.8

Yearly increase in cash flow = 44.8*1800 = $80640

R = 15%

Present value of yearly cash inflows = 80640*(1 – 1/(1+R)^n)/R = 80640*(1-1/1.15^8)/.15

Present value of yearly cash inflows = $361857.61

Investment amount = $260000

Net present value = 361857.61 – 260000 = 101857.61

Investment in packaging machine

Life (n) = 8 years

R = 15%

Yearly operations of hours = 1400 hrs.

Cash inflows per hour = Savings in labor cost per hour = $21

Yearly cash inflows = 21*1400 = $29400

Present value of cash inflows = 29400*(1-1/(1+R)^n)/R = 29400*(1-1/1.15^8)/.15

Present value of cash inflows = $131927.25

Initial investment = $85000

Net present value = 131927.25 - 85000 = $46927.25

b.

Present value index for sewing machine = Present value of cash inflows / investment

Present value index for sewing machine = 361857.61/260000 = 1.39

Present value index for packaging machine = Present value of cash inflows / investment

Present value index for packaging machine =131927.25/85000 = 1.55

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