Net Present Value and Investment Criteria

Capital Budgeting and Investment Decisions

• The capital budgeting question is arguably the most significant issue in corporate finance.

• The process involves allocating or budgeting capital, which is more complex than simply deciding on a single fixed asset purchase.

• Fundamental business decisions regarding the product line include:

  • Identifying which services or products to offer.

  • Determining the markets in which the company will compete.

  • Deciding which new products should be introduced.

• A business must essentially determine whether launching a new product or entering a new market will create value for its owners.

Net Present Value (NPV)

• Net Present Value (NPV) is the difference between an investment’s market value and its cost.

• It serves as a measure of how much value is created or added today by undertaking an investment.

• Capital budgeting is essentially a search for investments with positive net present values.

• An investment is worth undertaking if it creates value for owners, meaning it is worth more once in place than it costs to acquire.

• Investment decisions are simplified when a market exists for assets similar to the proposed investment. The process becomes more difficult when market prices for comparable investments cannot be observed.

Estimating Net Present Value

• Estimating NPV involves three primary steps:

  1. Estimate the future cash flows expected from the business.

  2. Apply basic discounted cash flow (DCF) procedures to estimate the present value of those cash flows.

  3. Calculate the NPV as the difference between the present value (PV) of future cash flows and the initial cost of the investment.

• Discounted Cash Flow (DCF) Valuation: The process of valuing an investment by discounting its future cash flows.

• NPVs are estimates; coming up with accurate cash flow projections and discount rates is more challenging than the calculations themselves.

NPV Calculation Example: Organic Fertilizer Business

• Imagine a business starting up to produce organic fertilizer with the following estimates:

  • Launch Cost: $30,000$

  • Revenues: $20,000$ per year.

  • Cash Costs (including taxes): $14,000$ per year.

  • Net Cash Flow (Revenue - Cost): $6,000$ per year ($20,000 - 14,000$).

  • Business Duration: $8$ years.

  • Salvage Value (Plant, Property, Equipment): $2,000$ at the end of year 8.

  • Required Discount Rate: $15\%$

  • Shares Outstanding: $1,000$

• Present Value Calculation:

  • $PV = 6,000 \times [1 - (1 / 1.15^8)] / 0.15 + (2,000 / 1.15^8)$

  • $PV = (6,000 \times 4.4873) + (2,000 / 3.0590)$

  • $PV = 26,924 + 654 = 27,578$

• NPV Calculation:

  • $NPV = -30,000 + 27,578 = -2,422$

• Investment Decision: Since the NPV is negative, this is not a good investment.

• Impact on Share Price: Taking this project would result in a loss of value of $-2,422 / 1,000 = -2.42$ per share.

The Net Present Value Rule

• An investment should be accepted if the NPV is positive and rejected if it is negative.

• If the NPV is zero, the investment is a break-even proposition in an economic sense, where value is neither created nor destroyed.

The Payback Rule

• The payback period is the amount of time required for an investment to generate cash flows sufficient to recover its initial cost.

• Payback Period Rule: An investment is acceptable if its calculated payback period is less than or equal to some prespecified number of years.

Shortcomings of the Payback Rule

• Time Value of Money (TVM): The rule completely ignores the time value of money.

• Risk: High-risk and low-risk projects are treated the same as the rule fails to consider risk differences.

• Cutoff Rationale: There is no economic rationale for choosing a specific cutoff point.

• Cash Flow beyond Payback: The rule ignores all cash flows that occur after the payback period, which can lead to biased decisions.

Analyzing Payback Bias

• Comparing two projects, "Short" and "Long," both costing $250$ with a required return of $15\%$

  • Short Project Cash Flows: Year 1: $100$; Year 2: $200$. Payback = $1 + (150/200) = 1.75$ years.

  • Long Project Cash Flows: Year 1: $100$; Year 2: $100$; Year 3: $100$; Year 4: $100$. Payback = $2 + (50/100) = 2.5$ years.

• Using a 2-year cutoff, only "Short" is acceptable. However:

  • $NPV(\text{Short}) = -250 + 100/1.15 + 200/1.15^2 = -11.81$

  • $NPV(\text{Long}) = -250 + 100 \times [1 - (1/1.15^4)]/0.15 = 35.50$

• The payback rule biases toward shorter-term, potentially less valuable investments and away from long-term value creation.

Redeeming Qualities of the Payback Rule

• It is often used by large companies for minor decisions where the cost of detailed NPV analysis would exceed the potential loss.

• It provides a crude adjustment for risk by ignoring uncertain later-year cash flows.

• It is biased toward liquidity, highlighting projects that return cash quickly.

The Discounted Payback Rule

• Discounted payback is the length of time required for an investment’s discounted cash flows to equal its initial cost.

• It represents breaking even in an economic/financial sense (recovering the cost plus interest that could have been earned elsewhere).

• Rule: An investment is acceptable if its discounted payback is less than some prespecified number of years.

• Advantages:

  • If a project ever pays back on a discounted basis, it must have a positive NPV.

  • It ensures the firm won't take projects with negative estimated NPV.

• Disadvantages:

  • It is not significantly simpler than NPV, leading to its rare use in practice.

  • It still requires an arbitrary cutoff and ignores cash flows after that cutoff.

The Average Accounting Return (AAR)

• AAR is defined as an investment’s average net income divided by its average book value.

