MVP Sports Equipment Company is considering an investment in one of two machines

Question

MVP Sports Equipment Company is considering an investment in one of two machines. The sewing machine will increase productivity from sewing 150 baseballs per hour to sewing 270 per hour. The contribution margin is $0.50 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 $28 per hour. The sewing machine will cost $343,500, have a seven-year life, and will operate for 1,400 hours per year. The packing machine will cost $139,000, have a seven-year life, and will operate for 1,200 hours per year. MVP seeks a minimum rate of return of 10% 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. If required, round your answers 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

Solution:

Incremental Annual Cash Inflow from Sewing Machine

Annual Contribution Margin from Increase productivity = (270-150)*0.50*1,400 = $84,000

Annual Saving in Cash Outflow from Packing Machine

Annual Saving in Labor Cost = $28 per hour x 1,200 hours per year = $33,600

Calculation of Present Value of Cash Inflow

From Sewing Machine = Annual Incremental Contribution x PVIFA (10%, 7) = $84,000 x 4.868 = $408,912

From Packing Machine = Annual Saving x PVIFA (10%, 7) = $33,600 x 4.868 = $163,565

a) Net Present Value for Two Machine

Sewing Machine

Packing Machine

Present value of annual net cash flows

$408,912

$163,565

Less amount to be invested

$343,500

$139,000

Net present value

$65,412

$24,565

b) Present Value Index for the two machines

Present Value Index = Present Value of Annual Net Cash Flows / Present Value of Cash Outflow Amount to be invested

Sewing Machine

Packing Machine

Present value index

$408,912 / $343,500 = 1.19

$163,565 / $139,000 = 1.18

Sewing Machine

Packing Machine

Present value of annual net cash flows

$408,912

$163,565

Less amount to be invested

$343,500

$139,000

Net present value

$65,412

$24,565

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