# Cash Flow Estimation And Risk Analysis, Lecture Notes - Financial Management, Study notes for Financial Management. University of Michigan (MI)

## Financial Management

Description: Relevant cash flows, Incorporating inflation, Types of risk, Risk Analysis
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CHAPTER 12 Cash Flow Estimation

12-1

CHAPTER 12 Cash Flow Estimation and Risk Analysis

 Relevant cash flows

 Incorporating inflation

 Types of risk

 Risk Analysis

12-2

Proposed Project

 Total depreciable cost  Equipment: \$200,000

 Shipping: \$10,000

 Installation: \$30,000

 Changes in working capital  Inventories will rise by \$25,000

 Accounts payable will rise by \$5,000

 Effect on operations  New sales: 100,000 units/year @ \$2/unit

 Variable cost: 60% of sales

12-3

Proposed Project

 Life of the project

 Economic life: 4 years

 Depreciable life: MACRS 3-year class

 Salvage value: \$25,000

 Tax rate: 40%

 WACC: 10%

12-4

Determining project value  Estimate relevant cash flows

 Calculating annual operating cash flows.  Identifying changes in working capital.  Calculating terminal cash flows.

0 1 2 3 4

Initial OCF1 OCF2 OCF3 OCF4 Costs + Terminal

CFs

NCF0 NCF1 NCF2 NCF3 NCF4

12-5

Initial year net cash flow

 Find Δ NOWC.  ⇧ in inventories of \$25,000

 Funded partly by an ⇧ in A/P of \$5,000  Δ NOWC = \$25,000 - \$5,000 = \$20,000

 Combine Δ NOWC with initial costs. Equipment -\$200,000 Installation -40,000 Δ NOWC -20,000 Net CF0 -\$260,000

12-6

Determining annual depreciation expense

Year Rate x Basis Depr 1 0.33 x \$240 \$ 79 2 0.45 x 240 108 3 0.15 x 240 36 4 0.07 x 240 17 1.00 \$240 Due to the MACRS ½-year convention, a 3-year asset is depreciated over 4 years.

12-7

Annual operating cash flows

1 2 3 4

Revenues \$200.0 \$200.0 \$200.0 \$200.0

- Op Costs -120.0 -120.0 -120.0 -120.0

- Depr’n Expense -79.2 -108.0 -36.0 -16.8

Operating Income (BT) 0.8 -28.0 44.0 63.2

- Tax (40%) 0.3 -11.2 17.6 25.3

Operating Income (AT) 0.5 -16.8 26.4 37.9

+ Depr’n Expense 79.2 108.0 36.0 16.8

Operating CF \$79.7 \$91.2 \$62.4 \$54.7

(Thousands of dollars)

12-8

Terminal net cash flow

Recovery of NOWC \$20,000 Salvage value 25,000 Tax on SV (40%) -10,000 Terminal CF \$35,000 Q. How is NOWC recovered? Q. Is there always a tax on SV? Q. Is the tax on SV ever a positive cash flow?

12-9

Should financing effects be included in cash flows?

 No, dividends and interest expense should not be included in the analysis.

 Financing effects have already been taken into account by discounting cash flows at the WACC of 10%.

 Deducting interest expense and dividends would be “double counting” financing costs.

12-10

Should a \$50,000 improvement cost from the previous year be included in the analysis?

 No, the building improvement cost is a sunk cost and should not be considered.

 This analysis should only include incremental investment.

12-11

If the facility could be leased out for \$25,000 per year, would this affect the analysis?

 Yes, by accepting the project, the firm foregoes a possible annual cash flow of \$25,000, which is an opportunity cost to be charged to the project.

 The relevant cash flow is the annual after- tax opportunity cost.

 A-T opportunity cost = \$25,000 (1 – T)

= \$25,000(0.6)

= \$15,000

12-12

If the new product line decreases the sales of the firm’s other lines, would this affect the analysis?

 Yes. The effect on other projects’ CFs is an “externality.”

 Net CF loss per year on other lines would be a cost to this project.

 Externalities can be positive (in the case of complements) or negative (substitutes).

12-13

Proposed project’s cash flow time line

0 1 2 3 4

-260 79.7 91.2 62.4 54.7

Terminal CF → 35.0

89.7  Enter CFs into calculator CFj Key and

enter I/YR = 10%. NPV = -\$4.03 million  IRR = 9.3% MIRR = 9.6%  Payback = 3.3 years

12-14

-260 79.7 91.2 62.4 89.7

0 1 2 3 4

Evaluating the project: Payback period

Payback = 3 + 26.7 / 89.7 = 3.3 years.

Cumulative: -260 -180.3 -89.1 -26.7 63.0

12-15

If this were a replacement rather than a new project, would the analysis change?

 Yes, the old equipment would be sold, and new equipment purchased.

 The incremental CFs would be the changes from the old to the new situation.

 The relevant depreciation expense would be the change with the new equipment.

 If the old machine was sold, the firm would not receive the SV at the end of the machine’s life. This is the opportunity cost for the replacement project.

12-16

What are the 3 types of project risk?

 Stand-alone risk

 Corporate risk

 Market risk

12-17

What is stand-alone risk?

 The project’s total risk, if it were operated independently.

 Usually measured by standard deviation (or coefficient of variation).

 However, it ignores the firm’s diversification among projects and investor’s diversification among firms.

12-18

What is corporate risk?

 The project’s risk when considering the firm’s other projects, i.e., diversification within the firm.

 Corporate risk is a function of the project’s NPV and standard deviation and its correlation with the returns on other projects in the firm.

