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 $27 per hour. The sewing machine will cost $216,200, have a five-year life, and will operate for 1,400 hours per year. The packing machine will cost $98,100, have a five-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

Answer 1

(1) Net present value is difference between present value of cash flow and initial investment. project with higher NPV is more profitable.

we will first prepare the cash flow table

sewing machine

additional balls stiched per hour [270-150]	120
increase in contribution margin per ball stiched	$0.42
increase in contribution margin per hour [120balls*0.42]	$50.4
hours per year	1400
increase in margin per year [50.4$*1400]	$70,560
useful years	5
PV factor of $1 compounded at 12% for 5years	3.605
present value of cash flows [70560*3.605]	$254,369

packing machine

Increase in contribution margin due to labor savings	$27 per hour
operating hours per year	1200
increase in contribution margin per year [27*1200]	$32,400
useful life	5 years
PV factor of $1 compounded at 12% for 10years	$3.605
present value of annual cash flow [32400*3.605]	$116,802

	sewing machine	packing machine
present value of annual cash flow	$254,369	$116,802
amount to be invested	$216,200	$98,100
Net present value	$38,169[254369-216200]	$18,702[116802-98100]

sewing machine has a higher NPV it is better to invest in sewing machine

2. present value index= net present value/initial investment

	sewing machine	packing machine
present value index	0.18[38169/216200]	0.19[18702/98100]

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