Chapter 8: Net Present Value and Other Investment Criteria

Net Present Value (NPV)# Definitions and Concept* Net Present Value (NPV): Defined as the difference between an investment’s market value and its cost. It is the primary tool used in capital budgeting to determine if a project creates value for the firm.* Discounted Cash Flow (DCF) Valuation: The process of valuing an investment by discounting all of its expected future cash flows to the present using an appropriate discount rate.# NPV Example Calculation* Project Parameters:- Cash revenues from a fertilizer business: $£20,000$ per year.- Cash costs (including taxes): $£14,000$ per year.- Project duration: 8 years.- Salvage value of plant, property, and equipment at year 8: $£2,000$.- Initial investment cost: $£30,000$.- Discount rate: $15\%$.* Cash Flow Analysis:- Net Inflow (Years 1–7): Revenues ($£20,000$) - Costs ($£14,000$) = $£6,000$.- Net Inflow (Year 8): Revenues ($£20,000$) - Costs ($£14,000$) + Salvage ($£2,000$) = $£8,000$.* Formula for Total Present Value:The present value (PV) is calculated using the annuity formula for the $£6,000$ flows and the lump sum formula for the salvage value:$PV = £6,000 \times \frac{1 - (\frac{1}{1.15^8})}{0.15} + \frac{2,000}{1.15^8}$PV = (£6,000 \times 4.4873) + \frac{2,000}{3.0590}$PV = £26,924 + 654 = £27,578$* Calculation of NPV:$NPV = -\text{Initial Cost} + \text{PV of Cash Flows}$NPV = -£30,000 + 27,578 = -£2,422* Conclusion: Since the NPV is negative, the project should be rejected.# NPV Decision Rule* Accept Criteria: Accept the project if the NPV is greater than zero (NPV > 0$).* <strong>Reject Criteria:</strong> Reject the project if the NPV is less than zero ($NPV < 0$).* <strong>Neutral:</strong> If$NPV = 0, the project is expected to earn exactly the required return.# NPV Strengths* Uses Cash Flows: Focuses on actual cash inflows and outflows rather than accounting earnings, which can be manipulated by non-cash items.* Uses All Cash Flows: Unlike some other methods, NPV considers every cash flow throughout the entire life of the project.* Discounts Cash Flows: Fully incorporates the time value of money by discounting future values back to the present.# The Payback Rule# Definition and Concept* Payback Period: The amount of time required for an investment to generate cash flows sufficient to recover its initial cost.# Payback Decision Rule* Accept Criteria: Accept if the calculated payback period is less than a pre-specified benchmark/cutoff period.* Reject Criteria: Reject if the calculated payback period is greater than the benchmark.# Payback Period Example* Data:- Initial Investment (Year 0): -£50,000$- Year 1:$£30,000$- Year 2:$£20,000$- Year 3:$£10,000$- Year 4:$£5,000$* <strong>Calculation:</strong> After Year 1,$-£20,000$remains. By the end of Year 2, the full$£50,000$is recovered ($30,000 + 20,000). Thus, the Payback Period is exactly 2 years.# Advantages and Disadvantages of Payback (Table 8.3)* Advantages:1. Easy to understand and calculate.2. Adjusts for the uncertainty of later cash flows (by ignoring them).3. Biased towards liquidity.* Disadvantages:1. Ignores the time value of money.2. Requires an arbitrary cutoff point.3. Ignores cash flows occurring after the cutoff date.4. Biased against long-term projects, such as research and development (RE&D).# Discounted Payback Period# Definition and Concept* Discounted Payback Period: The length of time required for an investment’s discounted cash flows to equal its initial cost.# Discounted Payback Decision Rule* Accept Criteria: Accept if the discounted payback period is less than a pre-specified benchmark period.* Reject Criteria: Reject if the discounted payback period is greater than the benchmark.# Example: Ordinary vs. Discounted Payback (Table 8.4)* Scenario: Cash flow of €100$per year for 5 years.* <strong>Year 1:</strong> Undiscounted =$€100$; Discounted =$€89$; Accumulated Undiscounted =$€100$; Accumulated Discounted =$€89$.* <strong>Year 2:</strong> Undiscounted =$€100$; Discounted =$€79$; Accumulated Undiscounted =$€200$; Accumulated Discounted =$€168$.* <strong>Year 3:</strong> Undiscounted =$€100$; Discounted =$€70$; Accumulated Undiscounted =$€300$; Accumulated Discounted =$€238$.* <strong>Year 4:</strong> Undiscounted =$€100$; Discounted =$€62$; Accumulated Undiscounted =$€400$; Accumulated Discounted =$€300$.* <strong>Year 5:</strong> Undiscounted =$€100$; Discounted =$€55$; Accumulated Undiscounted =$€500$; Accumulated Discounted =$€355.# Average Accounting Return (AAR)# Definition and Concept* Average Accounting Return (AAR): An investment’s average net income divided by its average book value. It is defined as:AAR = \frac{\text{Average Net Income}}{\text{Average Book Value}}# AAR Example* Scenario Details:- Store improvement cost: £500,000$.- Project life: 5 years (at the end, it reverts to mall owners).