• General Formula: $AAR = \text{Average Net Income} / \text{Average Book Value}$

AAR Calculation Example

• Proposed store in a mall costing $500,000$. Depreciated straight-line over $5$ years ($100,000$/year). Tax rate is $25\%$

• Yearly Net Income Estimates: Year 1: $100,000$; Year 2: $150,000$; Year 3: $50,000$; Year 4: $0$; Year 5: $-50,000$

• Average Net Income: $(100,000 + 150,000 + 50,000 + 0 - 50,000) / 5 = 50,000$

• Average Book Value: $(500,000 + 0) / 2 = 250,000$

• AAR: $50,000 / 250,000 = 0.20$, or $20\%$

• Decision Rule: Accept the investment if the AAR exceeds a target benchmark.

Shortcomings of AAR

• It is not a true rate of return because it ignores the time value of money.

• It relies on accounting net income and book value rather than cash flow and market value.

• It lacks an objective cutoff point.

The Internal Rate of Return (IRR)

• IRR is the discount rate that makes the NPV of an investment zero.

• It is an "internal" rate because it depends only on the cash flows of the specific project, not on external rates.

• Calculation: Finding the IRR usually requires trial and error unless it is a simple one-period project.

• For a project costing $100$ with $60$ cash flows for two years:

  • $NPV = 0 = -100 + 60/(1 + IRR) + 60/(1 + IRR)^2$

  • Solving this yields an IRR of approximately $13.1\%$

• IRR Rule: An investment is acceptable if the IRR exceeds the required return. It should be rejected if the IRR is less than the required return.

IRR and NPV Comparison

• The IRR rule and NPV rule lead to identical decisions if:

  1. The project’s cash flows are conventional (initial cost followed by positive cash inflows).

  2. The project is independent (the decision to accept does not affect other decisions).

• Net Present Value Profile: A graphical representation showing the relationship between an investment’s NPV and various discount rates. The point where the curve crosses the horizontal axis is the IRR.

Problems with the IRR Rule

Nonconventional Cash Flows

• If cash flows change sign more than once (e.g., negative cost, positive inflow, then negative restoration cost), multiple IRRs may exist.

• Example (Strip Mining): Cost $60$ now, Inflow $155$ in Year 1, Cost $100$ in Year 2.

  • This project results in two IRRs: $25\%$ and $33.33\%$

  • With multiple rates, there is no single unambiguously correct answer, making the IRR rule unreliable.

Mutually Exclusive Investments

• A situation where taking one investment prevents taking another. In such cases, the project with the highest IRR might not be the project with the highest NPV.

• Example: Investment A (IRR $24\%$) vs Investment B (IRR $21\%$).

  • If the required return is $10\%$, B might have a higher NPV despite A's higher IRR.

  • If the required return is $15\%$, A might have the higher NPV.

• Crossover Rate: The discount rate at which the NPVs of two projects are equal.

Investing vs. Financing

• Investing Type: High initial cost followed by inflows. Accept if IRR is greater than required return.

• Financing Type: Initial inflow (like a loan) followed by outflows. Accept if IRR is lower than the required return (i.e., it is an inexpensive source of funds).

Modified Internal Rate of Return (MIRR)

• Proposed to solve the multiple IRR problem by modifying cash flows before calculation.

MIRR Methods

1. Discounting Approach: Discount all negative cash flows to the present and add them to the initial cost. Then find the IRR.

2. Reinvestment Approach: Compound all cash flows (except the first) to the end of the project's life using a reinvestment rate, then find the IRR.

3. Combination Approach: Discount negative cash flows back to the present and compound positive flows to the end. The IRR is then calculated from these two values.

MIRR Critique

• MIRR depends on an externally supplied discount or compounding rate, meaning it is not strictly "internal."

• Value of a project does not depend on what the firm does with generated cash; therefore, some argue NPV is a more direct and sufficient measure.

Profitability Index (PI)

• Also known as the benefit-cost ratio.

• Formula: $PI = \text{Present Value of Future Cash Flows} / \text{Initial Cost}$

• Interpretation: A PI of $1.1$ means that for every dollar invested, the project creates $1.10$ in value (or $0.10$ in NPV).

• If NPV is positive, PI will be greater than $1$. If NPV is negative, PI will be less than $1$.

The Practice of Capital Budgeting

• While NPV is theoretically superior, firms often use multiple criteria to assess reliability due to uncertainty about the future.

• IRR remains very popular because people prefer communicating in terms of percentage returns rather than dollar values.

• Corporate Examples (2020 estimates):

  • ExxonMobil: $33 to $35 billion in expected capital outlays (up from $30 billion in 2019).

  • Chevron: $18 to $20 billion planned (compared to $19.8 billion in 2019).

  • Walmart: ~$11 billion projected.

  • AT&T: ~$20 billion projected.

Summary of Investment Criteria

• NPV: Measures value created. Accept if NPV > 0. No serious flaws. The primary decision tool.

• Payback: Measures liquidity. Accept if period is less than a cutoff. Ignores TVM and cash flows after cutoff.

• AAR: Measures accounting return. Accept if AAR > \text{target}. Not a true economic rate.

• IRR: Measures profitability as a percentage. Accept if IRR > \text{required return}. Unreliable with nonconventional flows or mutually exclusive projects.

• PI: Measures value created per dollar. Useful for capital rationing. Closely related to NPV.