case study of accounting
Case – Canyon Buff’s Chemical Equipment This case is a simple capital budgeting exercise that should reinforce your understanding of the following topics: • Incremental unlevered net income • Free cash flow • Sensitivity analysis and scenario analysis
Before solving this case, you must watch the video “Capital Budgeting in-class exercise solution” in the Lecture 6 folder, which provides the basis for this case. You need to finish both lectures 6 and 7 to be able to complete the case study.
Introduction Canyon Buff Corp. has developed a new construction chemical that greatly improves the durability and weatherability of cement-based materials. After spending $500,000 on the research of the potential market for the new chemical, Canyon Buff is considering a project that requires an initial investment of $9,000,000 in manufacturing equipment. • The equipment must be purchased before the chemical production can begin. For tax purposes, the equipment is subject to a 5-year straight-line depreciation schedule, with a projected zero salvage value. For simplicity, however, we will continue to assume that the asset can actually be used out into the indefinite future (i.e., the actual useful life is effectively infinite).
• Canyon Buff anticipates that the sales will be $30,000,000 in the first year (Year 1). They expect that sales will initially grow at an annual rate of 6% until the end of sixth year. After that, the sales will grow at the estimated 2% annual rate of inflation in perpetuity.
• The cost of goods sold is estimated to be 72% of sales.
• The accounting department also estimates that at introduction in Year 0, the new product’s required initial net working capital will be $6,000,000. In future years accounts receivable are expected to be 15% of the next year sales, inventory is expected to be 20% of the next year’s cost of goods sold and accounts payable are expected to be 15% of the next year’s cost of goods sold.
• The selling, general and administrative expense is estimated to be $6,000,000 per year, but $1 million of this amount is the overhead expense that will be incurred even if the project is not accepted.
• The market research to support the product was completed last month at a cost of $500,000 to be paid by the end of next year.
• The annual interest expense tied to the project is $1,000,000.
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• Canyon Buff has a cost of capital of 20% and faces a marginal tax rate of 30% and an average tax rate is 20%.
Instructions
I posted an incomplete Excel template for your analysis. You need to figure out how to construct the pro forma income statements and calculate the incremental unlevered net income. You should include ONLY the factors that will affect your capital budgeting decision. Revise the template if necessary.
Note that your analysis should be set up so the assumptions that impact the cash flow estimates can be easily changed to identify the sensitivity of your calculations to these assumptions. Never hardcode in excel (see the pdf “Using Excel in Capital Budgeting” on blackboard).
There are three sheets in the template. Use the worksheet “NPV” for questions 1 to 4, and the other two sheets for questions 5 and 6.
Submit your Excel spreadsheet through the blackboard. Clearly show your work so that I can trace your numbers.
Questions
1. Use Excel to construct six-year pro forma income statements and calculate the incremental unlevered net income for the first six years.
• When calculating incremental unlevered net income, should we include all the expenses mentioned in the case? If not, what expenses should we exclude and why? Clearly and concisely state your reasons in the cell E9 of the excel template. If you just forecast the unlevered net income but don’t given any explanations on why you exclude certain expenses, a penalty of 30 points will deducted from your grade for the case study.
2. Calculate six-year projections for free cash flows. Remember to include cash flows from the income statement and depreciation, changes in net working capital, and capital expenditures or dispositions.
Hint: You need to calculate the level of net working capital (NWC) and change in NWC. Pay attention to the timing of NWC.
3. Canyon Buff expects that free cash flow from Year 6 onwards will increase at a constant rate of 2%/year into the indefinite future. Calculate PV(terminal value that captures the value of future free cash flows in Year 6 and beyond). That is, calculate the terminal value first, then find its value in Year 0 (today).
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Hint: We went over this in Lecture Note 6, so let me briefly review the key points: a. Assuming the cash flows grow at a constant rate g after Year N+1, then Year N TV = (Year N+1 CF)/(r−g) (from growing perpetuity formula). where r is discount rate For example, if {FCF6, FCF7, FCF8, …} is a growing perpetuity, then Year 5 TV = Year 6 FCF/(r-g). Similarly, if {FCF7, FCF8, FCF9, …} is a growing perpetuity, then Year 6 TV = Year 7 FCF/(r-g).
b. We should discount this Terminal Value back to Year 0.
4. Determine the NPV of the project. Remember to net out any initial cash outflows.
5. Perform a sensitivity analysis by varying the four parameters as follows:
Parameter Initial Assumption Worst Case Best Case Sales in Year 1 $30,000 $27,000 $33,000 NPV Sales Growth through Year 6 6% 0% 10% NPV Cost of Goods Sold (% of Sales) 72% 77% 67% NPV Cost of Capital 20% 23% 17% NPV
For example, vary the parameter “Sales in Year 1” from the worst case $27,000 to the best case $33,000, holding all the other parameters fixed (at the level of initial assumptions). Then fill in the highlighted blank boxes for NPV in Excel (the sheet “Sensitivity Analysis”)
Do the same thing for the other three parameters.
Suppose you are the financial manager, if you are asked to use limited resources to refine the assumption on ONLY ONE of the above four parameters, which one should you choose and why? Clearly state the reason. Write your answer in Excel.
6. Perform a scenario analysis by simultaneously varying the two parameters below:
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Sales Growth through Year 6
% Cost of Goods Sold NPV Scenario 1 (Baseline) 5% 71% Scenario 2 6% 72% Scenario 3 8% 73% Scenario 4 9% 74%
Which scenario generates the highest NPV? Write your answer in Excel.
