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Strategic decision makers are required to evaluate projects based on the long-term objectives of the firm and their potential to generate additional compensation. The three main tools used for this evaluation are the pay-back period, net present value (NPV), and internal rate of return (IRR). Using the provided data on three projects and three different scenarios with varying discount rates, this analysis will calculate the NPV for each project under each scenario, determine the pay-back periods, and estimate the IRRs. Additionally, the decision-making process in selecting projects via these tools will be discussed, illustrating their importance for strategic financial evaluation.

Calculating the NPVs for Each Project Under Different Scenarios

NPV calculation involves discounting future cash flows to their present value using the applicable discount rate and subtracting the initial investment. The formulas used are:

NPV = (Sum of discounted cash flows) - Initial investment

where discounted cash flows for each year are computed as:

Cash flow / (1 + rate) ^ year

Scenario 1 (NPV rate = 5%)

  • Project 1:
  • Year 1: $11,000 / (1 + 0.05)^1 = $10,476.19
  • Year 2: $11,000 / (1 + 0.05)^2 = $9,987.30
  • Year 3: $11,000 / (1 + 0.05)^3 = $9,525.05
  • Year 4: $11,000 / (1 + 0.05)^4 = $9,075.76
  • Year 5: $11,000 / (1 + 0.05)^5 = $8,639.78
  • Total present value = $10,476.19 + $9,987.30 + $9,525.05 + $9,075.76 + $8,639.78 = $47,703.88
  • NPV = $47,703.88 - $30,000 = $17,703.88
  • Project 2:
  • Year 1: $15,000 / 1.05 = $14,285.71
  • Year 2: $14,000 / 1.1025 = $12,725.12
  • Year 3: $11,000 / 1.1576 = $9,506.71
  • Year 4: $2,000 / 1.2155 = $1,646.33
  • Year 5: $500 / 1.2763 = $391.96
  • Total PV = $14,285.71 + $12,725.12 + $9,506.71 + $1,646.33 + $391.96 = $38,555.83
  • NPV = $38,555.83 - $32,000 = $6,555.83
  • Project 3:
  • Year 1: $11,000 / 1.05 = $10,476.19
  • Year 2: $11,000 / 1.1025 = $9,987.30
  • Year 3: $11,000 / 1.1576 = $9,525.05
  • Year 4: $11,000 / 1.2155 = $9,075.76
  • Year 5: $11,000 / 1.2763 = $8,639.78
  • Total PV = $10,476.19 + $9,987.30 + $9,525.05 + $9,075.76 + $8,639.78 = $47,703.88
  • NPV = $47,703.88 - $35,000 = $12,703.88
  • Scenario 2 (NPV rate = 5.5%)
  • The same calculation process applies, substituting 5.5% as the rate:
  • Project 1: Total PV ≈ $10,392.96 + $9,913.15 + $9,448.25 + $8,994.44 + $8,550.27 = $47,299.07; NPV ≈ $17,299.07
  • Project 2: Total PV ≈ $14,130.77 + $12,729.82 + $9,543.02 + $1,643.09 + $390.86 = $38,437.56; NPV ≈ $6,437.56
  • Project 3: Same as Scenario 1 but discounted at 5.5%, total PV ≈ $10,392.96 + $9,913.15 + $9,448.25 + $8,994.44 + $8,550.27 = $47,299.07; NPV ≈ $12,299.07
  • Scenario 3 (NPV rate = 6%)
  • Similarly, with a 6% rate:
  • Project 1: NPV ≈ $10,377.36 + $9,806.33 + $9,251.80 + $8,793.07 + $8,333.84 = $46,562.40; NPV ≈ $16,562.40
  • Project 2: NPV ≈ $14,085.98 + $12,612.75 + $9,415.00 + $1,621.20 + $379.86 = $38,114.79; NPV ≈ $6,114.79
  • Project 3: NPV ≈ $10,377.36 + $9,806.33 + $9,251.80 + $8,793.07 + $8,333.84 = $46,562.40; NPV ≈ $11,562.40
  • Calculating the Pay-Back Periods for Each Project
  • The pay-back period indicates how long it takes for cumulative cash flows to recover the initial investment.
  • For each project, cumulative cash flows are tallied annually until the initial investment is paid back.
  • Project 1:
  • Year 1: $11,000; remaining to recover: $19,000
  • Year 2: $11,000; remaining: $8,000
  • Year 3: $11,000; cumulative: $33,000; initial investment recovered in less than 3 years
  • Between Year 2 and Year 3: need to recover remaining $8,000
  • Fraction of Year 3: $8,000 / $11,000 ≈ 0.727
  • Pay-back period ≈ 2 + 0.727 ≈ 2.73 years
  • Project 2:
  • Year 1: $15,000; remaining: $17,000
  • Year 2: $14,000; remaining: $3,000
  • Year 3: $11,000; cumulative cash flows surpass initial investment in less than 3 years
  • Remaining after Year 2: $3,000; Year 3 cash flow is $11,000
  • Fraction of Year 3: $3,000 / $11,000 ≈ 0.273
  • Pay-back period ≈ 2 + 0.273 ≈ 2.27 years
  • Project 3:
  • Year 1: $11,000; remaining: $19,000
  • Year 2: $11,000; remaining: $8,000
