1. FINA1129 Corporate Financial Management
Lecture 5
Investment Appraisal – Risk Uncertainty, Sensitivity Analysis
Dr Lianfeng Quan
Office QA 348

2. Essential Readings:
Watson and Head Chapter 7
Glen Arnold Chapter 6

3. Recap Lecture 5
Understand what are mutually exclusive and independent projects.
Understand the techniques to be employed in order to arrive at the best investment decision if capital is rationed.
Application of profitability index (PI) technique.
Understand the rules to follow when investment appraisal is done in an environment inflation.

4. Learning Objectives By the end of this session, you will be able to:
Understand risk, uncertainty and risk adjusted discount rate.
Application of the following analysis to investment project.
Sensitivity analysis
Breakeven analysis
Scenario analysis
Simulation

5. Why Assessing Risk in Investment Appraisal
Problems of making decisions about the future.
Financial data (inflow & outflow) for the future is usually estimated.
Estimated financial data provided may not necessarily be correct due to ever changing business environment.
How do you deal with Risk and Uncertainty?

6. Risk and Uncertainty
Risk refers to a set of unique circumstances which can be assigned probabilities.
Risk increases with variability of returns.
Uncertainty implies probabilities cannot be assigned to different sets of circumstances.
Uncertainty increases with project life.
In practice, the terms ‘risk’ and ‘uncertainty’ are often used interchangeably.

7. Risk Adjusted Discount Rate
Investors need a risk premium in addition to the risk free rate of return.
The greater the risk of an investment, the greater the risk premium required.
Risk premium for a specific investment is not easy to determine.
One solution is to put projects in risk classes and allocate risk premiums.

8. Review Net Present Value
A five-step approach can be utilized to compute the NPV
3. Determine the riskiness of the project and estimate the appropriate cost of capital:
The cost of capital is the discount rate used in determining the present value of the future expected cash flows
The riskier the project, the higher the cost of capital for the project

9. Risk and PV Higher risk projects require a higher rate of return
Higher required rates of return cause lower PVs

10. Risk and FV Higher risk projects require a higher rate of return
Higher required rates of return cause higher FVs

11. Risk and PV Example Example
Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6% and a risk premium of 6%, what is the PV of the project?

12. Adjusting for Risk through the Discount Rate
Need higher future cash flows

13. Sensitivity Analysis
Evaluate how changes in a project variables affect the NPV of a project.
Calculate the effect on the NPV of changes in one input variable at a time.
Can be used to establish which variables are most influential on the success or failure of a project.
In a sensitivity analysis, the manager can choose which variables to change and by how much.

14. Sensitivity Analysis Example
Acmart plc has developed a new product line called Marts
Likely demand for Marts is 1,000,000 per year, at a price of £1, for the four-year life of the project.

15. Sensitivity Analysis Example (Cont.)
Required rate of return on a project of this risk class is 15%
Expected NPV:

16. Sensitivity Analysis Example (Cont.)

17. Sensitivity Analysis Example (Cont.)

18. Sensitivity Analysis Example (Cont.)

19. Sensitivity Analysis Example (Cont.)
What other variables?

20. Sensitivity Analysis: Advantages & Disadvantages
Information for decision making
To direct search
To make contingency plans
Disadvantages
The absence of any formal assignment of probabilities to the variations of the parameters
Each variable is changed in isolation while all other factors remain constant
Questions

21. Break-Even Analysis
Common tool for analyzing the relationship between sales volume and profitability.
Finding a change in a variable which gives a zero NPV.

22. Break-Even Analysis Example
Required: Assess the sensitivity of the project to changes in initial investment, selling price, sales volume.

23. Break-Even Analysis Example (Cont.)
Answer

24. Break-Even Analysis Example (Cont.)
Answer – Sensitivity
Initial Investment
If initial investment increases by £774,720, the NPV becomes zero:
£774,720 / £7,000,000 = 11.1%
Discuss clue, part A, B, C

25. Break-Even Analysis Example (Cont.)
Answer – Sensitivity
Sales price
The relative decrease in selling price per unit that makes the NPV zero is the ratio of the NPV to the present value of sales revenue
∆P/P=774,720 /22,352,320 = 3.5%
The amount of change or % change

26. Break-Even Analysis Example (Cont.)
Answer – Sensitivity
Sales volume
The relative decrease in sales volume that makes the NPV zero is the ratio of the NPV to the present value of contribution
∆Units/Units=774,720 / 7,774,720 = 10.0%

27. Break-Even Analysis Example (Cont.)
Initial Investment
If initial investment increases by £774,720, the NPV becomes zero: £774,720 / £7,000,000 = 11.1%
Sales price
∆P/P=774,720 /22,352,320 = 3.5%
Sales volume
∆Units/Units=774,720 / 7,774,720 = 10.0%

28. Scenario Analysis
Scenario analysis creates scenarios that consist of changes in several of the input variables and calculates the NPV for each scenario.
Although corporations could do a large number of scenarios, in practice they usually do only three.

29. Input Variables and NPV for Scenario Analysis

30. Scenario Analysis Example
Acmart plc has developed a new product line called Marts
Likely demand for Marts is 1,000,000 per year, at a price of £1, for the four-year life of the project

31. Worst-case Scenario Example
Acmart plc:
Question? Why 17% increased?

32. Worst-case Scenario Example (Cont.)

33. Best-case Scenario Exercise
2.2096= Annuity Factor

34. Best-case Scenario Exercise (Cont.)

35. Simulation Models
Simulation models calculate expected NPV through repeated analysis based on probability distributions for each project variable.
Simulation models determine effect of simultaneous changes in several variables.
Variable values can be selected by probability-based random numbers.
Computer makes large number of runs with random numbers reselected at each run.

36. Recap of Lecture
Understand risk, uncertainty and risk adjusted discount rate.
Application of the following analysis to investment project.
Sensitivity analysis
Breakeven analysis
Scenario analysis
Simulation