> in Year 6 Onward
% of Next Year Sales
% of Next Year COGS
% of Next Year COGS
1 2 6 Unlevered Net Income CF from Change in NWC &”CG Times,Bold”&11Joyce’s Juice: Solution &”CG Times,Regular”&11Page &P
NPV NPV NPV NPV 6% 72% Opportunity Costs The opportunity cost of using a resource is the value it could have provided in its best alternative use. E.g. suppose a firm bought a production line which will be placed in a warehouse that the company could have otherwise rented out for $20,000 per year. Should you include this opportunity cost when calculating free cash flow? Example 1 See notes underneath the slide Q: Should you include this opportunity cost when calculating free cash flow? Opportunity Costs If take the project, but exclude the opportunity cost when calculating FCFs. Prone to make wrong decisions. 2 Years Years How to Account for Opportunity Costs Conclusion from the above timeline: Don’t take the project. Right decision. 3 Years Sunk Costs For example, suppose after having spent $10,000 on market research, you believe 100% that your new product will generate an NPV of $100 (e.g., PV(benefits)=5,100, PV(costs)=5,000) Sunk Costs Firm spent 10K in Year -1 (last year). Suppose+ + =5K. Should you take the project? Years Lecture 7: Capital Budgeting Part II 1 Last lecture 2 Outline 3 In-class exercise I use the example from our last lecture to illustrate how we can use the three methods to evaluate the uncertainty and the risk of the project. Sensitivity Analysis 5 Suppose your boss is more optimistic (or pessimistic) about the assumptions you made on sale price, the unit of sales, sales growth, or cost of capital (discount rate to discount cash flows), how does the NPV change in one of the assumptions, holding the other assumptions constant? Sensitivity Analysis Based on the baseline (initial) assumptions, NPV=$21,232 (see cell B31 in the sheet “Baseline” of EXCEL file “In-class exercise – DCF analysis”) Sensitivity Analysis For example, what is the NPV when units sold = 8,000, holding the other assumptions constant (i.e., the other values are based on initial or baseline assumptions: sale price =25, sales growth = 0%, cost of capital = 15%)? Sensitivity Analysis For example, when sales growth is -5%, holding the other assumptions constant (i.e., the other values are based on initial assumptions: sale price =25, units sold= 10,000, cost of capital = 15%), just change the cell B2 from 0% to -5%, then NPV = 1,934. Sensitivity Analysis Red bars show the NPV under the best-case assumptions. 9 Sensitivity Analysis 10 Scenario Analysis In the sheet “Baseline” of EXCEL file “In-class exercise – DCF analysis”, change both the sale price and expected units, i.e. change the cell B3 from 25 to 23, and cell C15 from 10,000 to 12,000, then NPV = 11,846. Scenario Analysis Price increase strategy generates the highest NPV. Break-Even Analysis 13 Accounting Break-Even A variable cost can be thought as cost of goods sold. It depends on production output. The variable cost of production is a constant amount per unit produced. As the volume of production and output increases, variable costs will also increase. Accounting Break-Even All sales and costs are incremental. Template for Accounting Break Even Hint: work backwards from EBIT to find the gross profit. Accounting Break-Even Example If we can find the total amount of gross profit, then we just calculate the number of units to be sold by dividing that number by gross profit per unit ($30/unit). Accounting Break-Even Example 18 Accounting break-even generates no tax liability because EBIT=0. Accounting Break-Even Example Accounting break-even results in free cash flows equal to depreciation in year 1 to 3 (note ΔNWC = 0 in this example) 19 Accounting break-even requires EBIT = 0, so unlevered net income = 0. After we add back depreciation, we can find the FCFs. Economic Break-Even 20 Economic Break-Even 21 Economic break-even requires NPV=0 (PV(FCFs from Year 1 to 3) + PV(FCF in Year 0) = 0) Recall PV(Annuity) 21 Economic Break-Even 22 Economic break-even requires NPV=0 Now we have free cash flows, then we should be able to work backwards to find the gross profit. 22 Template for Economic Break-Even Work backwards from free cash flow to the total gross profit. Once we calculate the total gross profit, then the economic break-even level of quantity sold is just: Template for Economic Break-Even Method 1: Work backwards from free cash flow to find the total gross profit: Economic Break-Even 25 Intuitively, at the accounting break-even level of quantity, the NPV is negative. To achieve the economic break-even level of quantity, that is to get NPV=0, we need to sell more products so that we have more net income and more free cash flows such that NPV becomes zero. Economic Break-Even 26 Assuming all other variables remain unchanged (e.g. sale price, sales growth, cost of capital) Economic Break-Even In Excel, use IRR function 27 ABC Corp. has decided to ask suppliers to bid on the 10,000 cartons of precision machine screws that ABC Corp. needs to purchase per year to support its manufacturing needs over the next five years. You have decided to submit a bid to supply the machine screws. Given the assumptions on the capital expenditure, costs, and cost of capital, what is the minimum price per carton that you should bid? Summary Lecture 6: Capital Budgeting 1 -8.4 1 Outline 2 Which projects to take? The table shows the projects that Elon Musk’s (the CEO of Tesla and SpaceX) companies are taking on. Put yourself in his shoes and think about how you should determine which projects to take on. Capital Budgeting Capital Budgeting 1. Example See notes underneath the slide Example: 7 cash flows from net income with depreciation added back Cash flow from investment For each stage, I want you to think about how each term will affect cash flows. 8 Convert net income to operating cash flows Check the notes underneath the figure on typical project cash flows (previous slide) to see all cash flow effects I, II, and III. ∆Net Working Capital and Operating Cash Flows Simplification steps: FYI. 9 10 We generally exclude interest expense because any incremental interest expenses will be related to the firm’s decision regarding how to finance the project. Here we wish to evaluate the project on its own, separate from the financing decision. 