Question

Net Present Value Method and Present Value Index

Diamond and 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 270 per hour. The contribution margin per unit is $0.42 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 $19 per hour. The sewing machine will cost $235,000, have a six-year life, and will operate for 1,400 hours per year. The packing machine will cost $71,600, have a six-year life, and will operate for 1,200 hours per year. Diamond and Turf seeks a minimum rate of return of 15% on its investments.

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	3.353	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

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.

Sewing Machine Packing Machine
Present value of annual net cash flows $ $
Amount to be invested $ $
Net present value $ $

b. Determine the present value index for the two machines. If required, round your answers to two decimal places.

Sewing Machine Packing Machine
Present value index

Answer 1

Answer a

Determination of NPV for the Sewing Machine

NPV of Sewing Machine = Present value of annual net cash flows (using 6 year Annuity factor @ 15%) - Amount to be invested

NPV of Sewing Machine = [$70560 * 3.785] - $235000 = $32,070

Determination of NPV for the automatic packing Machine

NPV of automatic packing Machine = Present value of annual net cash flows (using 6 year Annuity factor @ 15%) - Amount to be invested

NPV of automatic packing Machine = [$22800 * 3.785] - $71600 = $14,698

Working

Calculation of increase in contribution margin per year in case of Sewing Machine

Annual net cash flow i.e.Increase in contribution margin per year = [270 baseballs per hour - 150 baseballs per hour]*$0.42 per baseball * 1400 hours = $70,560

Calculation of saving in labour cost per year in case of automatic packing Machine

Annual net cash flows i.e.Savings in labour cost per year = 1200 hours * $19 per hour = $22,800

Answer b

Calculation of present value index for two machines

Present value index = Present value of annual cash flows / Amount to be invested

Sewing Machine

Packing Machine

Present value of annual cash flows

$267,070

$86,298

/ Amount to be invested

$235,000

$71,600

Present Value Index

1.14

1.21