12-19

What is market risk?

 The project’s risk to a well-diversified investor.

 Theoretically, it is measured by the project’s beta and it considers both corporate and stockholder diversification.

12-20

Which type of risk is most relevant?

 Market risk is the most relevant risk for capital projects, because management’s primary goal is shareholder wealth maximization.

 However, since total risk affects creditors, customers, suppliers, and employees, it should not be completely ignored.

12-21

Which risk is the easiest to measure?

 Stand-alone risk is the easiest to measure. Firms often focus on stand- alone risk when making capital budgeting decisions.

 Focusing on stand-alone risk is not theoretically correct, but it does not necessarily lead to poor decisions.

12-22

Are the three types of risk generally highly correlated?

 Yes, since most projects the firm undertakes are in its core business, stand-alone risk is likely to be highly correlated with its corporate risk.

 In addition, corporate risk is likely to be highly correlated with its market risk.

12-23

What is sensitivity analysis?

 Sensitivity analysis measures the effect of changes in a variable on the project’s NPV.

 To perform a sensitivity analysis, all variables are fixed at their expected values, except for the variable in question which is allowed to fluctuate.

 Resulting changes in NPV are noted.

12-24

What are the advantages and disadvantages of sensitivity analysis?

 Identifies variables that may have the greatest potential impact on profitability and allows management to focus on these variables.

 Does not reflect the effects of diversification.

 Does not incorporate any information about the possible magnitudes of the forecast errors.

12-25

What if there is expected inflation of 5%, is NPV biased?

 Yes, inflation causes the discount rate to be upwardly revised.

 Therefore, inflation creates a downward bias on PV.

 Inflation should be built into CF forecasts.

12-26

Annual operating cash flows if expected inflation = 5%; Adjust Revenues and Op. Costs by 5% annually

1 2 3 4 Revenues 210 220 232 243 Op. Costs (60%) -126 -132 -139 -146 - Deprn Expense -79 -108 -36 -17 - Oper. Income (BT) 5 -20 57 80 - Tax (40%) 2 -8 23 32 Oper. Income (AT) 3 -12 34 48 + Deprn Expense 79 108 36 17 Operating CF 82 96 70 65

12-27

Considering inflation: Project net CFs, NPV, and IRR

0 1 2 3 4

-260 82.1 96.1 70.0 65.1

Terminal CF → 35.0

100.1

 Enter CFs into calculator CFLO register, and enter I/YR = 10%.  NPV = \$15.02 million.

 IRR = 12.6%.

12-28

Perform a scenario analysis of the project, based on changes in the sales forecast

 Suppose we are confident of all the variable estimates, except unit sales. The actual unit sales are expected to follow the following probability distribution:

Case Probability Unit Sales

Worst 0.25 75,000

Base 0.50 100,000

Best 0.25 125,000

12-29

Scenario analysis

 All other factors shall remain constant and the NPV under each scenario can be determined.

Case Probability NPV

Worst 0.25 (\$27.8)

Base 0.50 \$15.0

Best 0.25 \$57.8

12-30

Determining expected NPV, NPV, and CVNPV from the scenario analysis

 E(NPV) = 0.25(-\$27.8)+0.5(\$15.0)+0.25(\$57.8)

= \$15.0

 NPV = [0.25(-\$27.8-\$15.0) 2 + 0.5(\$15.0-

\$15.0)2 + 0.25(\$57.8-\$15.0)2]1/2

= \$30.3.

 CVNPV = \$30.3 /\$15.0 = 2.0.

12-31

If the firm’s average projects have CVNPV ranging from 1.25 to 1.75, would this project be of high, average, or low risk?

 With a CVNPV of 2.0, this project would be classified as a high-risk project.

 Perhaps, some sort of risk correction is required for proper analysis.

12-32

Is this project likely to be correlated with the firm’s business? How would it contribute to the firm’s overall risk?

 We would expect a positive correlation with the firm’s aggregate cash flows.

 As long as correlation is not perfectly positive (i.e., ρ  1), we would expect it to contribute to the lowering of the firm’s total risk.

12-33

If the project had a high correlation with the economy, how would corporate and market risk be affected?

 The project’s corporate risk would not be directly affected. However, when combined with the project’s high stand-alone risk, correlation with the economy would suggest that market risk (beta) is high.

12-34

If the firm uses a +/- 3% risk adjustment for the cost of capital, should the project be accepted?

 Reevaluating this project at a 13% cost of capital (due to high stand-alone risk), the NPV of the project is -\$2.18 (using inflation adjusted CFs).

 If, however, it were a low-risk project, we would use a 7% cost of capital and the project NPV is \$34.17.

12-35

What subjective risk factors should be considered before a decision is made?

 Numerical analysis sometimes fails to capture all sources of risk for a project.

 If the project has the potential for a lawsuit, it is more risky than previously thought.

 If assets can be redeployed or sold easily, the project may be less risky.

12-36

What is real option analysis?

 Real options exist when managers can influence the size and riskiness of a project’s cash flows by taking different actions during the project’s life.

 Real option analysis incorporates typical NPV budgeting analysis with an analysis for opportunities resulting from managers’ decisions.

12-37

What are some examples of real options?

 Investment timing options – as to when to begin a project, now or later

 Abandonment/early shutdown options if project is not profitable, e.g. New Coke

 Growth/expansion options, if first project is profitable, e.g. Starbucks in India

 Flexibility options, to modify operations, e.g. BMW plant in S.C. for both coupes and SUVs