Project Cashflow Risk Introduced #
Keypoints
- Solely depending on the discount rate to account for risk is not reliable, as the cost of equity usually is not reliable for strong assumptions made in estimating it.
- It suffices to estimating the cash flows more precisely with a reasonable discount rate.
Sensitivity Analysis #
General #
Concept: Analyse the effect of changing an input variable, holding all else constant
Process
- Estimate NPV using optimistic estimate of variable
- Estimate NPV using pessimistic estimate of variable
- Calculate the range of NPV from the optimistic to pessimistic
- Repeat the process for each variables in turn
Keypoints
- Benefits
- Identifies the underlying key variables
- Indicates where addtional information may be useful - e.g. when the selling price takes a significant change in NPV, try to obtain more info on selling price
- Gives managers a chance to think about possible consequences of using incorrect forecasts - e.g. the expected cashflow is higher than the actual cashflow, and that the worst scenario of cashflows gives an insight of NPV about the possible lower cashflow
- Limitations
- It uses ambiguous/subjective estimates
- Underlying variables are likely to be interrelated - when fixing all other variables, there is an underlying hypothesis that all variables are independent
Break-even analysis #
Concept: Similar to sensitivity analysis, but it focuses on the changes to one variable when the NPV is equal to zero
Process
- Estimate the expected NPVs and expected variables
- Estimate when the NPV equates 0, the changes made to each variables
Keypoints
- Similar to sensitive analysis, it assumes that only one variable change at a time, ignoring the correlation between variables.
Simulation analysis #
Monte-Carlo simulation analysis: Using random numbers (that obeys some probability distribution) as inputs to deterministic, and iteratively evaluates NPV and gives a range
Process
- Identify relevant variables (only key variables) and specify the probability distribution of each variable
- Specify any inter-relations between the variables
- Use a computer to
- Randomly choose values for each variable from its specified probability distribution
- Calculate a NPV given the input values selected
- Repeat until a probability distribution for NPV is generated
Keypoints
- Simulation analysis can provide answers to the probability of destroying/creating wealth or the NPV range within some confidence level
- Benefits
- Can see how changes in inputs simultaneously (by taking into account their possible inter-relations) affect the project value
- Limitations
- It is typically costly - it takes computational resources
- Hard to specify the distribution of inputs and their correlation
- Necessary for projects that are complex and have bigger cost of errors
Decision Tree Analysis #
Keypoints
- Decision tree analysis provides method of evaluating alternatives involving a sequence of decisions over time
- Roll back procedure is used when there are more than one decisions to make
- Benefits
- Forces you to link today’s decisions with all possible future investment decisions
- Possible problems
- Can become very complex very quickly (100 binary decisions, leading to $2^{100}$ trees in total) - indicating it is impossible to account for all branches -Discount rates may change over time and may be different on different paths
Roll back procedure
- Assessing the most distance decision first, then roll back to the next most distance decision
- Repeat until we reach today’s decision