Question

Calculate the present worth of all costs for a newly acquired machine with an initial cost of $40,000, no trade-in value, a life of 12 years, and an annual operating cost of $17,000 for the first 5 years, increasing by 10% per year thereafter. Use an interest rate of 10% per year. The present worth of all costs for a newly acquired machine is determined to be

Answer 1

The present worth of all costs is calculated as follows

Present worth = $40,000+ * 10 000 $17,000((1+0.10)5-1] 17. +7 $17,000 X (1 + 0.10) -- 0.10X(1+0.10)

For the first 5 years, the present worth of costs is found using the present value of annuity equation. After the 5th year, the operating costs increases by 10% and the interest rate is also 10% i.e. ( r = g) . The present value of growing annuity when r = g is nA , where n is the number of years and A is the annuity amount.

Present worth of all costs for a newly acquired machine is determined to be = $ 185,721.97 $\approx$ $ 185,722

Present worth of all costs for a newly acquired machine is determined to be = $ 185,722