10 11 Convert net income to operating cash flows We have seen how to convert net income to operating cash flows. We just need to take out the cash flow from investment to get FCF. Free cash flow Discount FCFs back to Year 0 (today) to get the NPV of a project. See notes underneath the slide convention: Calculating unlevered net income 13 Pro-Forma Financial Statements This is what a pro-forma net income statement looks like. Other Issues 15 A firm generally identifies its marginal tax rate by determining the tax bracket that it falls into based on its overall level of pretax income. Marginal vs. Average Corporate Tax Rates Note that while marginal rates fluctuate and rise as high as 39%, average rates increase steadily with taxable income, until the 35% level is reached. For example, if a firm’s current taxable income falls into the bracket of $0-50,000, say $50,000, and it expect the new project will generate a pre-tax income of 20,000, then for the new project, you should use the marginal tax rate of 25%. Net Effect of Depreciation Depreciation shows up in two places. Depreciation tax shield Note: first deduct depreciation when calculating unlevered net income, then add back depreciation to the taxable net income. The net effect of depreciation on FCF is: 18 Called depreciation tax shield. See notes underneath the slide The larger depreciation, the higher FCF. Depreciation Methods In the example in slide 6, the annual depreciation is Purchase value 90,000 minus salvage value 0, then divide by a 3-year life, so annual depreciation is $30,000. 20 FYI: Accelerated Depreciation Example Which depreciation schedule has more tax savings? See notes underneath the slide Question: 21 Terminal Value Sometimes the firm explicitly forecasts free cash flow over a shorter horizon than the full horizon of the project or investment. This is necessarily true for investments with an indefinite life, such as an expansion of the firm. Terminal Value Example After year 4, Base Hardware expects free cash flow from the stores to increase at a rate of 5% per year. If the appropriate cost of capital for this investment is 10%, what terminal value in year 4 captures the value of future free cash flows in year 5 and beyond? What is the NPV of the new stores? Do you recognize that part of the cash flow streams look like a growing perpetuity? Solution (why? b/c Year N Terminal Value = Year N+1 FCF/(r-g)) Note this terminal value is at Year 4. 24 1. 24 Terminal Value Example The total cash flows at Year 4 have two parts: 25 Year 4 PV of cash flows in short horizon Remember to correctly discount terminal value. Calculating the NPV NPV of a project: See notes underneath the slide Again, in capital budgeting, a convention is that the project starts at year 0, which is today. Considerations in DCF Analysis 27 We will look at these effects because Opportunity Costs Q: Should you include this opportunity cost when calculating free cash flow? Project Externalities 29 Sunk Costs For example, suppose after having spent $10,000 on market research, you believe 100% that your new product will generate a NPV of $100. Allocated Overhead Shut Down Costs Reviews of Capital budgeting Important concepts 34 Important concepts 35 In-class exercise Something to think about before you work on it. 8.2 Determining Free Cash Flow and NPV 245
USING EXCEL
Capital Budgeting Capital budgeting forecasts and analysis are most easily performed in a spreadsheet program. Create a Project Dashboard Color Code for Clarity Maintain Flexibility Never Hardcode 1 Case – Canyon Buff’s Chemical Equipment
This case is a simple capital budgeting exercise that should reinforce your understanding of the • Incremental unlevered net income Before solving this case, you must watch the video “Capital Budgeting in-class exercise solution” Introduction
Canyon Buff Corp. has developed a new construction chemical that greatly improves the durability • The equipment must be purchased before the chemical production can begin. For tax purposes,
• Canyon Buff anticipates that the sales will be $30,000,000 in the first year (Year 1). They
expect that sales will initially grow at an annual rate of 6% until the end of sixth year. After
• The cost of goods sold is estimated to be 72% of sales.
• The accounting department also estimates that at introduction in Year 0, the new product’s
required initial net working capital will be $6,000,000. In future years accounts receivable
• The selling, general and administrative expense is estimated to be $6,000,000 per year, but
$1 million of this amount is the overhead expense that will be incurred even if the project
• The market research to support the product was completed last month at a cost of $500,000
to be paid by the end of next year. • The annual interest expense tied to the project is $1,000,000. 2
• Canyon Buff has a cost of capital of 20% and faces a marginal tax rate of 30% and an
average tax rate is 20%. Instructions I posted an incomplete Excel template for your analysis. You need to figure out how to construct Note that your analysis should be set up so the assumptions that impact the cash flow estimates There are three sheets in the template. Use the worksheet “NPV” for questions 1 to 4, and the other Submit your Excel spreadsheet through the blackboard. Clearly show your work so that I can trace Questions
1. Use Excel to construct six-year pro forma income statements and calculate the incremental • When calculating incremental unlevered net income, should we include all the 2. Calculate six-year projections for free cash flows. Remember to include cash flows from
Hint: You need to calculate the level of net working capital (NWC) and change in NWC. 3. Canyon Buff expects that free cash flow from Year 6 onwards will increase at a constant 3 Hint: For example, if {FCF6, FCF7, FCF8, …} is a growing perpetuity, then Year 5 TV = Year Similarly, if {FCF7, FCF8, FCF9, …} is a growing perpetuity, then Year 6 TV = Year 7 b. We should discount this Terminal Value back to Year 0.
4. Determine the NPV of the project. Remember to net out any initial cash outflows.
5. Perform a sensitivity analysis by varying the four parameters as follows:
Parameter Initial Assumption Worst Case Best Case For example, vary the parameter “Sales in Year 1” from the worst case $27,000 to the best Do the same thing for the other three parameters.
Suppose you are the financial manager, if you are asked to use limited resources to refine 6. Perform a scenario analysis by simultaneously varying the two parameters below: 4
Sales Growth % Cost of Scenario 1 (Baseline) 5% 71% Which scenario generates the highest NPV? Write your answer in Excel.
NPV
Case – NPV Calculation
Assumptions (Amounts in $ Thousands Unless Otherwise Indicated)
Initial Capital Expenditure
Useful Life of Equipment
Annual Depreciation
Sales
Year
1
Sales Growth through Year
6
Question: When calculating incremental unlevered net income, what expenses should we exclude and why?
