Posted: April 25th, 2025

Business Finance – Management Homework: NPV Assignment

 

Homework: NPV Assignment

 

Homework Discount Cash-Flow Analysis Assignment

Project Analysis Assignment

Homework: NPV Assignment

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BUSI 530

Chapter 9: Using Discounted Cash-Flow Analysis to Make Investment Decisions

Chapter 9 Learning Objectives

1. Identify the cash flows properly attributable to a proposed new project.

2. Calculate the cash flows of a project from standard financial statements.

3. Understand how the company’s tax bill is affected by depreciation and how this affects project value.

4. Understand how changes in working capital affect project cash flows.

Cash Flows

Chapter 8 introduced valuation techniques based on discounted cash flows.

This chapter develops criteria for properly identifying and calculating cash flows.

Chapter 9 Outline

· Identifying Cash Flows

· Discount Cash Flows, Not Profits

· Discount Incremental Cash Flows

· Discount Nominal Cash Flows by the Nominal Cost of Capitol

· Separate Investment & Financing Decisions

· Calculating Cash Flows

· Example:
Blooper Industries

Identifying Cash Flows: Cash Flow vs. Accounting Income

Discount actual cash flows, not necessarily net income.

Using accounting income, rather than cash flow, could lead to erroneous decisions.

NPV: Accounting Income

Example

A project costs $2,000 and is expected to last 2 years, producing cash income of $1,500 and $500 respectively. The cost of the project can be depreciated at $1,000 per year. Given a 10% required return, compare the NPV using cash flows to the NPV using accounting income.

NVP: Cash Flows

Example (ctd)

A project costs $2,000 and is expected to last 2 years, producing cash income of $1,500 and $500 respectively. The cost of the project can be depreciated at $1,000 per year. Given a 10% required return, compare the NPV using cash flows to the NPV using accounting income.

Which is correct?

Incremental Cash Flows

· Discount

Incremental Cash Flows

· Include All Indirect Effects
· Forget Sunk Costs
· Include Opportunity Costs
· Recognize the Investment in Working Capital
· Beware of Allocated Overhead Costs
· Remember Shutdown Cash Flows
Incremental Cash Flow
Cash Flow with Project
Cash Flow without Project
=
–

Incremental Cash Flow
– The
extra cash flows produced by a project.

Inflation and Discounting Cash Flows

Discounting Rule:

Real cash flows must be discounted at a real discount rate, nominal cash flows at a nominal rate.

Inflation – rising price levels

Inflation Example: Nominal Rates

Example

You own a lease that will earn you $8,000 next year, increasing at 3% a year for 3 additional years (4 years total). If discount rates are 10% what is the present value of the lease?

Inflation Example: Real Rates

Example (ctd)

You own a lease that will earn you $8,000 next year, increasing at 3% a year for 3 additional years (4 years total). If discount rates are 10%, what is the present value of the lease?

Include all Indirect Effects

Indirect Effect Rule:
You must include all indirect effects in your analysis.

Sunk Costs

· A cost that cannot be recovered

Sunk Cost Rule:
Always ignore sunk costs

Opportunity Cost

· Benefit or cash flow foregone as a result of an action

Opportunity Cost Rule:

Be sure to recognize the opportunity cost (that which is foregone).

Investments in Working Capital

Working Capital Rule:
Investments in working capital, just like investments in plant and equipment, result in cash outflows.

Common ways working capital is overlooked:
1.
Forgetting about working capital entirely.

2.
Forgetting that working capital may change during the life of the project.

3.
Forgetting that working capital is recovered at the end of the project.

Net Working Capital
– Current assets minus current liabilities

Additional Considerations

1.
Remember Terminal Cash Flows

2.
Beware of Allocated Overhead Costs

3.
Separation of Investment & Financing Decisions

Final Thought: Incremental Cash Flows

Ask the following question:

Would the cash flow still exist if the project does not exist?

