A. Correct Explanation

The internal rate of return (IRR) is the discount rate that makes the net present value (NPV) equal to zero.
Since the NPV of Project 1 is `$0`, the discount rate must equal its IRR.

0 = -\`$1`,000 + \frac{\`$400`}{(1+IRR)^1} + \frac{\`$400`}{(1+IRR)^2} + \frac{\`$400`}{(1+IRR)^3}

• IRR = 9.7%
• Calculator setup:
  • $CF_0 = -1,000$
  • $CF_1 = 400$
  • $CF_2 = 400$
  • $CF_3 = 400$
  • Solve for IRR → 9.7%

Next, use this discount rate to calculate the NPV of Project 2:

NPV = -\`$1`,300 + \frac{\`$500`}{(1+0.097)^1} + \frac{\`$500`}{(1+0.097)^2} + \frac{\`$500`}{(1+0.097)^3} = -\`$50`

• Calculator setup:
  • $CF_0 = -1,300$
  • $CF_1 = 500$
  • $CF_2 = 500$
  • $CF_3 = 500$
  • $I = 9.7$
  • Solve for NPV → –`$50`

Intuitive reasoning:

• The discount rate for Project 1 must be positive.
• Project 2 has a greater initial investment (`1`,300)** for the same **net cash flow (\`200`) as Project 1.
• Therefore, Project 2’s NPV must be negative.

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B. Incorrect Explanation

Although the NPV of Project 1 is `0`, the NPV of Project 2 is **–\`50**. A candidate might incorrectly assume both NPVs are \$0` because:

• The same discount rate is used for both projects, or
• Both have the same net cash flow (`$200`).

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C. Incorrect Explanation

The NPV of Project 2 is negative, not positive.
A candidate might mistakenly choose this answer because:

• Project 2’s future cash flows are greater, or
• The net cash flow (`$200`) is positive.