Advanced Capital Budgeting

• Lecture 5 covers advanced capital budgeting, including sensitivity, break-even, simulation, and decision tree analyses; textbook chapter 11 provides more detail.

Corporate Finance

• Investors get a return on their capital through assets generating cash flow.
• Capital from investors can be divided into:
  • Current and fixed assets
  • Short-term and long-term debt
  • Shareholders’ equity

Project Cash Flow Risk

• Project riskiness is reflected in the discount rate (k).
• Relying solely on the discount rate to manage risk has problems:
  • Cost of debt may be straightforward, but the cost of equity can be subjective.
  • Models estimating the cost of equity use strong assumptions and can lead to errors.
• Warren Buffett's approach can be used, which emphasizes focusing on future cash flows and a margin of safety rather than over-analyzing the discount rate.
• A "reasonable" cost of equity should be used, higher than the cost of debt, while focusing on future cash flows and the margin of safety.
• Finance tools to analyse project risk include:
  • Sensitivity Analysis
  • Break-even Analysis
  • Simulation Analysis

Project Risk Example

• A division considers a 3-year project with a $40,000 initial cash outlay, a required 10% return, and the following annual estimates:
  • Selling price: $70 per unit
  • Variable cost: $60 per unit
  • Sales volume: 2000 units
• Net Present Value = $9,737, which means the project should be accepted.
• Important to consider how sensitive the NPV result is to changes in selling price, variable cost, and sales volume.

Sensitivity Analysis

• Examines the impact of changing one input variable while keeping all other variables constant; similar to "what if" analysis.
• To conduct a sensitivity analysis:
  • Estimate NPV using an optimistic estimate of a variable.
  • Estimate NPV using a pessimistic estimate of the same variable.
  • Calculate the range of NPV estimates from the optimistic and pessimistic values.
  • Repeat the process for each key variable.
• A variable is considered most sensitive to the project's success if it demonstrates the largest range between optimistic and pessimistic NPV results.
• Optimistic, best, and pessimistic estimates for the project are:
  • Selling price: $73, $70, $63
  • Variable cost: $55, $60, $61
  • Sales volume: 2300, 2000, 1900
• Analysis of NPV and Sensitivity:
  • Selling Price: Difference between optimistic and pessimistic NPV is $49,737
  • Variable Costs: Difference between optimistic and pessimistic NPV is $29,843
  • Sales Volume: Difference between optimistic and pessimistic NPV results is $9,948
• Benefits include identifying key variables, and where additional information may be useful.
• Gives managers a chance to think about possible consequences of using incorrect forecasts.
• Scenario analysis is a specific form; imagine scenarios where best and worst values occur simultaneously.
• Can have ambiguous/subjective estimates and underlying interrelated variables.

Break-Even Analysis

• Determines how low sales or how high costs can be before the resulting NPV equals zero.
• Selling price can fall to $68.04 (-2.8% from expected value) before there is 0 NPV.
• Variable costs can increase to $61.96 (+3.3% from expected value) before there is 0 NPV.
• Sales volume can fall to 1608 units (-19.9% from expected value) before there is 0 NPV.
• Like sensitivity analysis, break-even analysis typically assumes just one variable changes at a time.

Simulation Analysis: Monte Carlo

• A technique that iteratively evaluates a deterministic model using random numbers as inputs.
• Identify the relevant key variables and establish the probability distribution of each variable.
• Establish any interrelations between the variables.
• Use a computer to:
  • Randomly select values for each variable based on its probability distribution.
  • Calculate a Net Present Value (NPV) using the chosen input values.
  • Repeat the steps many times to generate an NPV probability distribution.
• Project modeling assumptions:
  • Sales volume follows a normal distribution (mean=1250, standard deviation=200).
  • Variable cost follows a normal distribution (mean=50, standard deviation=10).
  • Selling price fluctuates with change in sales volume
  • SP = $70*[1+(SV-1,250)/1,250]
• The Excel file provides a good example
  • Generates a set of input variables.
  • Calculates the NPV.
  • Repeats it 10,000 times.
• Simulation Results include statistics:
  • Minimum NPV: -$109,030
  • Maximum NPV: $324,768
  • Mean NPV: $27,842
  • Probability (NPV<0) = 33.7%
  • NPV at 2.5% = -$61,891
  • NPV at 97.5% = $151,141
• You can see how different changes in all inputs affect the project value.
• This is typically costly, so hard to implement.
• Necessary for projects that have complex costs and large errors.

Decision Tree Analysis

• In traditional NPV (Net Present Value) analysis, investment decisions are often based on an autopilot approach that doesn't account for future alternatives.
• It offers a method for evaluating alternatives involving a series of decisions made over time.
• Requires estimating the probability of an event occurring and understanding the cash flows related to the event.
• When multiple decisions must be made, a roll-back procedure is used.
• The roll-back procedure involves:
  • Assessing the most distant decision first.
  • Once the first is assessed and addressed, we move to the next distant decision.
  • The process runs until decisions converge to the present day.
• Company needing expansion:
  • Overseas expansion requires an investment of $3 million
  • Domestic expansion has $0.5 million cost
  • Overseas has 30% success rate, 80% domestically
  • Success overseas results in $10 million, failure is $2 million
  • Success domestically results in $3 million, failure is $1 million
  • Opp cost of capital is 10%.
• For if decision to fail in the first year, one will choose not to advertise.
• Based on decision tree analysis in Australia it's $26,033.06 Net Present Value vs $21,545.46 for Japan.
• The decision would be to say in Australia.
• The advantages force the user to link today's decision with future investment decisions.
• Problems are that it can be very complex very quickly if:
  • There are multiple decisions
  • Multiple outcomes
  • Impossible to account for all branches
• Discount rate should change over time and be different on different paths of branches.