If
yes, do not include it in your analysis.

If
no, include it.

Calculating Cash Flows

Cash flows are made up of three separate parts.

Total cash flow =
+ cash flows from capital investments
+ cash flows from changes in working capital
+ operating cash flows

Calculating Cash Flows

Capital Investments
Changes in Working Capital
Operating Cash Flows Operating cash flow = Revenue – Costs – Taxes

Cash Flow from operations: Three Methods of Calculation

·
Method 1: Dollars in Minus Dollars Out

·
Method 2: Adjusted Accounting Profits

·
Method 3: Tax Shields

Depreciation Tax Shield
– Reduction in taxes attributable to depreciation.

Calculating Cash Flow: Example

Year 0

Year 1

Year 2

Year 3

Year 4

Fixed Assets

Purchase of Factory (sale in 4 years)

-$100,000

$ 0

$ 0

$ 0

$ 50,000

Total Cash Flow from Fixed Assets

-$100,000

$ 0

$ 0

$ 0

$ 50,000

Working Capital

CF from Inventory (- buildup,+ sell off)

$ 0

-$ 20,000

-$ 10,000

$ 10,000

$ 20,000

CF from Accounts Receivable

$ 0

-$ 35,000

-$ 25,000

$ 30,000

$ 30,000

Total Cash Flow from Working Capital

$ 0

-$ 55,000

-$ 35,000

$ 40,000

$ 50,000

Operations

Revenues

$ 0

$120,000

$125,000

$150,000

$150,000

Expenses

$ 0

$ 60,000

$ 61,250

$ 70,000

$ 70,000

Depreciation

$ 0

$ 12,500

$ 12,500

$ 12,500

$ 12,500

Pre-Tax Profits

$ 0

$ 47,500

$ 51,250

$ 67,500

$ 67,500

After-Tax Profits (tax rate = 35%)

$ 0

$ 30,875

$ 33,313

$ 43,875

$ 43,875

Total Cash Flow from Operations

$ 0

$ 43,375

$ 45,813

$ 56,375

$ 56,375

Total Cash Flow

-$100,000

-$11,625

$10,813

$ 96,375

$106,375

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BUSI 530

Chapter 10: Project Analysis

Chapter 10 Learning Objectives

1. Appreciate the practical problems of capital budgeting in large corporations.

2. Use sensitivity, scenario, and break-even analyses to see how project profitability would be affected by an error in your forecasts.

3. Understand why an overestimate of sales is more serious for projects with high operating leverage.

4. Recognize the importance of managerial flexibility in capital budgeting.

Project Analysis

Chapters 8 and 9 develop a framework for project analysis.

This chapter analyzes the robustness of a project’s value by asking some “What If” Questions.

Chapter 10 Outline

· How Firms Organize the Investment Process

· Some “What If” Questions

· Sensitivity Analysis

· Scenario Analysis

· Break Even Analysis

· Real Options and the Value of Flexibility

Capital Budget – The list of planned investment projects.

Capital Budgeting: The Decision Process

1. Stage 1: The Capital Budget

2. Stage 2: Project Authorization

· Outlays required by law or company policy

· Maintenance or cost reduction

· Capacity expansion in existing business

· Investment for new products

Potential Capital Budgeting Problems

· Ensuring forecasts are consistent

· Eliminating conflicts of interest

· Reducing forecast bias

· Proper selection criteria (NPV and others)

What-if Testing

·

Sensitivity Analysis –
Analysis of the effects on project profitability of changes in sales, costs,

etc.

·

Scenario Analysis –
Project analysis given a particular combination of assumptions.

·

Simulation Analysis –
Estimation of the probabilities of different possible outcomes.

·

Break-Even Analysis –
Analysis of the level of sales at which the company breaks even.

Sensitivity Analysis:
Analysis of the effects on project profitability of changes in sales, costs,

etc.

Why is sensitivity analysis useful?

