First Principles Thinking: Terminal Cash Flows
A is correct. This problem introduces salvage value, which is the residual value you recover when selling or scrapping an asset at the end of the project's life. From first principles, a project's total cash flows include: (1) initial investment outflow at t=0, (2) periodic operating cash flows during the project's life, and (3) terminal cash flows at the end, which combine the final year's operations plus any salvage value recovered. Think of salvage value like selling a used car after you are done with it; you get some money back. In Year 5, you receive both the normal 40,000 dollar operating cash flow and an additional 20,000 from selling the equipment, totaling 60,000 for that year. Memory hook: Salvage equals SAVE some value at the end. The 11 percent discount rate reflects the project's risk-adjusted required return.
BA II Plus Steps: (1) CF, 2nd CLR WORK. (2) Initial: 150000 +/- ENTER (CF0=-150,000), down. (3) Years 1-4 are identical: 40000 ENTER, down, 4 ENTER (F01=4 means this cash flow repeats 4 times), down. (4) Year 5 combines operating and salvage: 40000 + 20000 = 60000 ENTER, down, down (F05=1), down. (5) NPV, 11 ENTER (I=11), down, CPT. Result: approximately 9,702.
Manual verification: PV annuity Years 1-4 = 40,000 multiplied by [(1 - 1/1.11^4) / 0.11] = 40,000 times 3.1024 = 124,096. PV Year 5 = 60,000 / 1.11^5 = 60,000 / 1.68506 = 35,606. Total PV inflows = 124,096 + 35,606 = 159,702. NPV = 159,702 - 150,000 = 9,702. Interpretation: Positive NPV of 9,702 dollars means the project creates shareholder value and should be accepted. The salvage value is critical here; without it, Year 5 would only have 40,000, reducing total PV inflows and potentially making NPV negative or much smaller. This illustrates why analysts must carefully consider all cash flows, including terminal values. Salvage values matter enormously for capital-intensive projects (manufacturing, real estate, infrastructure) where assets retain significant residual value.
Edge case: If the salvage value were taxable as a capital gain or loss, you would subtract the tax to get after-tax salvage value. Always use after-tax cash flows for NPV. For example, if the 20,000 salvage creates a 5,000 tax, the after-tax salvage is 15,000, not 20,000. The equipment's book value at Year 5 matters for tax calculation.
B is wrong because 27,500 dollars might result from averaging undiscounted cash flows or using wrong discount rate. C is wrong because 60,000 dollars is just the Year 5 cash flow, ignoring all other years and the initial investment. It also ignores time value of money. Using undiscounted totals or single-year cash flows leads to nonsensical NPV calculations.