Sales Growth Year 6 Onward
Answer:
Free Cash Flow
Cost of Goods Sold (% of sales)
Incremental SG&A Expense
Market Research Expense
Initial Net Working Capital
Accounts Receivable
Inventory
Accounts Payable
Interest Expense
Tax Rate
Cost of Capital
Year Year Year Year Year Year Year
Unlevered Income Statements
0
3
4
5
Sales
Unlevered Net Income
Working Capital Calculations
Inventory
Accounts Receivable
Accounts Payable
NWC Level
Change in NWC
CF from Change in NWC
Unlevered Cash Flows
Add Back: Depreciation
CF from Capital Expenditure
Free Cash Flow
Year 5 Terminal Value (FCFs in Year 6 and beyond)
Discount Factor
FCF Present Value
NPV
in which
PV(Year 5 Terminal Value)
Sensitivity Analysis
Copy your baseline projections to this sheet, so that your sensitivity analysis won’t alter your baseline result in the NPV sheet.
Sensitivity Analysis
Parameter
Initial Assumption
Worst Case
Best Case
Sales in Year 1
$30,000
$27,000
$33,000
NPV
Sales Growth through Year 6
6%
0%
10%
Cost of Goods Sold (% of Sales)
72%
77%
67%
Cost of Capital
20%
23%
17%
Question: Suppose you are the financial manager, if you are asked to use limited resources to refine the assumption on ONLY ONE of the above four parameters, which one should you choose and why? (fill in the blanks highlighted in yellow)
Answer:
Scenario Analysis
Copy your baseline projections to this sheet, so that your scenario analysis won’t alter your baseline result in the NPV sheet.
Scenario Analysis
Sales Growth
through Year 6% Cost of Goods Sold
Scenario 1 (Baseline)
5%
71%
Scenario 2
Scenario 3
8%
73%
Scenario 4
9%
74%
Question: Which scenario generates the highest NPV? (fill in the blanks highlighted in yellow)
Answer:
A: Yes, because the firm forgoes $20,000 when choosing to place the production line in the warehouse instead of having it rented out.
The opportunity cost would reduce the firm’s incremental sales annually by the amount of $20,000
e.g. if incremental sales =$5,000, then the firm is better off by having the warehouse rented out.
The opportunity cost would reduce the firm’s incremental cash flows annually by this amount:
$20,000× (1 − Tax Rate)
1
If don’t take the project, just rent out the warehouse
Tend to accept this project, but it is a WRONG decision.
EBIT
0
1
2
3
4
0
20K
20K
20K
20K
EBIT
0
1
2
3
4
-4K
5K
5K
5K
5K
Should include the opportunity cost when evaluating the project
Because the firm forgoes $20,000 when choosing to place the production line in the warehouse instead of having it rented out.
How? deduct the opportunity cost from the incremental sales
EBIT
0
1
2
3
4
-4K
5K−20K
5K −20K
5K −20K
5K −20K
Sunk costs are costs that have been or will be paid regardless of the decision whether or not the investment is undertaken.
Sunk costs should NOT be included in the incremental earnings analysis.
Past Research and Development Expenditures
Money that has already been spent on R&D is a
sunk cost and therefore irrelevant. The decision to continue or abandon a project should be based only on the incremental costs and benefits of the product going forward.
Timeline helps
4
See notes underneath the slide
Note this already spent market research expense is NOT in the calculation of NPV (or PV(costs)) of the project you haven’t undertaken.
Does the market research expense of $10,000 you have already spent affect your decision of the new project?
No. That is a sunk cost.
Should you take the project?
Yes, because the NPV is positive.
What if the NPV of the project is just $1? Again this already spent market research expense is NOT in the calculation of NPV of the project. Should you take the project?
Yes, because the NPV is positive, so PV(benefits) > PV(costs). Note all the costs for this project have been taken out.
4
Yes. Because if you do the project, you can still get a PV of 5K. If you don’t do the project, you will get nothing. Note the timing: you make the decision today, not at Year -1.
10K is a sunk cost. Should exclude sunk cost when making capital budgeting decisions.
5
Cash flow
-1
0 (Today)
1
2
-10K
Break-even, Sensitivity, and Scenario Analysis
Berk, DeMarzo 3rd edition, Chapter 8
Section 8.5
Capital budgeting:
Estimate incremental cash flows in the project.
Determine a cost of capital used for discounting
Calculate NPV
Accept or reject the project
Question: There is significant uncertainty in estimating cash flows. How do we know whether the NPV result is accurate?
2
Methods to assess uncertainty and evaluate project risk:
Sensitivity Analysis
Scenario Analysis
Break-Even Analysis
3
As the finance manager of a company, you are presented with the following project. The company is considering the purchase of a new piece of equipment which would cost $200,000. This equipment will have a five-year useful life and have a salvage value of $0 at the end of the five-year period. It is estimated that
the new equipment will be able to produce 10,000 shelves per year.
the incremental overhead for running the equipment will be $20,000 per year.
they can sell the shelves for $25 each.
the cost of sales is $15 per shelf.
Net Working Capital requirements for the project are as follows:
Year 0 = $10,000
Year 1 = $15,000
Year 2 = $17,000
Year 3 = $15,000
Year 4 = $10,000
The company has a 30% marginal tax rate and a cost of capital of 15%.
4
Would you accept this project (support your answer with NPV)?
4
Sensitivity analysis shows how the NPV varies with a change in one of the assumptions, holding the other assumptions constant.
Example: how does the NPV change when the sale price is $20 per unit? or $30?
Various cash flow assumptions are used.
Best and worst cases are developed and NPVs compared.
5
6
Parameter Initial Assumption Worst Case Best Case
Sale price($/unit) 25 20 30
NPV 21,232 ? ?
Units sold (000s) 10
NPV 21,232
Sales growth 0%
NPV 21,232
Cost of capital 15%
NPV 21,232
What is the NPV when sale price is $20 per unit? $30?
Answer: Just change the price from $25 (cell B3) to $20, then NPV (cell B31) becomes -96,093.
