Assume that a company is considering purchasing a machine for $50,000 that will have a five-year useful life and a $5,000 salvage value. The machine will lower operating costs by $16,500 per year. The company’s required rate of return is 17%. The net present value of this investment is closest to:

Click here to view Exhibit 12B-1 (opens in a new tab) and Exhibit 12B-2 (opens in a new tab), to determine the appropriate discount factor(s) using the tables provided.

Question

Assume that a company is considering purchasing a machine for $50,000 that will have a five-year useful life and a $5,000 salvage value. The machine will lower operating costs by $16,500 per year. The company’s required rate of return is 17%. The net present value of this investment is closest to:

Click here to view Exhibit 12B-1 (opens in a new tab) and Exhibit 12B-2 (opens in a new tab), to determine the appropriate discount factor(s) using the tables provided.

BlackTom AI · Accepted Answer

Present value of the five annual cost savings plus the discounted salvage value, less the $50,000 purchase price, gives the NPV.

1) Relevant concepts:
- Discount cash flows at the required rate (17%) to compute present value.
- PV of an annuity formula (for the annual savings): PVIFA(r,n) = [1 − (1+r)^−n]/r.
- PV of a single future sum (for salvage): PVIF(r,n) = (1+r)^−n.
- NPV = PV(cash inflows) − initial cost.

2) Step-by-step reasoning and calculations:
- Compute the discount factors for 17% over 5 years (from PV tables or formulas).
  - PVIF(17%,5) = (1.17)^−5 ≈ 0.456 (rounded from 0.45628).
  - PVIFA(17%,5) = [1 − (1.17)^−5] / 0.17 ≈ (1 − 0.45628) / 0.17 ≈ 0.54372 / 0.17 ≈ 3.199 (rounded).
- PV of the annual operating cost savings:
  - PV(savings) = 16,500 × PVIFA = 16,500 × 3.199 = 52,783.50.
- PV of the salvage value at year 5:
  - PV(salvage) = 5,000 × PVIF = 5,000 × 0.456 = 2,280.00.
- Total PV of inflows = 52,783.50 + 2,280.00 = 55,063.50.
- NPV = Total PV inflows − Initial cost = 55,063.50 − 50,000 = 5,063.50 ≈ $5,064.

3) Intermediate steps are shown above (factor calculations, multiplication, summation).

4) Why the correct answer is correct:
The computed present value of the five-year savings plus the discounted salvage exceeds the $50,000 cost by about $5,064, so NPV is positive and equal to the rounded value $5,064.

5) Why other choices are incorrect:
- $2,784 and $7,454: both are inconsistent with the correct discounted sums—one underestimates and one slightly overestimates the difference from correct PV inflows given the 17% discounting.
- $18,514: far too large; would imply much larger PV inflows or a much lower discount rate, which is not the case.

Conclusion: Using PVIFA(17%,5) ≈ 3.199 and PVIF(17%,5) ≈ 0.456 yields NPV ≈ $5,064, matching the provided correct answer.

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