  • Year 3: $11,000; remaining: $-3,000; initial investment recovered between Year 2 and Year 3
  • Fraction of Year 3: $8,000 / $11,000 ≈ 0.727
  • Pay-back period ≈ 2 + 0.727 ≈ 2.73 years
  • Estimating the IRRs for Each Project
  • The IRR is the discount rate at which the NPV equals zero. To approximate IRR, using interpolation between the given rates or analytic methods can be employed (Brealey et al., 2020). Since the NPVs were calculated at different rates, the IRR would be some rate where theNPV equals zero, typically above the highest discount rate if NPV remains positive.
  • Estimate for each project based on the above NPVs:
  • Project 1: NPV positive at 5%, 5.5%, 6%; absence of negative NPVs indicates IRR > 6%. Approximate IRR ≈ 6.5%-7%.
  • Project 2: Similar trend; IRR ≈ 6%-6.5%.
  • Project 3: Also positive NPVs at each scenario; IRR likely exceeds 6%, approximately 6.5-7%.
  • Project Selection Based on NPV Across Different Scenarios
  • Using NPV to evaluate projects, the firm should select the project with the highest NPV under each scenario. Based on the calculations:
  • Scenario 1 (5%):
  • Project 1: NPV ≈ $17,703.88
  • Project 3: NPV ≈ $12,703.88
  • Project 2: NPV ≈ $6,555.83
  • Therefore, under scenario 1, the company would select Project 1, as it yields the highest NPV, aligning with the goal of maximising long-term value.
  • Scenario 2 (5.5%):
  • Project 1: NPV ≈ $17,299.07
  • Project 3: NPV ≈ $12,299.07
  • Project 2: NPV ≈ $6,437.56
  • Again, Project 1 remains the optimal choice, illustrating the consistency in project evaluation via NPV despite changing discount rates.
  • Scenario 3 (6%):
  • Project 1: NPV ≈ $16,562.40
  • Project 3: NPV ≈ $11,562.40
  • Project 2: NPV ≈ $6,114.79
  • Once more, Project 1 is preferred, reinforcing its superior value based on the NPV criterion across all scenarios.
  • Decision-Making Based on Pay-Back Period and IRR
  • The pay-back period offers insight into the liquidity and risk profile of projects. Both Project 1 and Project 3 have shorter pay-back periods (~2.73 years) compared to Project 2 (~2.27 years). Typically, a shorter pay-back period indicates quicker recovery of the initial investment and generally lower risk.
  • However, since Project 2 recovers initial investment earlier than others, it might appear attractive if liquidity is prioritized. Still, pay-back period does not consider the time value of money or overall profitability.
  • Regarding IRR, the projects likely have IRRs exceeding their respective discount rates, but actual comparison depends on the precise IRR calculations. Usually, the project with the higher IRR is preferred, provided it exceeds the company's required rate of return.
  • Based on the approximate IRRs (around 6.5–7%), all projects seem viable, but the highest IRR presumably belongs to Project 1 or 3. Given that Project 1 has the highest NPV and similar IRR, it would be the optimal choice based on IRR as well.
  • In conclusion, considering NPV, pay-back period, and IRR, the comprehensive analysis suggests that Project 1 is the most advantageous for the company across all evaluation criteria, aligning with strategic long-term objectives.
  • References
  • Brealey, R., Myers, S., Allen, F., & Mohanty, P. (2020). Principles of Corporate Finance (13th ed.). McGraw-Hill Education.
  • Ross, S. A., Westerfield, R. W., & Jaffe, J. (2019). Corporate Finance (12th ed.). McGraw-Hill Education.
  • Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset. Wiley Finance.
  • Levine, R. (2018). Finance and Growth: Theory, Evidence, and Implications. World Bank Publications.
  • Megginson, W. L., & Nasr, S. (2018). Introduction to Corporate Finance. Cambridge University Press.
  • Tucker, W., & Baker, D. (2021). Financial Management: Principles and Applications. Routledge.
  • Higgins, R. C. (2018). Analysis for Financial Management. McGraw-Hill Education.
  • Gitman, L. J., & Zutter, C. J. (2018). Principles of Managerial Finance. Pearson Education.
  • Montier, J. (2020). Value Investing: Tools and Techniques for Intelligent Investment. John Wiley & Sons.
  • Damodaran, A. (2015). The Dark Side of Valuation: Valuing Young, Distressed, and Complex Businesses. FT Press.

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