Similarly, when price = $30, then NPV = 138,557
6
7
Parameter Initial Assumption Worst Case Best Case
Sale price($/unit) 25 20 30
NPV 21,232 -96,093 138,557
Units sold (000s) 10 8 12
NPV 21,232 ? ?
Sales growth 0% -5% 5%
NPV 21,232 ? ?
Cost of capital 15% 18% 12%
NPV 21,232 ? ?
Answer: just change the unit (cell C15 in sheet “Baseline”) from 10,000 to 8,000, then the NPV = -25,698.
Similarly, you can find the NPVs for all other cases. Again, in sensitivity analysis, we want to see how the NPV varies with a change in one of the assumptions, holding the other assumptions constant (the other values are based on initial assumptions)
7
8
Parameter Initial Assumption Worst Case Best Case
Sale price($/unit) 25 20 30
NPV 21,232 -96,093 138,557
Units sold (000s) 10 8 12
NPV 21,232 -25,698 68,162
Sales growth 0% -5% 5%
NPV 21,232 1,934 42,405
Cost of capital 15% 18% 12%
NPV 21,232 5,141 39,342
8
9
Units Sold
Sales Growth
$20
$25
$30
8K
12K
10K
-5%
0%
5%
18%
15%
12%
The most important parameter assumptions are ?
Blue bars indicate the NPV under the worst-case assumptions.
Orange bars represent the baseline assumptions.
The most important parameter assumptions are on the sale price per unit and the number of units sold, because NPVs change dramatically in different cases and NPVs dropped significantly in the worst case (e.g. NPV=-96,093 when sale price =$20 in worst-case).
These assumptions deserve the greatest scrutiny during the estimation process. In addition, as the most important drivers of the project’s value, these factors deserve close attention when managing the project.
In contrast, when sales growth and the cost of capital change, NPVs do not change that much and stay positive. These two factors are not as important as the sale price and units sold.
Worst Case 5141.2707123555665 1934.0843084341795 -25698.172083122317 -96093.42914136179 Baseline 21231.999289037303 21231.999289037303 21231.999289037303 21231.999289037303 Best Case 39341.527734909505 42404.89203263411 68162.170661196957 138557.42771943641 Project NPV
Benefit: identifies critical assumptions.
In this example, pay special attention to the assumptions on the sale price per unit and the number of units sold.
We can invest further resources to refine these assumptions.
e.g., market research to analyze market size, customer demand, and competitors.
Process – Test particular combinations of assumptions to see the result on NPV.
Example – A major competitor may react differently to your project and your assumptions change with their reactions.
11
Strategy Sale Price
($/unit) Expected Units Sold(thousands) NPV
($thousands)
Current strategy 25 10 21,232
Price reduction 23 12 ?
Price increase 27 9 ?
11
Benefit: scenario analysis is appropriate when assumptions are interrelated.
12
Strategy Sale Price
($/unit) Expected Units Sold(thousands) NPV
($thousands)
Current strategy 25 10 21,232
Price reduction 23 12 11,846
Price increase 27 9 40,004
Analysis of the level of sales (or other parameters) at which the company “breaks even”.
Two types of Break-Even:
Accounting Break-Even focuses on the level of a parameter for which a project’s EBIT=0 (sales cover costs; unlevered net income is zero).
Economic Break-Even focuses on the value of a parameter for which NPV is zero.
13
Projects have Revenues, Variable Costs, Fixed Costs, and Depreciation.
Variable costs: costs that vary with the level of production.
Fixed costs: costs that do not vary with the level of production.
Accounting Break-Even measures the level of a parameter for which EBIT=0
(Revenues – Variable Costs – Fixed Costs – Depreciation= 0)
Example:
The Accounting Break-Even level of quantity sold indicates how many units you need to sell to satisfy EBIT=0
14
Fixed costs can be thought of as Selling, General, and Administrative expenses (SG&A).
14
Example
Assumptions for a project with a 3-year life:
Revenue $100 per unit for a Printer
Variable Costs $70 per unit → Gross Profit $30 per unit
Fixed Costs $300,000
$900,000 Investment with a salvage value of 0, annual depreciation of $300,000 for three years
Taxes 35%
Question: how many units you need to sell such that EBIT=0? (EBIT = Revenues – Variable Costs – Fixed Costs – Depreciation)
15
15
Revenues ($100/unit)
Variable Costs ($70/unit)
Actual Gross Profit
Gross Profit Required ? ($30/unit)
Fixed Costs – 300,000
Depreciation – 300,000
EBIT 0
16
← accounting break-even asks EBIT = 0
Question: how many units you need to sell such that EBIT=0?
16
Revenues ($100/unit)
Variable Costs ($70/unit)
Actual Gross Profit
Gross Profit Required 600,000 ($30/unit)
Fixed Costs – 300,000
Depreciation – 300,000
EBIT 0
17
Gross profit = Fixed Costs + Depreciation = 300,000+300,000 = 600,000
← accounting break-even asks EBIT = 0
So how to find the total amount of gross profit?
Step 1.
accounting break-even means EBIT = 0, i.e.,
Revenues – Variable Costs – Fixed Costs – Depreciation= 0
where gross profit = Revenues – Variable Costs
Gross profit – Fixed Costs – Depreciation= 0
Step 2.
Gross profit = Fixed Costs + Depreciation = 300,000+300,000 = 600,000
Step 3.
the number of units to be sold to satisfy accounting break-even EBIT=0 is
Quantity (accounting break-even) = 600,000/ 30 = 20,000.
17
Accounting break-even for quantity
total Gross Profit /Gross Profit per Unit
$600,000/$30 = 20,000 units
Accounting break-even generates no tax liability.
What is the project’s NPV under accounting break-even?
This accounting break-even level of 20,000 units will be used in a few slides.
18
Investors will not be happy if the company simply returns their original investment over time.
Accounting break-even always results in a NEGATIVE NPV.
