A newspaper is considering buying locked vending machines to replace open newspa

Question

A newspaper is considering buying locked vending
machines to replace open newspaper racks in the downtown
area. The vending machines cost $45 each. It is expected
that the annual revenue from selling the same quantity of
newspapers will increase $12 per vending machine. The
useful life of the vending machine is unknown.
a) To determine the sensitivity of rate of return to useful
life, prepare a graph for rate of return versus useful
life for lives up to 8 years.
b) If the newspaper requires a 12% rate of return, what
minimum useful life must it obtain from the vending
machines?
c) What would be rate of return if the vending machines
were to last indefinitely?

Explanation / Answer

b) One way to solve it is to use an annuity table. 45/12= 3.75. If we go to an annuity table at a 12% rate we find the factor is 3.6048 for 5 years and 4.1114 for 6 years. If we interpolate (3.75-3.6048)/(4.1114-3.6048) we get .28 so we have 5.28 years. c) This is just the formula for a consol (perpetuity) 12/45= 26.7%.

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