The manager of a canned-food processing plant has two labeling machine options. on the basis of a rate of return analysis with a marr of 20% per year, determine (a) which model is economically better, and (b) if the selection changes, provided both options have a 4-year life and all other estimates remain the same.

We need to compare the present values (PV) of all the expenses of all the investments to make an investment decision. The formula of PV = ((C1/(1+r)1) + ((C2/(1+r)2) + ((C3/(1+r)3) +…….+ ((Cn/(1+r)n) + present value of investment – present value of the salvage value

Where, Cn refers to the expense incurred in the nth period and r is the rate of interest per period.

For Machine A, present value of the expenses is

= ((1600/(1+0.20)1) + ((1600/(1+0.20)2) + 15,000 – ((3000/(1+0.20)2)

= 1333.33 + 1111.11 + 15000 – 2083.33

= 15361.11

For Machine B, present value of the expenses is

= ((400/(1+0.20)1) + ((400/(1+0.20)2) + ((400/(1+0.20)3) + ((400/(1+0.20)4) + 25,000 - ((4000/(1+0.20)2)

= 333.33 + 277.77 + 25,000 – 2777.77

= 22833.33

We can see that Machine A is the least cost alternative; therefore, Machine A should be selected.