Diamond & Turf Inc. is considering an investment in one of two machines. The sewing machine will increase productivity from sewing 150 baseballs

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.

a. Determine the net present value for the two machines. Use the present value of an annuity of $1 table in the chapter (Exhibit 2). Round to the nearest dollar.

b. Determine the present value index for the two machines. Round to two decimal places.

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:

a. Annual net cash flow—Sewing Machine: 

$80,640 =  1,800 hours × (290 baseballs – 150 baseballs) × $0.32 per baseball 

Annual net cash flow—Packing Machine: 

$29,400 =  1,400 hours × $21 labor cost saved per hour 

Sewing Machine: 

Annual net cash flow (at the end of each of 8 years)………………………… $  80,640 

× Present value of an annuity of $1 at 15% for 8 years (Exhibit 2)…………   4.487 

Present value of annual net cash flows………………………………………… $361,832 

Less amount to be invested………………………………………………………   260,000 

Net present value…………………………………………………………………… $101,832 

Packing Machine:  

Annual net cash flow (at the end of each of 8 years)………………………… $  29,400 

× Present value of an annuity of $1 at 15% for 8 years (Exhibit 2)…………   4.487 

Present value of annual net cash flows………………………………………… $131,918 

Less amount to be invested………………………………………………………     85,000 

Net present value…………………………………………………………………… $  46,918 

b. Present Value Index = 

Total Present Value of Net Cash Flow 

Amount to Be Invested 

Present value index 

of the sewing machine: = 

Present value index 

of the packing machine: = 

$361,832 

$260,000 

$131,918 

$85,000 

=  1.39 

=  1.55 

c. The present value index indicates that the packing machine would be the 

preferred investment, assuming that all other qualitative considerations are 

equal. Note that the net present value of the sewing machine is greater than 

the packing machine’s. However, the sewing machine requires over triple the 

investment than the packing machine ($260,000 vs. $85,000), for barely 

double the extra net present value ($101,832 vs. $46,918). Thus, the present 

value index indicates the packing machine is favored. If there were sufficient 

capital for both investments, then they would both be attractive opportunities. 

This solution does not consider the alternative use of remaining cash, which is 

an additional complexity beyond the scope of this text.