Answer: positive

## Explanation Given that Project 1 has an NPV of $0, we can determine the discount rate (IRR) for Project 1. The cash flows for Project 1 are: - Year 0: -$1,000 - Year 1: $400 - Year 2: $400 - Year 3: $400 For NPV = 0, the present value of inflows equals the initial investment: $400/(1+r) + $400/(1+r)² + $400/(1+r)³ = $1,000 This is an annuity of $400 for 3 years. The IRR can be found by solving: $400 × PVIFA(r, 3) = $1,000 PVIFA(r, 3) = 2.5 Looking at PVIFA tables or calculating, when PVIFA = 2.5 for 3 periods, r ≈ 9.7%. Now for Project 2: - Year 0: -$1,300 - Year 1: $500 - Year 2: $500 - Year 3: $500 At the same discount rate (9.7%), let's calculate the present value of inflows: PV = $500 × PVIFA(9.7%, 3) PV = $500 × 2.5 = $1,250 NPV = $1,250 - $1,300 = -$50 Wait, this suggests negative NPV. But let's reconsider: The IRR for Project 2 would be: $500 × PVIFA(r, 3) = $1,300 PVIFA(r, 3) = 2.6 For PVIFA = 2.6 for 3 periods, r ≈ 7.7%. Since Project 2 has a lower IRR (7.7%) than Project 1 (9.7%), and they use the same discount rate (which must be 9.7% since Project 1's NPV = 0), Project 2's NPV at 9.7% would be negative. However, let me recalculate more precisely: For Project 1 at IRR: $400/(1+r) + $400/(1+r)² + $400/(1+r)³ = $1,000 Let x = 1/(1+r) $400(x + x² + x³) = $1,000 x + x² + x³ = 2.5 For Project 2: $500(x + x² + x³) = $500 × 2.5 = $1,250 NPV = $1,250 - $1,300 = -$50 So Project 2's NPV is negative at the discount rate where Project 1's NPV is zero. **Therefore, the correct answer is A: negative.** **Key Insight:** When comparing two projects with the same cash flow pattern but different scales, if the smaller project has NPV = 0 at a given discount rate, the larger project with proportionally larger cash flows but proportionally even larger initial investment will have negative NPV at that same rate.

Author: LeetQuiz .