1

Capital Budgeting - Risk Analysis

 Types of risk: stand-alone, corporate, and market  Project risk and capital structure  Risky outflows  Effects of abandonment possibilities  Real options  Optimal capital budget

What does risk mean in capital budgeting?

 Uncertainty about a projects future profitability.  Measured by WNPV, WIRR, beta.  Will taking on the project increase the firms and stockholders risk?

Is risk analysis based on historical data or subjective judgment?

 Can sometimes use historical data, but generally cannot.  So risk analysis in capital budgeting is usually based on subjective judgments.

What three types of risk are relevant in capital budgeting?

 Stand-alone risk  Corporate risk  Market (or beta) risk

How is each type of risk measured, and how do they relate to one another? 1. Stand-Alone Risk: The projects risk if it were the firms only asset and there were no shareholders. Ignores both firm and shareholder diversification.

Measured by the W or CV of NPV, IRR, or MIRR.

Probability Density
Flatter distribution, larger W, larger stand-alone risk.

E(NPV)

NPV

Such graphics are increasingly used by corporations.

2. Corporate Risk: Reflects the projects effect on corporate earnings stability. Considers firms other assets (diversification within firm). Depends on: projects W, and its correlation with returns on firms other assets. Measured by the projects corporate beta.

Profitability Project X Total Firm Rest of Firm

Years

1. Project X is negatively correlated to firms other assets. 2. If r < 1.0, some diversification benefits. 3. If r = 1.0, no diversification effects.

3. Market Risk:

Reflects the projects effect on a well-diversified stock portfolio. Takes account of stockholders other assets. Depends on projects W and correlation with the stock market. Measured by the projects market beta.

10

How is each type of risk used?

 Market risk is theoretically best in most situations.  However, creditors, customers, suppliers, and employees are more affected by corporate risk.  Therefore, corporate risk is also relevant.

11

 Stand-alone risk is easiest to measure, more intuitive.  Core projects are highly correlated with other assets, so stand-alone risk generally reflects corporate risk.  If the project is highly correlated with the economy, stand-alone risk also reflects market risk.

12

What is sensitivity analysis?

 Shows how changes in a variable such as unit sales affect NPV or IRR.  Each variable is fixed except one. Change this one variable to see the effect on NPV or IRR.  Answers what if questions, e.g. What if sales decline by 30%?

13

Illustration
Change from Base Level Resulting NPV (000s) Unit Sales Salvage k

-30% -20 -10 0 +10 +20 +30

$ 10 35 58 82 105 129 153

$78 80 81 82 83 84 85

$105 97 89 82 74 67 61

14 NPV (000s) Unit Sales

82 k

Salvage

-30

-20

-10 Base 10 Value

20

30

15

Results of Sensitivity Analysis

 Steeper sensitivity lines show greater risk. Small changes result in large declines in NPV.  Unit sales line is steeper than salvage value or k, so for this project, should worry most about accuracy of sales forecast.

16

What are the weaknesses of sensitivity analysis?

 Does not reflect diversification.  Says nothing about the likelihood of change in a variable, i.e. a steep sales line is not a problem if sales wont fall.  Ignores relationships among variables.

17

Why is sensitivity analysis useful?

 Gives some idea of stand-alone risk.  Identifies dangerous variables.  Gives some breakeven information.

18

What is scenario analysis?

 Examines several possible situations, usually worst case, most likely case, and best case.  Provides a range of possible outcomes.

19

Assume we know with certainty all variables except unit sales, which could range from 900 to 1,600. Scenario Worst Base Best Probability 0.25 0.50 0.25 NPV(000) $ 15 82 148

E(NPV) = $ 82 W(NPV) = 47 CV(NPV) = W(NPV)/E(NPV) = 0.57

20

If the firms average project has a CV of 0.2 to 0.4, is this a high-risk project? What type of risk is being measured?

 Since CV = 0.57 > 0.4, this project has high risk.  CV measures a projects standalone risk. It does not reflect firm or stockholder diversification.

21

Would a project in a firms core business likely be highly correlated with the firms other assets?

 Yes. Economy and customer demand would affect all core products.  But each product would be more or less successful, so correlation < +1.0.  Core projects probably have correlations within a range of +0.5 to +0.9.

22

How do correlation and W affect a projects contribution to corporate risk?

