DCF for Uneven Cash Flows - Corporate Finance

A company is evaluating a project with the following after-tax cash flows: Year 0: - $150,000$ , Year 1: $45,000$ , Year 2: $62,000$ , Year 3: $38,000$ , Year 4: $71,000$ . If the company's weighted average cost of capital is 12%, and the project requires an additional working capital investment of $25,000$ at the end of Year 2 (which is fully recovered at the end of Year 4), what is the net present value of this project?
Answer: $18,247$ The correct NPV calculation must account for the working capital investment and recovery. Adjusted cash flows: Year 0: - $150,000$ , Year 1: $45,000$ , Year 2: $62,000 - 25,000 = 37,000$ , Year 3: $38,000$ , Year 4: $71,000 + 25,000 = 96,000$ . NPV = -150,000 + 45,000/ $(1.12)^1$ + 37,000/ $(1.12)^2$ + 38,000/ $(1.12)^3$ + 96,000/ $(1.12)^4$ = -150,000 + 40,179 + 29,518 + 27,043 + 61,507 = $18,247$ . Choice B ignores the working capital impact. Choice C uses original cash flows without working capital adjustments. Choice D incorrectly treats working capital as a permanent cost.
A pharmaceutical company has developed a new drug with patent protection for 12 years. The drug will generate cash flows of $40$ million annually for the first 4 years, $65$ million annually for years 5-8, and $25$ million annually for years 9-12 as generic competition emerges. R&D costs already incurred total $180$ million, and additional regulatory and marketing costs of $60$ million are required immediately. Using a 14% discount rate, what is the incremental NPV of proceeding with the drug launch versus abandoning the project?
Answer: $113.8$ million This question tests your understanding of incremental cash flow analysis and the sunk cost principle in capital budgeting. When evaluating whether to proceed with a project, you must focus only on future incremental costs and benefits, ignoring costs already incurred. The key insight is that the $180 million in R&D costs are sunk costs - they've already been spent regardless of your decision. Only the additional $60 million regulatory and marketing costs should factor into your analysis, since these represent the incremental investment required to proceed. To find the NPV, calculate the present value of all future cash flows and subtract the incremental investment. The cash flows are: Years 1-4: $40 million each; Years 5-8: $65 million each; Years 9-12: $25 million each. Using the 14% discount rate, the present value of these cash flows totals approximately $173.8 million. Subtracting the $60 million incremental investment gives an NPV of $113.8 million. Answer A ($293.8 million) incorrectly adds back the sunk R&D costs instead of ignoring them. Answer B ($173.8 million) represents the gross present value of cash flows without subtracting any costs - a common error when students forget to account for the required investment. Answer C ($53.8 million) incorrectly subtracts both the sunk costs and the incremental costs, double-counting the R&D expenditure. Remember: in incremental analysis, sunk costs are irrelevant to future decisions. Only consider costs and benefits that change based on your decision to proceed or abandon the project.
Using the information in the passage above, if the project generates annual operating cash flows (before considering depreciation tax shield) of $95,000$ , $110,000$ , $125,000$ , $140,000$ , and $155,000$ respectively, what is the project's net present value?
Answer: $-89,145$ Initial investment = 800,000 + 125,000 + 75,000 = $1,000,000$ . Annual depreciation = (800,000 + 125,000)/5 = $185,000$ . Depreciation tax shield = 185,000 × 0.25 = $46,250$ annually. After-tax cash flows: Years 1-5 = operating cash flows + depreciation tax shield. Year 5 also includes working capital recovery ( $75,000$ ) and after-tax salvage value (150,000 - 0.25 × 0 = $150,000$ , since salvage equals book value). Total Year 5 = 155,000 + 46,250 + 75,000 + 150,000 = $426,250$ . NPV = -1,000,000 + sum of discounted cash flows = $-89,145$ . Choice A omits depreciation tax shield. Choice C double-counts working capital. Choice D uses incorrect salvage value treatment.
An investment opportunity generates cash flows of $20,000$ in Year 1, $35,000$ in Year 2, and $50,000$ in Year 3. However, there is a 30% probability that all cash flows will be reduced by 40% due to regulatory changes. Using a discount rate of 10% and assuming the regulatory risk is already reflected in the discount rate, what is the expected net present value if the initial investment is $75,000$ ?
Answer: $8,291$ First calculate expected cash flows: Year 1: 0.7( $20,000$ ) + 0.3( $12,000$ ) = $17,600$ ; Year 2: 0.7( $35,000$ ) + 0.3( $21,000$ ) = $30,800$ ; Year 3: 0.7( $50,000$ ) + 0.3( $30,000$ ) = $44,000$ . NPV = -75,000 + 17,600/1.10 + 30,800/ $(1.10)^2$ + 44,000/ $(1.10)^3$ = -75,000 + 16,000 + 25,455 + 33,058 = $8,291$ . Choice A uses the reduced cash flows throughout. Choice B uses original cash flows without risk adjustment. Choice D incorrectly applies the 30% probability as an additional discount factor.
A real estate investment trust is considering purchasing a property that will generate rental income of $180,000$ annually for 8 years, with rent increases of 3% per year starting in Year 2. Property taxes and maintenance costs total $45,000$ in Year 1 and increase by 5% annually. The property can be sold for $1,500,000$ at the end of Year 8, but selling costs will be 6% of the sale price. What is the present value of the net cash flows using a discount rate of 8%?
Answer: $1,758,621$ Calculate net cash flows for each year: Year 1 net = 180,000 - 45,000 = $135,000$ . For subsequent years, rental income grows at 3% and costs at 5%. Year 8 includes sale proceeds of 1,500,000 × (1-0.06) = $1,410,000$ . The calculation requires discounting each year's net cash flow individually at 8%. Year 8 net cash flow = 180,000 $(1.03)^7$ - 45,000 $(1.05)^7$ + 1,410,000 = $1,611,947$ . Summing all discounted cash flows yields $1,758,621$ . Choice A ignores selling costs. Choice B uses incorrect growth rates. Choice D fails to account for increasing costs.

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