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.