Week 4

Question 1

Why is risk analysis important? How do we typically perform risk analysis?

Answer 1

Risk analysis allows us to look behind our NPV number (and other numbers) to see how stable our estimates are, to perform these we start with a base case, estimating the NPV based on initial cash flow projections, we then perform sensitivity analysis, scenario analysis, break-even analysis, or decision tree analysis.

Question 2

What does sensitivity analysis see? How do we perform this?

Answer 2

Sensitivity analysis asks if the value of a forecast variable changes, what difference does it make to the viability of the investment project. Only one variable is changed at a time. This allows us to ascertain how much a variable can change and leave the project with a positive NPV or IRR over the hurdle rate. We perform this by simply changing the variable and seeing the effect on NPV and IRR.

Question 3

What occurs in scenario analysis?

Answer 3

In scenario analysis we change multiple different variables at once to see the overall effect on NPV (or another variable). It evaluates the impact of simultaneous changes in a combination of variables.

Question 4

What are the two break-even levels?

Answer 4

The accounting break-even is the level of a input variable that results in zero net profit, this does not factor in time value of money. The financial break-even is the level of sales volume that generates an NPV of zero or an internal rate of return that equals the opportunity cost of capital.

Question 5

What is the difference between variable, and fixed costs?

Answer 5

Fixed costs are constant, regardless of output, over some time period. Variable costs are calculated as quantity*cost per unit. The total costs equal the fixed costs + the variable costs.

Question 6

How does the average cost per unit change as we produce more units?

Answer 6

Because the fixed costs stay the same the average cost per unit will typically go down.

Question 7

What is the marginal cost?

Answer 7

The marginal cost is the cost to produce one more unit, it is just the variable cost per unit.

Question 8

How do we find the accounting breakeven point? What will our net cash flow be at this point?

Answer 8

At the accounting breakeven point our net cash flow will be the depreciation. Our revenue will be the variable cost + fixed costs + depreciation.
The equation to find the break-even point in this case for sales Q(Sales) = Fixed costs (including depreciation)/(Price - variable cost).

Question 9

What do we know about out net present value if we are at the accounting breakeven point?

Answer 9

At the accounting break even point our net present value will be negative.

Question 10

What is the contribution margin?

Answer 10

The contribution margin = the sale price per unit - variable costs.

Question 11

How do we find the financial break-even point?

Answer 11

For Financial break-even we want to find the level of a variable that generates a net present value of zero or an internal rate of return that equals the opportunity cost of capital. The equation is: Initial investment = PVIFA(depreciation + (1-tax rate)((contribution margin*sales volume)-(fixed costs + depreciation)).

Question 12

What is the cash break-even point given by?

Answer 12

The cash break-even point is given by Q(sales) = fixed costs (no depreciation)/(contribution margin).

Question 13

What are the different break-even points for cash, accounting, and financial break-even points? What are the NPVs?

What is the IRR at the financial break-even point?

Answer 13

At cash break-even the operating cash flow is 0 and the NPV is negative. At the accounting break-even net income = 0, and NPV is negative. At the financial break-even, NPV equals 0 and IRR will be the required return.

Question 14

What does a Monte Carlo simulation attempt to do and how does it work?

Answer 14

Monte Carlo simulation is a step above sensitivity and scenario analysis. It attempts to model real-world uncertainty, and works by running thousands or more outcomes via simulation.

Question 15

What must we do with variables that interact in Monte Carlo simulation?

Answer 15

The interactions between the variables are explicitly specified in Monte Carlo simulation.

Question 16

What are the steps in the Monte Carlo simulation?

Answer 16

1. Specify the basic model.
2. Specify a distribution for each variable in the model.
3. The computer draws one outcome (a single outcome is made up of a random draw for each variable in the model).
4. Repeat the procedure randomly to create thousands/millions of outcomes, generating a distribution of variables of interest.
5. Calculate the net present value (associated with expected value of variable of interest.

Question 17

What are real options? Why are they important in valuations?

Answer 17

Managers will often take actions which will alter the pattern or magnitude of cash flow streams during a project’s life in response to new information. These opportunities to vary the nature or longevity of a project are called real options. They give the right, but not the obligation, to take some action in the future.
These real options have value for the firm and thus should be considered in project valuation.

Question 18

What are the most common real option types? When do they have value?

Answer 18

The most common real options are: The option to expand, this has value if the demand is higher than expected.

The option to abandon, this has value if demand is lower than expected.

The option to delay, this has value if the underlying variables are changing with a favorable trend.

Question 19

What is the market value of a project if we include real options?

Answer 19

The market value of a project is the sum of the net present value of the project without options and the value of the managerial options implicit in the project.

Question 20

How can we evaluate the option to abandon?

Answer 20

The option to abandon can be evaluated by either: including the feasibility of abandonment in the initial project NPV analysis, or by individually evaluating at any point in the project life, by comparing the abandonment value with the present value of future cash flows.

Question 21

Why are decision trees useful in project analysis?

Answer 21

Decision trees allow us to graphically represent the alternatives available to us in each period and the likely consequences of our actions, they help us identify the best course of action.
We can put the probabilities of each event and their associated net present value.

Question 22

What does a square and circle represent in a decision tree?

Answer 22

A square in a decision tree typically represents a choice, a circle typically represents receipt of information.

Question 23

How do we calculate the net present value of a decision tree?

Answer 23

To calculate the net present value of a decision tree we just work out the NPV for the end points and discount them back. We then dum the NPVs of each potential outcome weighted by their joint probability.