Year 0 1 2 3
Unlevered Net Income 0 0 0
Add Back Depreciation 300,000 300,000 300,000
Subtract Change in NWC
Subtract Capital Expenditure -900,000
Free Cash Flow -900,000 300,000 300,000 300,000
Because of time value of money, investors will not be happy if the company simply returns their original investment over time.
that is, not happy with the cash flow stream -900,000, 300,000, 300,000, 300,000
For simplicity, we ignore the cash impact of change in NWC. You can show that NPV is still negative when we consider the cash flow impact of NWC (you can calculate the present value of cash flow impact of NWC by discounting row 38 in the sheet “Baseline” of the Excel file “In-class exercise – DCF analysis”, which will give you a negative number).
Note if netting across row 38 from Year 0 to Year 5, we always get zero.
19
Economic Break-Even focuses on the level of a parameter for which NPV is zero.
Example:
Revenue $100 per unit for a Printer
Variable Costs $70 per unit. Gross Profit $30 per unit
Fixed Costs $300,000
Initial Investment $900,000, salvage value $0, useful life 3 years
Taxes 35%
Cost of capital= 10%
No cash flow effect of change in NWC (for simplicity)
Question: what is the economic break-even level of quantity sold? In other words, how many units a project need to sell such that NPV=0?
Year 0 1 2 3
Unlevered Net Income ? ? ?
Add Back Depreciation 300,000 300,000 300,000
Subtract Change in NWC
Subtract Capital Expenditure -900,000
Free Cash Flow -900,000 C C C
PV(FCFs from Year 1 to 3) = 900,000
The FCF stream from Year 1 to 3 is a 3-year annuity with payment C. PV(FCFs from Year 1 to 3)= =
, so
In this example, we assume unlevered net incomes remain unchanged from Year 1 to 3. Since there are no other cash flow adjustments (e.g. no cash impact of change in NWC for simplicity), we have the same FCFs from Year 1 to 3.
Year 0 1 2 3
Unlevered Net Income ? ? ?
Add Back Depreciation 300,000 300,000 300,000
Subtract Change in NWC
Subtract Capital Expenditure -900,000
Free Cash Flow -900,000 361,903 361,903 361,903
PV(FCFs from Year 1 to 3) = 900,000
The FCF stream from Year 1 to 3 is a 3-year annuity with payment C. PV(FCFs from Year 1 to 3)= =
, so
Revenues ($100/unit)
Variable Costs ($70/unit)
Gross Profit Required ? ($30/unit)
Fixed Costs – 300,000
Depreciation – 300,000
EBIT ?
Tax @ 35%
Unlevered net income ?
add back Depreciation +300,000
Free cash flow $
23
Fill in the blanks (Hint below: Work backwards from free cash flow to the total gross profit)
total gross profit/gross profit per unit
Again, in this example, for simplicity, we ignore the cash impact of change in NWC.
23
Revenues ($100/unit)
Variable Costs ($70/unit)
Gross Profit Required 695,235 ($30/unit)
Fixed Costs – 300,000
Depreciation – 300,000
EBIT 95,235 = 61,903/(1-0.35)
Tax @ 35%
Unlevered net income 61,903
add back Depreciation +300,000
Free cash flow $
24
Fill in the blanks (see details below: Work backwards from free cash flow to the total gross profit)
Unlevered net income = FCF – Depreciation = – 300,000 = 61,903
EBIT= Unlevered net income / (1-tax rate) = 61,903/0.65 = 95,235
Gross profit = Pretax profit + Depreciation + Fixed Costs = 95,235 + 300,000 +300,000 = 695,235
Method 2: Work from the top to the bottom.
(Gross profit – Fixed Costs – Depreciation) * (1-tax) + Depreciation = FCF
that is :
(Gross Profit – 300,000 – 300,000) * (1-0.35) + 300,000 =361,903
so Gross profit = (361,903-300,000)/(1-0.35) + 300,000 + 300,000 = 95,235
24
The economic break-even level of quantity:
Gross profit / Gross profit per unit = 695,235/30 = 23,174.5
Result: the economic break-even level of sales quantity is 23,175.
Quantity (Economic break-even) =23,175
Quantity (Accounting break-even) =20,000 (see slide 18)
Economic break-even > Accounting break-even
Does this relation make sense? (see notes underneath this slide)
Of course, when we sell more than the economic break-even level of quantity, the NPV will become positive.
25
Quantity (Economic break-even) =23,175
Quantity (Accounting break-even) =20,000 (see slide 18)
Test: positive, negative, or zero?
When quantity=19,000, unlevered net income is ___, NPV is ___
When quantity=20,000, unlevered net income is ___, NPV is ___
When quantity=22,000, unlevered net income is ___, NPV is ___
When quantity=23,175, unlevered net income is ___, NPV is ___
When quantity=24,000, unlevered net income is ___, NPV is ___
See solutions underneath this slide.
When quantity=19,000, unlevered net income is NEGATIVE, NPV is NEGATIVE
When quantity=20,000, unlevered net income is ZERO, NPV is NEGATIVE
When quantity=22,000, unlevered net income is POSITIVE, NPV is NEGATIVE
When quantity=23,175, unlevered net income is POSITIVE, NPV is ZERO
When quantity=24,000, unlevered net income is POSITIVE, NPV is POSITIVE
26
Economic break-even level for other parameters:
Price per unit (see the example underneath the slide)
Cost of capital.
At the break-even level of cost of capital, the project’s NPV=0 (that is, the break-even level of cost of capital is the discount rate that sets the NPV equal to zero, which is also called the internal rate of return (IRR)).
= IRR(-900,000, 361,903, 361,903, 361,903) = 10%
Year 0 1 2 3
Free Cash Flow -900,000 361,903 361,903 361,903
27
In capital budgeting, to assess uncertainty and evaluate project risk:
Sensitivity Analysis
identifies critical assumptions.
Scenario Analysis
tests interrelated assumption.
