Question

What is the annual worth of a machine with a first cost of $180,000, an annual operating cost of $14,500 per year, no overhaul cost, a salvage value of $16,000, a useful life of 10 years, and a cost rate of 4% per year?

Answer 1

Annual Worth of machine = -180000*(A/P,4%,10) -14500+16000*(A/F,4%,10)

= -180000*0.123291 -14500+16000*0.083291

= -35359.72

Answer 2

To calculate the annual worth of the machine, we'll use the Annual Worth method, which takes into account the initial cost, operating costs, salvage value, and the cost rate over the useful life of the machine. The formula for the annual worth is:

Annual Worth = (P/A, i, n) + (P/G, i, n)

Where: P = Present Worth (initial cost) A = Annual Worth factor G = Gradient (salvage value) i = Interest rate per period (cost rate) n = Number of periods (useful life)

Now, let's plug in the values:

P = $180,000 (initial cost) A = (P/A, i, n) = Annual Worth factor G = $16,000 (salvage value) i = 4% per year = 0.04 n = 10 years (useful life)

First, we need to calculate the Annual Worth factor (A). The formula for the Annual Worth factor is:

A = (i * (1 + i)^n) / ((1 + i)^n - 1)

Let's calculate A first:

A = (0.04 * (1 + 0.04)^10) / ((1 + 0.04)^10 - 1) A = (0.04 * 1.48886446624) / (1.48886446624 - 1) A = 0.0595545786496 / 0.48886446624 A = 0.121948417793

Now, let's calculate the Annual Worth:

Annual Worth = (P/A, i, n) + (P/G, i, n) Annual Worth = ($180,000 * 0.121948417793) + ($16,000 * 0.121948417793) Annual Worth = $21,950.9156034 + $1,951.89468469 Annual Worth = $23,902.8102881

So, the annual worth of the machine is approximately $23,902.81.