All-star, Inc., is considering an investment in one of two machines. The sewing machine will increase productivity from sewing 150 baseballs per hour to sewing 260 per hour. The contribution margin per unit is $0.54 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 $25 per hour. The sewing machine will cost $360,000, have an eight-year life, and will operate for 1,700 hours per year. The packing machine will cost $ 120,000, have an eight-year life, and will operates for 1,600 hours per year. All-star 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 two decimal places.

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

(c) If All-star has sufficient funds for only one of the machines and qualitative factors are equal between the two machines, in which machine should it invest?

 

(a)   Annual net cash flow x

            Sewing Machine:       $100,980 =    1,700 hours × 110 incremental baseballs × $0.54 per baseball

       Annual net cash flow x

            Packing Machine:        $40,000 = 1,600 hours × $25 labor cost saved per hour

       Sewing Machine:

        Annual net cash flow (at the end of each of 8 years)...................... $   100,980

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

        Present value of annual net cash flows............................................ $   453,097

        Less amount to be invested................................................................... 360,000

        Net present value............................................................................... $    93,097

       Packing Machine:

        Annual net cash flow (at the end of each of 8 years)........................ $   40,000

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

        Present value of annual net cash flows.............................................. $ 179,480

        Less amount to be invested..................................................................  120,000

        Net present value................................................................................. $  59,480

(b)   please see the attached file for the complete solution.

(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 triple the investment that the packing machine does ($360,000 vs. $120,000), for less than double extra net present value ($93,097 vs. $59,480). 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.