Net Present Value and Other Investment Criteria Flashcards

Capital Budgeting and Net Present Value

• Capital budgeting is the most important issue in corporate finance, focusing on the process of allocating capital to projects that create value for the owners.

• Fundamental business decisions involving capital budgeting include choosing product lines, entering new markets, launching new products, or deciding which services to offer.

• An investment is worth undertaking if it is worth more than it costs once it is in place.

• 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.

• The NPV rule states that an investment should be accepted if the NPV is positive and rejected if the NPV is negative.

• The capital budgeting process is essentially a search for investments with positive NPVs.

• Estimating NPV involves:

  • Estimating future cash flows expected from the business.

  • Applying discounted cash flow (DCF) valuation by discounting future cash flows to estimate their present value (PV).

  • Calculating the difference between the PV of subsequent cash flows and the initial cost.

Example: Estimating NPV for an Organic Fertilizer Business

• Initial investment cost: $-30,000$

• Estimated yearly cash revenues: $20,000$

• Estimated yearly cash costs (including taxes): $14,000$

• Net annual cash flow: $20,000 - 14,000 = 6,000$

• Project duration: $8$years

• Salvage value of equipment at year 8: $2,000$

• Required discount rate on new projects: $15\%$

• Present Value calculation:

  • $PV = 6,000 \times \frac{1 - \frac{1}{1.15^8}}{0.15} + \frac{2,000}{1.15^8}$

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

  • $PV = 26,924 + 654 = 27,578$

• NPV calculation:

  • $NPV = -30,000 + 27,578 = -2,422$

• Since the NPV is negative, this is not a good investment. If there are $1,000$ shares outstanding, taking this project would result in a loss of value of $2,422 / 1,000 = 2.42$ per share.

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.

• The payback rule states that an investment is acceptable if its calculated payback period is less than some prespecified number of years.

• Shortcomings of the payback rule:

  • The time value of money is completely ignored.

  • Risk differences between projects are not considered.

  • There is no economic rationale for picking a specific cutoff point.

  • It is biased toward shorter-term, liquid investments.

  • It ignores cash flows occurring after the payback period.

• Redeeming qualities of the payback rule:

  • It is simple to use for minor decisions where the cost of detailed analysis exceeds the potential loss.

  • The bias toward liquidity is useful for cash-constrained firms.

  • It accounts for the uncertainty of far-future cash flows by ignoring them.

• Example of payback period calculations:

  • An initial investment of $50,000$ that returns $30,000$ in Year 1 and $20,000$ in Year 2 has a payback of exactly $2$ years.

  • Project A: Payback is $2.6$ years.

  • Project B: Never pays back.

  • Project C: Payback of exactly $4$ years.

  • Project D: Has two correct payback periods of $2$ and $4$ years.

  • Project E: Pays back in $6$ months.

The Discounted Payback Rule

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

• This rule ensures that the project breaks even in an economic or financial sense, meaning the initial investment is recovered along with the interest that could have been earned elsewhere.

• A project that pays back on a discounted basis must have a positive NPV.

• Advantages:

  • Includes the time value of money.

  • Does not accept negative estimated NPV investments.

• Disadvantages:

  • May reject positive NPV investments.

  • Requires an arbitrary cutoff point.

  • Ignores cash flows beyond the cutoff.

  • Is as complex as NPV but lacks the conceptual rigor.

The Average Accounting Return (AAR)

• The AAR is an investment's average net income divided by its average book value.

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

• Example of a store investment:

  • Initial improvement cost: $500,000$

  • Project life: $5$years

  • Depreciation: Straight-line over $5$years ($100,000$ per year).

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

  • If average net income over the $5$ years is $50,000$, the AAR is $50,000 / 250,000 = 20\%$.

• AAR Rule: A project is acceptable if its AAR exceeds a target average accounting return.

• Drawbacks of AAR:

  • It is not a true rate of return because it uses accounting numbers (net income and book value) rather than cash flows and market value.

  • It ignores the time value of money.

  • It uses an arbitrary benchmark cutoff rate.

The Internal Rate of Return (IRR)

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

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

• IRR Rule: Accept the project if the IRR is greater than the required return; reject if it is less.

• The NPV profile is a graph illustrating the relationship between a project's NPV and various discount rates. The point where the curve crosses the x-axis (where NPV = 0) is the IRR.

• IRR and NPV rules generally lead to identical decisions if the project's cash flows are conventional (initial cost followed by all positive inflows) and the project is independent.

• Problems with the IRR:

  • Nonconventional cash flows: If cash flows change signs more than once, there may be multiple IRRs (multiple rates of return problem).

  • Mutually exclusive investments: Situations where taking one project prevents taking another. IRR may rank a project with a lower NPV higher than a project with a larger NPV.

  • Investing vs. Financing: For financing-type projects (where money is received initially), the project is only acceptable if the IRR is lower than the required return.

Modified Internal Rate of Return (MIRR)

• MIRR is used to address the multiple IRR problem by modifying cash flows before calculating the return.

• Method 1: The Discounting Approach

  • Discount all negative cash flows back to Year 0 and add them to the initial cost.

  • Calculate the IRR using these modified flows.

• Method 2: The Reinvestment Approach

  • Compound all cash flows except the initial one to the end of the project's life.

  • Example: For a $2$-year project with a $20\%$ required return, an initial cost of $-60$, and subsequent flows of $+155$ and $-100$, the modified Year 2 flow is $-100 + (155 \times 1.2) = 86$. The MIRR is $19.72\%$.

• Method 3: The Combination Approach

  • Negative cash flows are discounted to the present, and positive cash flows are compounded to the end.

• Critique of MIRR: It is not truly "internal" because it relies on an externally supplied discount or compounding rate. Reinvestment of interim cash flows does not change the project's inherent value.

The Profitability Index (PI)

• The Profitability Index, or benefit-cost ratio, is the present value of an investment’s future cash flows divided by its initial cost.

• Formula: $\text{PI} = \frac{\text{PV of Future Cash Flows}}{\text{Initial Cost}}$

• 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 $1$.

Capital Budgeting in Practice

• Firms often use multiple criteria (NPV, IRR, Payback, PI) to evaluate proposals because NPV is only an estimate based on uncertain future data.

• Large-scale capital spending examples (2020 projections):

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

  • Chevron: Expected $18$ to $20$ billion (similar to $19.8$ billion in 2019).

  • Walmart: Projected $11$ billion.

  • AT&T: Projected $20$ billion.

• Surveys indicate that NPV and IRR are the most frequently used techniques in modern practice.

Selected Concept Questions

• Under what circumstances will the IRR and NPV rules lead to the same accept-reject decisions? They align for independent projects with conventional cash flows.

• What does the profitability index measure? It measures the value created per dollar invested.

• What advantage(s) does the discounted payback have over the ordinary payback? It incorporates the time value of money.

• What are the weaknesses of the AAR rule? It ignores the time value of money, uses accounting book values instead of market values, and lacks an objective cutoff point.