MVP Sports Equipment Company, is considering an investment in one of two machine

Question

MVP Sports Equipment Company, is considering an investment in one of two machines. The sewing machine will increase productivity from sewing 120 baseballs per hour to sewing 220 per hour. The contribution margin is $0.36 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 $24 per hour. The sewing machine will cost $256,300, have a 10-year life, and will operate for 1,400 hours per year. The packing machine will cost $141,600, have a 10-year life, and will operate for 1,200 hours per year. MVP seeks a minimum rate of return of 12% on its investments.

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.

b. Determine the present value index for the two machines. If required, round your answers to two decimal places.

c. If MVP has sufficient funds for only one of the machines and qualitative factors are equal between the two machines, in which machine should it invest? (If both present value indexes are the same, either machine will grade as correct.)
SelectPacking MachineSewing MachineItem 9

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

Explanation / Answer

Assuming this is an ordinary annuity with constant cash flows, we find the annual cash flows from this equation

NPV = R x PVIFA(i%, n) - CF0
11,970 = R x PVIFA(12%, 4) - 91,000

PVIFA(12%, 4) = [1 - {1/(1+12%)^4]/12%
PVIFA(12%, 4) = [1 - {1/(1.12)^4]/12%
PVIFA(12%, 4) = [1 - {1/1.57351936]/12%
PVIFA(12%, 4) = [1 - 0.6355181]/12%
PVIFA(12%, 4) = [0.3644819]/12%
PVIFA(12%, 4) = [0.3644819]/0.12
PVIFA(12%, 4) = 3.0373493

11,970 = R x 3.0373493 - 91,000
R x 3.0373493 - 91,000 = 11,970
R x 3.0373493 = 11,970 + 91,000
R x 3.0373493 = 102,970
R = 102,970 / 3.0373493
R = $33,901.27

The net cash flows for the investment are $33,901.27 $33,901.27 $33,901.27 $33,901.27

Let us check to see if we get an NPV of $11,970 with these cash flows

I get the following results from this online NPV toolhttp://finance.thinkanddone.com/online-k…

NPV at 12%
DCF0 = -91000 / (1+12%)^0 = -91,000
DCF1 = 33901.27 /(1+12%)^1 = 30,268.99
DCF2 = 33901.27 /(1+12%)^2 = 27,025.88
DCF3 = 33901.27 /(1+12%)^3 = 24,130.25
DCF4 = 33901.27 /(1+12%)^4 = 21,544.87
NPV = $11,970 NPV calculation
http://finance.thinkanddone.com/online-k…

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