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.
| 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 | 3.456 | 3.170 | 3.037 | 2.855 | 2.589 |
| 5 | 4.212 | 3.791 | 3.605 | 3.353 | 2.991 |
| 6 | 4.917 | 4.355 | 4.111 | 3.785 | 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 |
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.
| Sewing Machine | Packing Machine | |
| Present value of annual net cash flows | $ | $ |
| Amount to be invested | $ | $ |
| Net present value |
Determine the present value index for the two machines. Round to two decimal places.
| Sewing Machine | Packing Machine | |
| Present value index |
Solution:
Annual cash inflows - Sewing machine = 1800*140*$0.32 = $80,640
Annual cash inflows - Packing machine = 1400*$21 = $29,400
| Computation of NPV | ||||||
| Sewing Machine | Packing Machine | |||||
| Particulars | Period | PV Factor (15%) | Amount | Present Value | Amount | Present Value |
| Cash outflows: | ||||||
| Initial investment | 0 | 1 | $260,000 | $260,000 | $85,000 | $85,000 |
| Present Value of Cash outflows (A) | $260,000 | $85,000 | ||||
| Cash Inflows | ||||||
| Annual cash inflows | 1-8 | 4.487 | $80,640 | $361,832 | $29,400 | $131,918 |
| Present Value of Cash Inflows (B) | $361,832 | $131,918 | ||||
| Net Present Value (NPV) (B-A) | $101,832 | $46,918 | ||||
| Present Value Index | ||
| Particulars | Sewing Machine | Packing Machine |
| Present value of cash inflows | $361,832 | $131,918 |
| Initial investment | $260,000 | $85,000 |
| Present value index ( PV of cash inflows/Initial investment) | 1.39 | 1.55 |
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