Question27 Northgate Signal Systems is considering a six-year project that requires installing new communications equipment at a cost of $468,200. This cost will be depreciated straight-line to zero over the project’s life. The equipment will save the company $141,300 per year in pretax operating costs, and the equipment requires an initial investment in net working capital of $26,400. All of the net working capital will be recovered at the end of the project. At the end of the project, the communications equipment is expected to be sold for $42,000. The tax rate is 24 percent and the discount rate is 12.8 percent.What is the net present value (NPV) of this project? $27,871.08 $40,686.98 $45,580.33 $67,086.98 ResetMaximum marks: 3 Flag question undefined单项选择题
A
$27,871.08
B
$40,686.98
C
$45,580.33
D
$67,086.98

Question

Question27 Northgate Signal Systems is considering a six-year project that requires installing new communications equipment at a cost of $468,200. This cost will be depreciated straight-line to zero over the project’s life. The equipment will save the company $141,300 per year in pretax operating costs, and the equipment requires an initial investment in net working capital of $26,400. All of the net working capital will be recovered at the end of the project. At the end of the project, the communications equipment is expected to be sold for $42,000. The tax rate is 24 percent and the discount rate is 12.8 percent.What is the net present value (NPV) of this project? $27,871.08 $40,686.98 $45,580.33 $67,086.98 ResetMaximum marks: 3 Flag question undefined单项选择题

A

$27,871.08

B

$40,686.98

C

$45,580.33

D

$67,086.98

BlackTom AI · Accepted Answer

Annual straight-line depreciation = 468,200 / 6 = 78,033.33 per year.

1) Relevant concepts
- Operating cash flow (OCF) for a project with depreciation: OCF = (Sales or savings)*(1 − tax) + (Depreciation*tax). This comes from OCF = (Savings − Depreciation)*(1 − tax) + Depreciation.
- Terminal cash flow includes after-tax salvage plus recovery of net working capital (NWC).
- NPV = −Initial investment + PV of annual OCFs + PV of terminal cash flow, discounted at the required rate.

2) Step-by-step reasoning and calculations
- Annual pretax savings = 141,300. Tax rate = 24%.
- After-tax portion of savings = 141,300*(1 − 0.24) = 141,300*0.76 = 107,388.00.
- Depreciation tax shield = Depreciation * tax = 78,033.33 * 0.24 = 18,728.00.
- Annual OCF = 107,388.00 + 18,728.00 = 126,116.00.

- Initial cash outflow at t=0 = Equipment cost + NWC = 468,200 + 26,400 = 494,600.00.

- At t=6: book value = 0 (fully depreciated), salvage = 42,000, tax on gain = 42,000*0.24 = 10,080, so after-tax salvage = 42,000 − 10,080 = 31,920. Recovery of NWC = 26,400. Terminal cash flow = 31,920 + 26,400 = 58,320.00.
- Total cash flow in year 6 = OCF + terminal = 126,116 + 58,320 = 184,436.

3) Discounting (showing intermediate steps)
- Discount rate r = 12.8% = 0.128. Present value factor for an n-year annuity: (1 − (1 + r)^(−n)) / r.
- Annuity PV factor for n=6, r=0.128: (1 − (1.128)^(−6)) / 0.128 ≈ 4.019695.
- PV of six annual OCFs = 126,116 * 4.019695 ≈ 506,948.93.
- PV of terminal lump sum (58,320 at t=6): PV = 58,320 / (1.128^6) ≈ 58,320 * 0.485438 ≈ 28,338.05.
- Total PV of inflows = 506,948.93 + 28,338.05 = 535,286.98.

4) Final NPV and interpretation
- NPV = Total PV inflows − Initial outflow = 535,286.98 − 494,600.00 = 40,686.98.
- Because NPV > 0, the project adds value and should be accepted.

5) Why the other choices are incorrect
- $27,871.08, $45,580.33, and $67,086.98 result from either omitting the depreciation tax shield, mishandling the after-tax salvage/NWC recovery, or using an incorrect discounting of the terminal cash flow. The correct treatment of depreciation tax shield, after-tax salvage, and full recovery of NWC yields $40,686.98.