- Depreciation: 100$£100,000$per year).- Tax rate:$25\%$.- Average Net Income: Assume$£50,000$.- Average Book Value:$\frac{£500,000 + 0}{2} = £250,000$.* <strong>Calculation:</strong>$AAR = \frac{£50,000}{£250,000} = 20\%# AAR Decision Rule* Accept Criteria: Accept if the AAR is greater than a target return.* Reject Criteria: Reject if the AAR is less than a target return.# Advantages and Disadvantages of AAR (Table 8.7)* Advantages:1. Easy to calculate.2. Information is usually readily available from accounting records.* Disadvantages:1. Not a true rate of return (ignores time value of money).2. Uses an arbitrary benchmark cutoff rate.3. Based on accounting (book) values rather than cash flows or market values.# Internal Rate of Return (IRR)# Definition and Concept* Internal Rate of Return (IRR): The discount rate that makes the NPV of an investment zero. It is the project's intrinsic rate of return.# IRR Decision Rule* Accept Criteria: Accept the project if the IRR is greater than the required discount rate (hurdle rate).* Reject Criteria: Reject the project if the IRR is less than the required discount rate.# IRR Example Calculation* Data: Investment costs €100$and yields$€60$/year for 2 years.* <strong>Equation:</strong>$NPV = -€100 + \frac{60}{1 + IRR} + \frac{60}{(1 + IRR)^2} = 0$* <strong>Result:</strong> Solving for IRR gives$13.1\%.# Problems with IRR# Non-Conventional Cash Flows* If cash flows change sign more than once (e.g., negative, positive, negative), there may be multiple IRRs.* Example:- Year 0: -€60$- Year 1:$+€155$- Year 2:$-€100$* This profile could yield IRRs at both$25\%$and$33.3\%.# Mutually Exclusive Investments* Situations where taking one investment prevents taking another.* Example Conflict:- Project A: IRR = 24\%$.- Project B:$IRR = 21\%$.- Although Project A has a higher IRR, Project B might have a higher NPV at lower discount rates. The "Crossover Point" where$NPV(A) = NPV(B)$in this example is$11.1\%.# Investing vs. Financing* Project A (Investing): Year 0 = -€100$, Year 1 =$+€130$. NPV decreases as discount rate increases.* <strong>Project B (Financing):</strong> Year 0 =$+€100$, Year 1 =$-€130. NPV increases as discount rate increases.# Advantages and Disadvantages of IRR (Table 8.9)* Advantages:1. Closely related to NPV, often leading to the same decision.2. Easy to understand and communicate.* Disadvantages:1. May result in multiple answers for non-conventional cash flows.2. May lead to incorrect decisions when comparing mutually exclusive projects.# Modified Internal Rate of Return (MIRR)# MIRR Approaches* Discounting Approach: Discount all negative cash flows back to the present at the required return and add them to the initial cost. Then find the IRR.* Reinvestment Approach: Compound all cash flows (positive and negative) except the first one out to the end of the project's life and then calculate the IRR.* Combination Approach: Negative cash flows are discounted to the present, and positive cash flows are compounded to the end of the project life.# MIRR Example Results (@ 20%)* Discounting Approach MIRR: 19.74\%$* <strong>Reinvestment Approach MIRR:</strong>$19.72\%$* <strong>Combination Approach MIRR:</strong>$19.87\%* Issue: There is no objective way to choose between these three methods, and interpreting MIRR remains complex.# Profitability Index (PI)# Definition and Concept* Profitability Index (PI): The present value of an investment's future cash flows divided by its initial cost. Also known as the benefit-cost ratio.* Calculation: PI = \frac{\text{PV of Future Cash Flows}}{\text{Initial Cost}}# Advantages and Disadvantages of PI (Table 8.10)* Advantages:1. Closely related to NPV, generally yielding identical decisions for independent projects.2. Easy to understand and communicate.3. Useful when investment funds are limited (capital rationing).* Disadvantages:1. May lead to incorrect decisions in comparisons of mutually exclusive investments.# The Practice of Capital Budgeting# Usage of Techniques by Country (Table 8.11)* USA: NPV (95\%$), IRR ($76\%$), Payback ($57\%$), AAR ($20\%$).* <strong>UK:</strong> NPV ($80\%$), IRR ($53\%$), Payback ($69\%$), AAR ($38\%$).* <strong>China:</strong> NPV ($84\%$), IRR ($89\%$), Payback ($84\%$), AAR ($9\%$).* <strong>Australia:</strong> NPV ($96\%$), IRR ($64\%$), Payback ($59\%$), AAR ($19\%$).* <strong>South Africa:</strong> NPV ($99\%$), IRR ($79\%$), Payback ($54\%$), AAR ($14\%).# Concept Quiz Questions* What is the net present value rule?* If we say an investment has an NPV of £1,000$$, what exactly do we mean?* Under what circumstances will the IRR and NPV rules lead to the same accept-reject decisions? When might they conflict?* What are the most commonly used capital budgeting procedures?* If NPV is conceptually the best procedure for capital budgeting, why do you think multiple measures are used in practice?