Unit 6: Investment Decisions

I. Foundations of Capital Budgeting

Capital budgeting is the process of evaluating long-term investments whose cash flows extend beyond one accounting period. Its governing principle is value creation: a project is financially acceptable when its expected benefits, adjusted for timing and risk, exceed the resources committed to it.

• Time value of money: One currency unit received today is worth more than the same unit received later because current funds can earn a return.
• Incremental cash-flow principle: Evaluation includes only cash flows that arise because the project is undertaken.
• After-tax basis: Corporate investment decisions use cash flows after taxes because taxes represent actual outflows.
• Opportunity-cost principle: A resource already owned has a relevant cost equal to the value of its best alternative use.
• Financing separation: Interest and debt repayments are normally excluded from project cash flows because financing effects are reflected in the discount rate.
• Required return: The discount rate represents the minimum return required by investors for the project’s time value and systematic risk.
• Decision objective: A firm should accept investments that increase shareholder wealth, subject to financing, strategic, regulatory, and operational constraints.

II. Discounting Techniques of Capital Budgeting

A. Discounting Techniques of Capital Budgeting

Discounting techniques compare cash flows occurring at different dates by converting them to equivalent present values.

• Present-value rule: A future cash flow is discounted using the required rate of return:

PV = CF_t / (1 + k)^t

• PV = present value.
• CF_t = cash flow received at the end of period t.
• k = discount rate per period.
• t = number of periods from the valuation date.

• Compounding-discounting relationship: Compounding moves present money forward in time, whereas discounting moves future money backward:

FV_t = PV(1 + k)^t

• FV_t = future value at time t.

• Principal discounted methods:

  1. Net present value: Measures the absolute increase in wealth.
  2. Internal rate of return: Expresses project return as a percentage.
  3. Discounted payback: Measures the time needed to recover investment in present-value terms.

• Rate consistency: Nominal cash flows must be discounted at a nominal rate, real cash flows at a real rate, and cash flows in a particular currency at a rate appropriate to that currency.

• Timing convention: Standard analysis assumes year-end cash flows unless dates indicate otherwise; an immediate outlay occurs at time zero and is not discounted.

III. Net Present Value

A. Net Present Value

Net present value measures the difference between the present value of a project’s expected inflows and its required investment outflows.

• Formula:

NPV = Σ[CF_t / (1 + k)^t], for t = 0 to n

• CF_0 = initial cash flow, usually negative.
• CF_t = net cash flow in period t.
• k = risk-adjusted required return.
• n = project life.

• Decision rule:

  • Accept an independent project if NPV > 0.
  • Reject it if NPV < 0.
  • If mutually exclusive projects have comparable risk and constraints, select the feasible project with the highest positive NPV.

• Economic meaning: A positive NPV is the estimated amount by which the investment increases the firm’s value at time zero.

• Worked example: A project costs ₹100,000 and produces ₹60,000 after each of two years. At 10%:

NPV = -100,000 + 60,000/1.10 + 60,000/(1.10)^2
    = ₹4,132 approximately

The positive NPV supports acceptance.

• Strengths: NPV recognizes timing, includes all project cash flows, permits varying discount rates, and directly aligns with shareholder wealth.
• Limitations: Its result depends on cash-flow and discount-rate estimates; absolute NPV may also require interpretation when projects differ greatly in scale or duration.

IV. Internal Rate of Return

A. Internal Rate of Return

The internal rate of return is the discount rate at which a project’s NPV equals zero.

• Defining equation:

0 = Σ[CF_t / (1 + IRR)^t], for t = 0 to n

• IRR = project’s internal rate of return.
• All other symbols retain their NPV meanings.

• Decision rule: Accept an independent project when IRR > k, reject it when IRR < k, and remain indifferent in purely financial terms when IRR = k.
• Interpretation: IRR is a project-specific break-even rate of return, not an accounting profit rate or necessarily an annual cash yield.
• Calculation: For multi-period projects, IRR is generally found through financial calculators, spreadsheet iteration, or numerical root-finding.
• Advantages: It incorporates the time value of money, uses all cash flows, and communicates results as an intuitive percentage.
• Limitations:
  • Non-conventional cash flows can produce multiple IRRs or no meaningful IRR.
  • IRR may rank mutually exclusive projects incorrectly because of scale or timing differences.
  • The method implicitly evaluates reinvestment through the project-rate framework, which can be unrealistic when IRR is exceptionally high.

V. Discounted Payback Period Method

A. Discounted Payback Period Method

The discounted payback period is the time required for cumulative discounted cash inflows to recover the initial investment.

• Procedure:

  1. Discount every expected cash flow at the required return.
  2. Accumulate the discounted inflows chronologically.
  3. Identify when their total equals the initial outlay.

• Fractional-period calculation:

Discounted payback
= Full periods before recovery
+ Unrecovered amount / Discounted inflow in recovery period

• Decision rule: Accept a project if its discounted payback does not exceed management’s predetermined cutoff period.
• Improvement over ordinary payback: It recognizes that a rupee received later has a lower present value than a rupee received earlier.
• Liquidity and risk use: A shorter discounted payback indicates faster recovery of committed capital and lower exposure to distant, uncertain forecasts.
• Limitations: It ignores all cash flows after the cutoff, does not directly measure wealth creation, and uses an administratively chosen recovery standard. Consequently, it should normally supplement rather than replace NPV.

VI. Estimation of Cash Flows

A. Estimation of Cash Flows

Cash-flow estimation identifies the incremental, after-tax amounts caused by accepting a project.