Sensitivity Analysis – Example

Base Case: Expected cash flows from a new project (with 8% Opportunity Cost of Capital; 40% average tax rate; variable costs are a constant 80% of sales; all numbers in $000s)

NPV = $1,382.47

IRR = 12.7%

Payback Period = 6 years

Profitability Index = .256

Sensitivity Analysis – Example

Possible Range of Variable

Sensitivity Analysis: Changing Sales

(with 8% Opportunity Cost of Capital; 40% average tax rate; variable costs are a constant 80% of sales; all numbers in $000s)

Pessimistic Case—
Sales = $14,000 Optimistic Case—
Sales = $18,000

NPV = -$426 NPV = $3,191
Note: It is recommended for practice that students calculate the other valuation techniques learned in Chapter 8 (IRR, etc)

Sensitivity Analysis: Changing Fixed Costs

(with 8% Opportunity Cost of Capital; 40% average tax rate; variable costs are a constant 80% of sales; all numbers in $000s)

Pessimistic Case—
Fixed Costs = $2,500 Optimistic Case—
Fixed Costs = $1,500

NPV = -$878 NPV = $3,643
Note: It is recommended for practice that students calculate the other valuation techniques learned in Chapter 8 (IRR, etc)

Limits to Sensitivity Analysis

· Ambiguous
· How do you consistently define “optimistic” or “pessimistic”?
· Interrelatedness of variables

Scenario Analysis

·

Scenario Analysis
– Project analysis given a particular combination of assumptions.

·

Simulation Analysis
–Estimation of the probabilities of different possible outcomes, e.g., from an investment project.

Scenario Analysis: Introducing Competition

Assume that it will take two years for competition to enter the market. At this time, sales drop 10% and variable costs increase to 82% (increased labor demand). What happens to NPV under this scenario?

Base Case – No Competition Scenario – Introduce Competition

NPV = $1,382 NPV = -$717

Break-even Analysis
– Analysis of the level of sales at which the project breaks even.

Why is this useful
?

Break-Even Analysis: Example

(with 8% Opportunity Cost of Capital; 40% average tax rate; variable costs are a constant 80% of sales; all numbers in $000s)

· Determine the number of units that must be sold in order to break even, on an NPV basis.
· Suppose each unit has a price point of $45,000
· All other variables are at their base case levels

Break-Even Point: Accounting

Break-Even Point (Accounting) – The break-even point is the number of units sold where net profits = $0.

What does the accounting break-even point not account for?

Break-Even Point: Finance

NPV Break-Even Point (Finance):

How can we find the present value of future cash flows? As long as cash flows are equal each year, we can use the Annuity Factor.

NPV break-even point
– Level of sales at which project net present value becomes positive.

Break-Even Analysis

Recall: the break-even point is the number of units sold where NPV = $0.

· Note: Think back to discussion of economic value added (EVA) in Chapter 4.
· A project that breaks even on a present value basis will have a positive accounting profit but zero economic value added.
· In other words, it will just cover
all its costs, including the cost of capital.

Note: The NPV break-even level of sales will be greater than the accounting break-even level of sales. Why?

Operating Leverage –
Degree to which costs are fixed.

Degree of Operating Leverage (DOL) –
Percentage change in profits given a 1% change in

sales.

Operating Leverage: Why is it useful?

Degree of Operating Leverage: Example

Real Options

1.
Option to expand

2.
Option to abandon

3.
Timing option

4.
Flexible production facilities

Real Options –
Options to invest in, modify, or dispose of a capital investment project

Real Options & the Value of Flexibility

Decision Trees – Diagram of sequential decisions and possible outcomes.

·
Decision trees help companies determine their options by showing various choices and outcomes.

·
The option to avoid a loss or produce extra profit has value.

·
The ability to create an option has value that can be bought or sold.

Decision Trees: Example

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Homework: Discount Cash-Flow Analysis Assignment

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Project Analysis Assignment

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