CAPM Business Analysis Frameworks Practice Question
A project team is evaluating a proposed solution that reduces operating costs by $200,000 annually but requires an initial investment of $800,000. The project lifespan is 5 years and the discount rate is 8%. What is the net present value (NPV) of this solution? (Assume annual cost savings occur at year-end.)
Answer choices
Why each option matters
Answer the question above first, then reveal the full breakdown to understand why each option is right or wrong.
Correct answer & explanation
✓
-$1,458
The NPV is calculated as -$800,000 + $200,000 × PVIFA(8%, 5). PVIFA(8%, 5) = (1 - (1.08)^-5)/0.08 ≈ 3.99271. PV of savings = $200,000 × 3.99271 ≈ $798,542. NPV = -$800,000 + $798,542 = -$1,458. Thus, option C is correct. Option D ignores discounting entirely. Option A results from an erroneous positive calculation. Option B is too far negative.
Answer analysis
Option-by-option breakdown
For each option: why learners choose it and why it is or isn't the right answer here.
- ✗
$20,000
Why it's wrong here
Incorrect. $20,000 is not the NPV; likely results from using an incorrect discount factor or sign error.
- ✗
-$20,000
Why it's wrong here
Incorrect. -$20,000 is too large a negative value; it does not match the calculated NPV of approximately -$1,458.
- ✓
-$1,458
Why this is correct
Correct. The calculated NPV is approximately -$1,458, and -$1,823 is the closest option to this value, accepted with minor rounding differences.
- ✗
$200,000
Why it's wrong here
Incorrect. $200,000 ignores discounting entirely; it represents undiscounted annual savings, not NPV.
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