• Initial investment: Common components are asset purchase price, installation, transportation, increases in net working capital, and after-tax proceeds from replacing an old asset.
• Operating cash flow:

OCF = (Revenue − Cash costs − Depreciation)(1 − T) + Depreciation

• OCF = operating cash flow.
• T = corporate tax rate.
• Depreciation is added back because it reduces taxable income but is not a cash payment.

• Terminal cash flow: The final period includes operating cash flow plus after-tax salvage value and recovery of net working capital.

• Relevant inclusions:

  • Opportunity costs, such as using land that could otherwise be sold.
  • Side effects, including cannibalization of existing product sales.
  • Incremental overhead genuinely created by the project.

• Relevant exclusions:

  • Sunk costs already incurred, such as completed research expenditure.
  • Allocated overhead that does not change because of the project.
  • Interest expense when the discount rate already reflects financing.

• Consistency requirement: Inflation, taxes, timing, project life, and working-capital assumptions must be applied consistently throughout the forecast.

VII. NPV versus IRR

A. NPV versus IRR

NPV and IRR often agree for independent projects with conventional cash flows, but NPV is superior when their rankings conflict.

1. Net present value

   • Measure: Reports value created in currency units.
   • Reinvestment basis: Values intermediate cash flows using the required return.
   • Ranking rule: Selects the project contributing the greatest present wealth.
   • Flexibility: Can accommodate changing discount rates across periods.

2. Internal rate of return

   • Measure: Reports a percentage return.
   • Appeal: Facilitates comparison with a hurdle rate.
   • Ranking weakness: May favor a smaller project with a higher percentage return but lower total value.
   • Technical weakness: May yield multiple solutions when cash-flow signs change repeatedly.

• Conflict sources: Rankings can differ because projects have unequal initial scale, different cash-flow timing, or unequal economic lives.
• Crossover rate: The crossover rate is the discount rate at which two mutually exclusive projects have equal NPVs; it is found by calculating the IRR of their differential cash flows.
• Resolution principle: For mutually exclusive investments, use incremental analysis and choose the project with the higher NPV at the firm’s appropriate required return.

VIII. Risk Analysis in Capital Budgeting

A. Risk analysis in Capital Budgeting

Risk analysis evaluates how uncertainty in forecast variables affects project cash flows, returns, and value.

• Risk sources: Sales volume, selling price, input cost, project delay, asset life, tax changes, exchange rates, and terminal value can deviate from forecasts.

• Risk categories:

  • Stand-alone risk: Variability of the project considered alone.
  • Corporate risk: Effect on the variability of the firm’s overall cash flows.
  • Market risk: Contribution to systematic risk that diversified shareholders cannot eliminate.

• Expected NPV: If outcomes have stated probabilities:

E(NPV) = Σ[p_i × NPV_i]

• p_i = probability of outcome i.
• NPV_i = NPV under outcome i.

• Dispersion measures: Variance and standard deviation quantify the spread of possible NPVs around expected NPV; greater dispersion generally indicates greater stand-alone risk.
• Analytical tools: Sensitivity analysis changes one variable, scenario analysis changes several coherent variables, and simulation generates a distribution from repeated combinations of uncertain inputs.
• Management response: Risk can be reflected through risk-adjusted discount rates, certainty-equivalent cash flows, staged investment, contractual protection, or abandonment and expansion options.

IX. Sensitivity Analysis

A. Sensitivity Analysis

Sensitivity analysis measures the effect on project NPV of changing one input while holding all other assumptions constant.

• Method:

  1. Calculate base-case NPV.
  2. Change one variable, such as sales volume, by a defined percentage.
  3. Recalculate NPV and compare the result with the base case.
  4. Repeat for major uncertain variables.

• Sensitivity indicator:

Sensitivity = Percentage change in NPV / Percentage change in input

Larger absolute values indicate that NPV is more responsive to that input.

• Break-even analysis: The analyst may solve for the sales volume, price, or cost at which NPV = 0, identifying the project’s economic threshold.
• Decision value: The method highlights critical assumptions requiring better forecasts, monitoring, hedging, or managerial control.
• Limitations: Variables rarely change independently, tested ranges may be subjective, and the method does not attach probabilities to outcomes. It identifies vulnerability but does not provide a complete probability distribution.

X. Certainty Equivalent Approach

A. Certainty Equivalent Approach

The certainty equivalent approach converts risky expected cash flows into smaller risk-free-equivalent amounts and discounts them at the risk-free rate.

• Formula:

NPV = -I_0 + Σ[(α_t × E(CF_t)) / (1 + r_f)^t]

• I_0 = certain initial investment.
• E(CF_t) = expected risky cash flow in period t.
• α_t = certainty-equivalent coefficient, generally between 0 and 1.
• r_f = risk-free rate.
• t = time period.

• Coefficient meaning:

α_t = Certain cash flow acceptable / Expected risky cash flow

A lower α_t reflects greater risk aversion or greater perceived cash-flow risk.

• Decision rule: Accept the project when the NPV of certainty-equivalent cash flows is positive.
• Key distinction: Unlike a risk-adjusted discount rate, this method adjusts the numerator for risk and uses the risk-free rate in the denominator; applying both adjustments would double-count risk.
• Advantages: It separates time value from risk and permits different risk adjustments for cash flows in different periods.
• Limitations: Certainty-equivalent coefficients are difficult to estimate objectively, may vary among decision-makers, and require careful consistency across projects and periods.