Capital Budgeting Practice
Initial Offer:
- Upfront payment: $1,000,000
- Opportunity cost per year: $500,000
- Writing time: 3 years
- Discount rate: 10%
NPV Analysis:
- Year 0: +$1,000,000
- Year 1: -$500,000 / (1 + 0.1) = -$454,545.45
- Year 2: -$500,000 / (1 + 0.1)^2 = -$412,146.41
- Year 3: -$500,000 / (1 + 0.1)^3 = -$372,230.61
- NPV = $1,000,000 - $454,545.45 - $412,146.41 - $372,230.61 = $160,077.53
IRR Calculation:
Using a financial calculator or spreadsheet, the IRR for this offer is approximately 12.6%.
Conclusion: The NPV is positive ($160,077.53), indicating accepting the offer would create value. However, the IRR (12.6%) is slightly higher than the opportunity cost (10%), suggesting the return might not be optimal compared to alternative investments.
Revised Offer:
- Upfront payment: $550,000
- Payment in year 4: $1,000,000
NPV Analysis:
- Year 0: +$550,000
- Year 4: +$1,000,000 / (1 + 0.1)^4 = $772,186.92
- NPV = $550,000 + $772,186.92 = $1,322,186.92
IRR Calculation:
There are two IRRs for this offer: approximately 14.3% and 36.4%. The lower IRR represents the minimum discount rate at which the project breaks even, while the higher IRR indicates a reinvestment rate that would also satisfy the NPV requirement.
Conclusion: Both NPV ($1,322,186.92) and IRR (14.3%) are favorable, suggesting this offer creates more value than the initial one.
Third Offer:
- Upfront payment: $750,000
- Payment in year 4: $1,000,000
NPV Analysis:
- Year 0: +$750,000
- Year 4: +$1,000,000 / (1 + 0.1)^4 = $772,186.92
- NPV = $750,000 + $772,186.92 = $1,522,186.92
IRR Calculation:
The IRR for this offer is approximately 18.9%, indicating a very attractive return on investment.
Conclusion: With an NPV of $1,522,186.92 and an IRR of 18.9%, this offer provides the highest financial benefit compared to the others.
NPV vs. IRR:
- NPV: Considers the cash flow across the entire project and provides a clear monetary value of the investment. It remains consistent at different discount rates.
- IRR: Reflects the internal rate of return on the investment. It can be multiple for complex cash flows like the revised offer.
Choosing Between Methods:
- IRR should be used with caution:
- It can lead to incorrect decisions when there are multiple IRRs or non-monetary considerations.
- It relies on reinvesting cash flows at the IRR, which might not be possible.
- NPV is generally preferred:
- It provides a clear dollar value of the investment's worth.
- It is easier to interpret and compare across different projects.
Final Decision:
Based on the NPV analysis, you should reject the initial offer and accept the final offer, as it provides the highest potential return ($1,522,186.92) and exceeds your opportunity cost.