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 $0.52 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 $475,400, have an eight-year life, and will operate for 1,400 hours per year. The packing machine will cost $117,000, have an eight-year life, and will operate for 1,200 hours per year. Diamond and Turf seeks a minimum rate of return of 10% 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

Internal Rate of Return Method

The internal rate of return method is used by Testerman Construction Co. in analyzing a capital expenditure proposal that involves an investment of $21,630 and annual net cash flows of $6,000 for each of the seven years of its useful life.

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

a. Determine a present value factor for an annuity of $1 which can be used in determining the internal rate of return. If required, round your answer to three decimal places.

b. Using the factor determined in part (a) and the present value of an annuityof $1 table above, determine the internal rate of return for the proposal.
%

Answer 1

ans 1	Sewing Machine	Packing Machine
Present value of annual net cash flows	559279	134442
	(324-180)*.52*1400*5.335	21*1200*5.335
Amount to be invested	$475,000	$117,000
Net present value	$84,279	$17,442.00
Note PV of Annuity at $1 for 10% ,8 is .5335
ans 2
	Sewing Machine	Packing Machine
Present value index	1.18	1.15
Present value of annual net cash flows/Initial investment	559279/475000	134442/117000
ans a
IRR is where NPV is $0 . We need to use trial and error method to calculate it
Let us take discount factor 20% so present value factor is at 20% for 7 years 3.605
answer 3.605
ans b
IRR is 20%
Present value of annual net cash flows	21630
	6000*3.605
Amount to be invested	$21,630
Net present value	$0

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