 If WP is relatively high, then projects corporate risk will be high unless diversification benefits are significant.  If project cash flows are highly correlated with the firms aggregate cash flows, then the projects corporate risk will be high if WP is high.

23

Would a core project in the furniture business be highly correlated with the general economy and thus with the market?

 Probably. Furniture is a deferrable luxury good, so sales are probably correlated with but more volatile than the general economy.

24

Would correlation with the economy affect market risk?

 Yes. High correlation increases market risk (beta). Low correlation lowers it.

25

With a 3% risk adjustment, should our project be accepted?

 Project k = 10% + 3% = 13%.  Thats 30% above base k.  NPV = $60,541.  Project remains acceptable after accounting for differential (higher) risk.

26

Should subjective risk factors be considered?

 Yes. A numerical analysis may not capture all of the risk factors inherent in the project.  For example, if the project has the potential for bringing on harmful lawsuits, then it might be riskier than a standard analysis would indicate.

27

Are there any problems with scenario analysis?

 Only considers a few possible outcomes.  Assumes that inputs are perfectly correlated--all bad values occur together and all good values occur together.  Focuses on stand-alone risk, although subjective adjustments can be made.

28

What is a simulation analysis?

 A computerized version of scenario analysis which uses continuous probability distributions.  Computer selects values for each variable based on given probability distributions.
(More...)

29

 NPV and IRR are calculated.  Process is repeated many times (1,000 or more).  End result: Probability distribution of NPV and IRR based on sample of simulated values.  Generally shown graphically.

30

Probability Density

xxxx xxxxxxx xx xxxxxxx xxx xxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxx

E(NPV)

NPV

Also gives WNPV, CVNPV, probability of NPV > 0.

31

What are the advantages of simulation analysis?

 Reflects the probability distributions of each input.  Shows range of NPVs, the expected NPV, WNPV, and CVNPV.  Gives an intuitive graph of the risk situation.

32

What are the disadvantages of simulation?

 Difficult to specify probability distributions and correlations.  If inputs are bad, output will be bad: Garbage in, garbage out.  May look more accurate than it really is. It is really a SWAG (Scientific Wild A__ Guess). (More...)

33

 Sensitivity, scenario, and simulation analyses do not provide a decision rule. They do not indicate whether a projects expected return is sufficient to compensate for its risk.  Sensitivity, scenario, and simulation analyses all ignore diversification. Thus they measure only stand-alone risk, which may not be the most relevant risk in capital budgeting.

34

Find the projects market risk and cost of capital based on the CAPM.

 Target debt ratio = 50%.  kd = 12%.  Tax rate = 40%.  kRF = 10%.  beta Project = 1.2.  Market risk premium = 6%.

35

 Beta = 1.2, so project has more market risk than average.  Projects required return on equity: ksP = kRF + (kM - kRF)bP
= 10% + (6%)1.2 = 17.2%.

WACCP = wdkd(1 - T) + weksP

36

How does the projects market risk compare with the firms overall market risk?

 Project k = 12.2% versus companys k = 10%.  Indicates that projects market risk is greater than firms average project.

37

Is the projects relative market risk consistent with its stand-alone risk?

 Yes. Project CV = 0.57 versus 0.3 for an average project, which is consistent with projects higher market risk.

38

Methods for estimating a projects beta

 Pure play. Find several publicly traded companies exclusively in projects business. Use average of their betas as proxy for projects beta.
Hard to find such companies.

39

 Accounting beta. Run regression between projects ROA and S&P index ROA.
Accounting betas are correlated (0.5-0.6) with market betas. But normally cant get data on new projects ROAs before the capital budgeting decision has been made.

40

Advantages and disadvantages of applying the CAPM in capital budgeting

 Advantages:  A projects market risk is the most relevant risk to stockholders, hence to determine the effect of the project on stock price.  It results in a definite hurdle rate for use in evaluating the project.

41

 Disadvantages: It is virtually impossible to estimate betas for many projects. People sometimes focus on market risk to the exclusion of corporate risk, and this may be a mistake.

42

Divisional Costs of Capital Debt Cost of Capacity Capital Low Avg. High 14% 10% 8%

Division Heirloom Maple School

Beta High Avg. Low

43

Project Risk Adjustments

 Crockett Furniture classifies each project within a division as high risk, average risk, and low risk. Crockett adjusts divisional costs of capital by:

Adding 2% for high risk project

44

What are the project costs of capital?

