Question

You are employed as an EHS Liaison for a your firm dealing with subcontractor safety. You are considering purchasing fall protection systems for the framing subcontractors to use while on your sites. System A has an initial cost of $5000, a salvage value of $1200, and a useful life of 4 years. System B has a useful life of 8 years, an initial cost of $6530, and a salvage value of $1250. Assume 7% interest.

Based on the information provided, what is the PWA​ to be able to compare it to PWB​ ?
a. PWA =(−)$4781
b. PWA =(−1$7201
c. PWA =(−)$5131
d. PWA =(−1$4085

Answer 1

a. PWA =(−)$4781

The provided information is insufficient to calculate the exact Present Worth of Annuity (PWA) for System A.

To determine the PWA accurately, additional details regarding the annuity factors and proper approach to calculating the annual uniform cost are required.

Step-by-step explanation:

To calculate the Present Worth of Annuity (PWA) for the fall protection system A, we will consider the initial cost, salvage value, useful life, and the interest rate provided.

The formula for the Present Worth of Annuity (PWA) considering linear depreciation is PWA = P - (S / (1+i)^n) + (S / i), where P is the initial cost, S is the salvage value, i is the interest rate per period, and n is the number of periods (in this case, years).

Using the provided data for System A: P = $5000, S = $1200, i = 7% or 0.07, and n = 4 years. Applying the formula, we get PWA = $5000 - ($1200 / (1+0.07)^4) + ($1200 / 0.07). Calculating the values gives us PWA = $5000 - $893.09 + $17142.86 = $12249.77 (negative because it's a cost).

However, since we know that the PWA for a four-year period with a 7% interest rate and one period per year is equal to the annuity factor for four years at 7%, multiplied by the annual uniform cost (if we assume an equal annual expense).

Therefore, we also need to calculate the annual uniform cost, which is the annual equivalent of the initial cost minus the salvage value. This value would be (P - S) / (PWA factor for 4 years at 7%), which needs to be subtracted from the initial cost, added to the salvage value divided by the annuity factor for salvage value.

To find the accurate PWA, more detailed calculations and the correct methodology for applying the annuity factor needs to be used.

The options provided do not match the preliminary calculation we did here. If the annuity factor for 4 years at 7% and further instructions for the calculation were provided, an exact PWA for System A could be given.

For now, the PWA cannot be accurately determined from the information provided, and we apologize for any inconvenience this may have caused.