Break-Even Analysis
accounting vs. economic break-even
calculate economic break-even level of quantity, price per unit, cost of capital
28
Berk, DeMarzo 3rd edition, Chapter 8
Section 8.
Capital Budgeting
To evaluate projects, use Discounted Cash Flow (DCF) Analysis
Considerations in DCF Analysis
Opportunity Costs, Sunk Costs, Cannibalization …
Examples
2
3
SpaceX
Landing
See notes underneath the slide
3
Capital Budget
Lists the projects and investments that a company plans to undertake
Capital Budgeting
Process used to analyze alternative investments and decide which ones to accept
Goal: decide to accept or reject a project based on its cash flow and NPV.
4
Steps:
Estimate incremental cash flows in the project
The amount by which a firm’s cash flows are expected to change as a result of the investment decision.
Determine a cost of capital used for discounting
Calculate NPV
Accept or reject the project
This process is also called as Discounted Cash Flow analysis (DCF)
5
See notes underneath the slide
Example of “Incremental”:
Suppose your firm is considering replacing outdated equipment with a new piece of equipment which is more efficient. The sales in the past year is $10,000, and you expect the new equipment will generate sales of $15,000 each year, then the incremental sales in each year is $5,000.
Note $5,000 is the incremental sales, not incremental cash flows, because there might be other costs, such as depreciation, and tax benefit of depreciation deduction.
Of course, you also have a cash outflow (purchasing equipment) at the beginning.
2.
For now, we assume that the cost of capital is given, and we focus on the rest steps, especially the first step (most challenging part), estimating the incremental cash flows.
5
6
Suppose you have an investment opportunity (e.g. purchase equipment), where you need to spend $90,000 (e.g. on equipment) at Year 0 (NOW). The salvage value (see below for definition) at the end of the asset is $0. For simplicity, we assume the project life is the same as the life of asset (3 years). Based on the forecast of sales and costs, change in net working capital, tax rate, and opportunity cost of capital (for discounting), should we accept this project?
I want you to think about two things when evaluating a project.
The components of cash flows (i.e., what contribute(s) to the cash flows?)
2. How does each factor affect the cash flow and your valuation?
For example
The more sales you have, all else equal, you should have more cash flows.
The higher tax rate, the less cash flows you will receive.
How does change in net working capital affect cash flows.
Definition:
Salvage value is the estimated value of property at the end of its useful life. It is what you expect to get for the property if you sell it after you can no longer use it productively.
The opportunity cost of capital (see lecture 3) is the best available expected return offered in the market on an investment of comparable risk and term. It provides the benchmark against which the cash flows of a new investment should be evaluated.
6
Typical Project Cash Flows
cash flow from change in net working capital
See notes underneath the slide
Start-up stage
purchasing equipment will reduce the cash available to a firm (this is cash flow from investment)
increases in net working capital (e.g. increase in inventory, account receivable, or decrease in account payable) will reduce the cash available to a firm (cash flow from change in net working capital, ∆NWC)
e.g. you buy beans before you open a coffee shop, inventory increases, net working capital increases, and this increase in NWC reduces the cash available to a firm.
note that decrease in accounts payable (everything else equal) will increase the net working capital (NWC) because NWC= inventory + accounts receivable – accounts payable
On-going
You have sales, costs, and net income, which will affect cash flows (cash flows from net income and depreciation)
recall we need to convert net income to operating cash flows
Change in NWC (again not the level) also affects the cash flows (cash flow from change in net working capital, ∆NWC)
Shut-down
Note the decrease in NWC will release the cash tied to NWC and increase the cash available to a firm (cash flow from change in net working capital, ∆NWC)
e.g. when you close a coffee shop, you want to sell you beans (i.e. decrease in NWC), which increases the cash available to you.
And you also want to collect any account receivable (i.e. decrease in NWC), which also increases the cash available to you.
Ultimately, the cash flows are affected by the following three parts:
cash flows from net income and depreciation
cash flows from change in net working capital, ∆NWC
cash flows from investment
7
Follow the Cash!!
Discount cash flows, not profits!!!!!!!
Most analysis will start with an accounting projection (forecast sales, costs, depreciation, and net income)
Net income must be converted to cash flows for NPV analysis
Recognize all cash flow effects
Cash flows from net income with depreciation added back
Cash flows from change in net working capital (∆NWC)
Cash flows from investment
See notes underneath the slide
We include the cash flows from I and II when we convert net income to operating cash flows in the last lecture. The incremental effect of a project on a firm’s available cash also includes the cash flows from investment.
Operating cash flow is a measure of the amount of cash generated by a company’s normal business operations.
8
Simplify:
Net Income
+ depreciation
– change in accounts receivable (change: current – previous)
– change in Inventory
+ change in accounts payable
Operating cash flow (Cash Flow from Operations)
Get:
Net Income
+ depreciation
– change in Net Working Capital (NWC= AR + Inventory – AP)
Operating cash flow
9
last lecture
See notes underneath the slide
– change in accounts receivable
– change in Inventory
+ change in accounts payable
=
– change in (accounts receivable + Inventory – accounts payable)
=
– change in Net Working Capital (NWC= AR + Inventory – AP)
Note:
change in NWC matters, NOT the level of NWC
The cash effect of ∆NWC is NEGATIVE ∆NWC.
any increases in net working capital represent an investment that reduces the cash that is available to the firm.
e.g. when ∆NWC = $100, the cash effect of ∆NWC is NEGATIVE $100. To help understand or remember this, you can think that $100 of ∆NWC is just an increase in inventory (e.g., buy extra beans for your coffee shop, holding all other components of NWC constant), which reduces the cash available to you, so the cash effect is NEGATIVE $100
e.g. when ∆NWC = NEGATIVE $100, the cash effect of ∆NWC is POSITIVE $100. To help understand or remember this, you can think that negative $100 of ∆NWC is just an decrease in inventory or accounts receivable, which increases the cash available to you, so the cash effect is POSITIVE $100
———————————————————————————————–
(p242 of Berk DeMarzo 3rd edition)
The text also includes cash in NWC calculation.
