Ignore income taxes in this problem.) Tangen Corporation is considering the purchase of a machine that would cost $386,000 and would last for 6 years. At the end of 6 years, the machine would have a salvage value of $83,000. By reducing labor and other operating costs, the machine would provide annual cost savings of $104,600. The company requires a minimum pretax return of 14\% on all investment projects. The net present value of the proposed project is closest to: Click here to view Exhibit 8B-1 and Exhibit 8B-2 to determine the appropriate discount factor(s) using tables. $103,789 $20,789 $17,059 $58,637
The Correct Answer and Explanation is:
To calculate the net present value (NPV) of Tangen Corporation’s proposed investment, we use the formula:
NPV=Present value of annual savings+Present value of salvage value−Initial investment\text{NPV} = \text{Present value of annual savings} + \text{Present value of salvage value} – \text{Initial investment}
Step 1: Present value of annual cost savings
Annual savings = $104,600 Project life = 6 years Discount rate = 14%
From Exhibit 8B-2 (present value of an annuity of $1 at 14% for 6 years), the factor is approximately 3.8887
PV of savings=104,600×3.8887=406,788.02\text{PV of savings} = 104,600 \times 3.8887 = 406,788.02
Step 2: Present value of salvage value
Salvage value = $83,000 From Exhibit 8B-1 (present value of $1 at 14% for 6 years), the factor is approximately 0.4564
PV of salvage=83,000×0.4564=37,881.20\text{PV of salvage} = 83,000 \times 0.4564 = 37,881.20
Step 3: Calculate NPV
NPV=406,788.02+37,881.20−386,000=58,669.22\text{NPV} = 406,788.02 + 37,881.20 – 386,000 = 58,669.22
Rounded to the nearest whole number, the NPV is approximately $58,637
Explanation:
The company is evaluating whether the machine is a worthwhile investment based on projected cost savings and salvage value. The annual cost savings are treated as an annuity and discounted to present value using a 14 percent discount rate. The salvage value is treated as a lump sum to be received at the end of year 6 and discounted accordingly. The net present value approach compares the total present value of the benefits to the initial outlay. A positive NPV indicates the investment exceeds the required return, so Tangen Corporation should accept the project.
Correct answer: $58,637