Maple

School

45

Evaluating Our Project

 Our project is a high risk project in the Heirloom division. Project cost of capital = 16% NPV = $42 thousand

46

Evaluating Risky Outflows

 Company is evaluating two alternative production processes. Plan W requires more workers but less capital. Plan C requires more capital but fewer workers.  Both systems have 3-year lives.  The choice will have no impact on revenues, so the decision will be based on relative costs.

47

Year 0 1 2 3

Plan W ($500) (500) (500) (500)

Plan C ($1,000) (300) (300) (300)

The two systems are of average risk, so k = 10%. Which to accept? PVCOSTS-W = -$1,743. PVCOSTS-C = -$1,746. Ws costs are slightly lower so pick W.

48

Now suppose Plan W is riskier than Plan C because future wage rates are difficult to forecast. Would this affect the choice?

 If we add a 3% risk adjustment to the 10% to get kW = 13%, new PV would be: PVCOSTS-W = -$1,681 which is < old PVCOSTS-W = -$1,743.  W now looks even better.

49

 Plan W now looks better, but since it is riskier, it should look worse!  When costs are being discounted, we must use a lower discount rate to reflect higher risk. Thus, the appropriate discount rate would be 10% - 3% = 7%, making PVCOSTS-W = -$1,812 > old -$1,743.  With risk adjustment, PVCOSTS-W > PVCOSTS-C, so now choose Plan C.

50

 Note that neither plan has an IRR.  IRR is the discount rate that equates the PV (inflows) to the PV (outflows).  Since there are only outflows, there can be no IRR (or MIRR).  Similarly, a meaningful NPV can only be calculated if a project has both inflows and outflows.  If CFs all have the same sign, the result is a PV, not an NPV.

51

Real Options

 Real options occur when managers have the opportunity to influence the cash flows of a project after the project has been implemented.  Real options also are called: Managerial options. Strategic options.

52

How do real options increase the value of a project?

 Real options allow managers to avoid negative project cash flows or magnify positive project cash flows. Increases size of expected cash flows. Decreases risk of expected cash flows.

53

How is the DCF method affected? (1) Its easy to quantify the increase in the size of the expected cash flows. (2) Its very hard to quantify the decrease in the risk of the expected cash flows. (3) The correct cost of capital cannot be identified, so the DCF method doesnt work very well.

54

Types of Real Options

 Flexibility options  Abandonment options  Options to contract or temporarily suspend operations  Options to expand volume of product  Options to expand into new geographic areas
(More...)

55

 Options to add complementary products  Options to add successive generations of the same product  Options to delay

56

What attributes increase the value of real options?

 All real options have a positive value.  Even if its not possible to determine a quantitative estimate of a real options value, its better to have a qualitative estimate than to ignore the real option.
(More...)

57

 Real options are more valuable if: They have a long time until you must exercise them. The underlying source of risk is very volatile. Interest rates are high.

58

Choosing the Optimal Capital Budget

 Finance theory says to accept all positive NPV projects.  Two problems can occur when there is not enough internally generated cash to fund all positive NPV projects: An increasing marginal cost of capital. Capital rationing

59

Increasing Marginal Cost of Capital

 Externally raised capital can have large flotation costs, which increase the cost of capital.  Investors often perceive large capital budgets as being risky, which drives up the cost of capital.
(More...)

60

 If external funds will be raised, then the NPV of all projects should be estimated using this higher marginal cost of capital.

61

Capital Rationing

 Capital rationing occurs when a company chooses not to fund all positive NPV projects.  The company typically sets an upper limit on the total amount of capital expenditures that it will make in the upcoming year.
(More...)

62

Reason: Companies want to avoid the direct costs (i.e., flotation costs) and the indirect costs of issuing new capital. Solution: Increase the cost of capital by enough to reflect all of these costs, and then accept all projects that still have a positive NPV with the higher cost of capital.
(More...)

63

Reason: Companies dont have enough managerial, marketing, or engineering staff to implement all positive NPV projects. Solution: Use linear programming to maximize NPV subject to not exceeding the constraints on staffing.
(More...)

64

Reason: Companies believe that the projects managers forecast unreasonably high cash flow estimates, so companies filter out the worst projects by limiting the total amount of projects that can be accepted. Solution: Implement a post-audit process and tie the managers compensation to the subsequent performance of the project.