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 180 baseballs per hour to sewing 324 per hour. The contribution margin per unit is $0.46 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 $27 per hour. The sewing machine will cost $400,800, have an eight-year life, and will operate for 1,400 hours per year. The packing machine will cost $133,600, have an eight-year life, and will operate for 1,200 hours per year. Diamond and Turf seeks a minimum rate of return of 12% 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

c. If Diamond and Turf has sufficient funds for only one of the machines and qualitative factors are equal between the two machines, in which machine should it invest? (If both present value indexes are the same, either machine will grade as correct.)
Packing Machine

Answer 1

Solution a:

Incremental cash inflows from sewing machine = 1400 * (324-180) * $0.46 = $92,736

Incremental cash inflow from packing machine = 1200 * $27 = $32,400

Computation of NPV
			Sewing Machine		Packing Machine
Particulars	Period	PV Factor (12%)	Amount	Present Value	Amount	Present Value
Cash outflows:
Initial investment	0	1	$400,800	$400,800	$133,600	$133,600
Present Value of Cash outflows (A)				$400,800		$133,600
Cash Inflows
Annual cash inflows	1-8	4.968000	$92,736	$460,712	$32,400	$160,963
Present Value of Cash Inflows (B)				$460,712		$160,963
Net Present Value (NPV) (B-A)				$59,912		$27,363

Solution b:

Present Value Index
Particulars	Sewing Machine	Packing Machine
Present value of cash inflows	$460,712.00	$160,963.00
Initial investment	$400,800.00	$133,600.00
Present value index ( PV of cash inflows/Initial investment)	$1.15	$1.20

Solution c:

As present value index for Packing machine is higher, thereofore Diamond and Turf should invest in packing machine.