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.
