Topic 3 - different ways to consider risk in capital budgeting

Question 1

what are deterministic models

Answer 1

models where the variables are known

Question 2

What 3 types of situations do we distinguish among

Answer 2

1. Certain situations: known variables with certainty
2. Risky situations: variables are known in terms of probability
3. Situations of total uncertainty: their respective probabilities are unknown

Question 3

The hypothesis of complete ignorance or perfect information are extreme and not really realistic, so we will focus on criteria based on statistical magnitudes:

Answer 3

• Probability: the ratio between the number of favorable cases and the number of possible cases of presentation of an event
• Expected value: indicator of central tendency of a random variable

Question 4

The amounts that make up an investment…

Answer 4

are random variables and must be assessed in terms of probability

Question 5

Different alternatives to finding the impact of risk on investment decisions:

Answer 5

• Simplistic approaches: either adjust the rate of risk or manipulate cash flows to consider risk
• Statistical approach: probability of the NPV being positive
• Monte Carlo Simulation
• Decision trees

Question 6

To understand risk analysis one must differentiate two concepts:

Answer 6

1. Sensitivity analysis: check how the NPV changes when only one variable is changed while the others remain unchanged, holding constant the other
2. Scenario analysis: check how the NPV changes when several variables are changed simultaneously, defining optimistic, pessimistic or probable scenarios

Question 7

The criteria used when cash flows are not subject to risk is

Answer 7

risk-free rate

Question 8

For risky projects we need to

Answer 8

increase the discount rate depending on the investment risk, so that:
r = rf + risk premium

Question 9

If cash flows are not known with certainty we can consider them

Answer 9

as random variables. The random variables will be represented at least by:
- the expected value
- the variance

In this environment it is not enough to verify that the expected net present value (NPV) is positive. We need to consider the risk and estimate the probability that the NPV is positive.

Question 10

When do we use each distribution?

Answer 10

• RECTANGULAR: If only we dare to estimate an optimistic and a pessimistic cash flow, assuming that all intermediate values have the same likelihood
• TRIANGULAR: If we are also prepared to estimate a ‘most likely’ scenario
• SIMPLIFIED BETA: When we have a higher confidence on the ‘most likely’ scenario

Question 11

Simulation models

Answer 11

• Simulation is useful when we face situations in which it is not possible or very expensive to obtain satisfactory information
• Thus, simulation models pretend to represent a reality in a simplified way, picking relations or laws that are considered fundamental and therefore decisive to simulate reality
• Simulation is carried out through a numerical model that represents the structure of a dynamic process that requires a number of assumptions