Question

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.

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. Round to two decimal places.

	Sewing Machine	Packing Machine
Present value index

c. If Diamond & 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?

Answer 1

A). NET PRESENT VALUES FOR TWO MACHINES IS AS FOLLOWS:

Particulars	Sewing Machine	Packing Machine
Present value of annual net cash flows	$3,61,832	$1,31,918
Amount to be invested	$2,60,000	$85,000
Net present value	$1,01,832	$46,918

Present value of annual net cash flows:-

SEWING MACHINE = Annual net cash Inflow x present value annuity factor @ 15% for 8 years

= $80,640 x 4.487

= $ 3,61,831.68 or to be round off as $3,61,832

Additional productivity due to purchase of Sewing machine = Increased Quantity - Existing Quantity
= 290 baseball per hour - 150 baseball per hour
= 140 baseball per hour
Total operative hours of machine during the year = 1,800 hours
Total increased productivity during the year = Total hours x Total additional productivity per hour
= 1,800 x 140
= 2,52,000
Contribution per basketball = $0.32
Total additional Contribution due to purchase of sewing machine per annum = 2,52,000 x $0.32
= $80,640

  

PACKING MACHINE

Total labor cost saved per hour due to Packing machine = $21 per hour
Total operative hours during the year = 1,400 hours
Total Cost saving due to new Packing machine per annum = 1,400 hours x $21 per hour
= $29,400

Total savings due to new packing machine = Annual cost saving x present value annuity factor @ 15% for 8 years
                   = $29,400 x 4.487
                   = $1,31,917.8 or round off to $1,31,918

B). PRESENT VALUE INDEX FOR TWO MACHINES IS AS FOLLOWS:-

PARTICULARS	SEWING MACHINE	PACKING MACHINE
Present Value Index

Present value Index = Present value of future cash flows / Initial Investment

SEWING MACHINE = $3,61,832 / $2,60,000 = 1.39
PACKING MACHINE = $1,31,918 / $ 85,000 = 1.55

OR
It can also be calculated as follows:-

Present value Index = (Net present value + Initial investment) / Initial Investment

SEWING MACHINE = ($ 1,01,832 + $ 2,60,000) / $2,60,000 = 1.39
PACKING MACHINE = ($ 46,918 + $ 85,000) / $ 85,000 = 1.55

C). RANKING

PARTICULARS	AS PER NET PRESENT VALUE CONCEPT	AS PER PRESENT VALUE INDEX CONCEPT
Sewing Machine	1	2
Packing Machine	2	1

If Diamond & Turf has sufficient funds for only one of the machines and qualitative factors are equal between the two machines then it should invest in Sewing machine because both the methods gives the different rank so In this circumstances the project which gives a higher net present value should be preferred because in doing so the firm will be able to maximize the wealth of shareholders.
As if we talk about the net present value of the given two machines then we find that NPV of sewing machine is greater than the NPV of packing machine.
but if we talk about the present value index of the given two machines then we find that Present value index of packing machine is greater than present value index of Sewing machine.