But be cautious that the cash is the cash tied to operation (e.g. cash held in cash registers for retail stores, similar to cash tied to inventory), such tied cash should be included in NWC calculation.
Note that for valuation purpose, NWC should EXCLUDE the cash that is invested to earn a market rate of return, because ultimately we will discount the incremental cash flows generated the project by an opportunity cost of capital that reflects the risk of the project, but cash, especially in large amounts, is invested by firms in treasury bills, short term government securities or commercial paper (e.g., at the end of 2008Q3, Apple has $243.7 billion cash, such cash (at least most cash) is unlikely to be tied to operations, but is rather invested to earn a market rate of return). They represent a fair return for riskless investments, so we should exclude such cash in NWC calculation.
———————————————————————————————–
Discounted Cash Flow Issues for
NPV Analysis
Only incremental cash flow matters.
Separate Investment and Financing Decisions.
When evaluating a capital budgeting decision, we generally do not include interest expenses.
Evaluate a project as if it will not use any debt to finance it (so unlevered). The corresponding net income is called unlevered net income.
Unlevered net income = EBIT * (1 – tax rate)
= (Revenues – Costs – Depreciation) * (1 – tax rate)
NO interest expense here
See notes underneath the slide
As a result, in unlevered net income calculation, there is NO interest expense.
Free cash flow
Free cash flow (FCF): the incremental effect of a project on the firm’s available cash
FCF is the cash flow “free” to be distributed to investors
Unlevered net income
+ depreciation
– change in Net Working Capital
= Operating cash flow
– Cash flow from investment (Capital expenditure or CapEx)
= Free cash flow
Discount FCFs to get the NPV of a project.
See notes underneath the slide
11
12
Year 0 1 2 3
Unlevered Net Income
Add Back Depreciation
Subtract Change in NWC
Subtract Capital Expenditure
Free Cash Flow
In capital budgeting, a project starts at year 0, which is today.
If the project is to purchase a new piece of equipment, then the cash flow occurs at date 0, and the depreciation starts from Year 1 to the end of its useful life (to match the sales)
The sales generated by the equipment will start from Year 1, NOT Year 0.
The firm needs to put in net working capital (e.g. buy beans for coffee shop) at Year 0 before it can sell its products in Year 1, so the level of net working capital at Year 0 is positive, so is the change in NWC at Year 0.
See the solution to the in-class exercise (in the last slide) on blackboard.
Pay special attention to the signs of change in NWC.
12
Recall the first step in evaluating a project is to forecast the incremental revenue and cost generated by the project.
In this step, we can get unlevered net income = (Revenues – Costs – Depreciation) * (1 – tax rate)
Again, it is important to identify revenues and costs that are generated only because of the project.
So only incremental revenues and incremental costs.
13
Pro-Forma Statement: financials under a set of hypothetical assumptions
Sales
– Cost of Goods Sold
Gross Profit
– Selling, General, and Administrative expenses
EBITDA
– Depreciation
EBIT
– Tax
Unlevered Net income (excluding Interest)
14
See notes underneath the slide
We make assumptions on the sales, costs, depreciation and etc, and based on these assumptions, we can calculate unlevered net income.
Note all revenues and costs are incremental.
14
Interest Expense
Not included in capital budgeting because we separate investment and financing decisions.
Which tax rate to use?
Corporate Taxes – Paid by the corporation out of profits before shareholders are paid.
System is progressive – Tax rate generally increases with income.
Marginal Tax Rate – Tax Rate on next dollar of income.
Average Tax Rate – Taxes paid/Pretax income
In capital budgeting, use Marginal Tax Rate because it captures the incremental effect of the project.
See notes underneath the slide
15
16
See notes underneath the slide
But if the firm’s current taxable income falls into the bracket of $50,001-75,000, say $75,000, and it expect the new project will generate the same pre-tax income of 20,000, then for the new project, you should use the marginal tax rate of 34%.
Bottom line: use marginal tax rate for capital budgeting.
16
Unlevered net income
+ depreciation
– change in Net Working Capital
= Operating cash flow
– Cash flow from investment (Capital expenditure or CapEx)
= Free cash flow
Question:
Where does deprecation show up in FCF estimation?
What is the net effect of depreciation on FCF?
17
See notes underneath the slide
when calculating unlevered net income, we deduct depreciation from sales.
when we add back depreciation to net income.
However, the net effect of depreciation is NOT zero, because of tax (see next slide).
17
Simplify FCF:
Positive effect on FCF
Why do we care about the net effect of depreciation on FCF, because financial managers care, why? You will see why it matters in few slides.
18
Straight-line depreciation
Annual depreciation =
depreciation = ___ in slide 6?
Accelerated depreciation method (e.g. MACRS, modified accelerated cost recovery system)
Depreciate more in earlier years
How does that affect free cash flows and NPV?
19
See notes underneath the slide
Accelerated depreciation
In practice the tax code allows a firm to “accelerate” the depreciation on the theory that an asset loses more value in the early years.
19
This table shows the schedule of MACRS (an accelerated depreciation)
FYI: MACRS only allows a half year of depreciation the year an asset is put in service (half-year convention)
Bottom line: in an accelerated depreciation schedule, assets depreciate more rapidly in early years.
See notes underneath the slide
—————————————————————————————————————
In the table of MACRS depreciation, you can find that for 3-year recovery, the depreciation is allowed in the first 4 years, not 3 years, because of the “half-year convention”.
Half-year convention. The half-year convention is used to calculate depreciation for tax purposes, and states that a fixed asset is assumed to have been in service for one-half of its first year, irrespective of the actual purchase date.
The lower amount in year 1 reflects a “half-year convention” in which the asset is presumed to be in use (and this depreciated) for half of the first year, no matter when it was
actually put into use. After year 1, it is assumed that the asset depreciates more rapidly in earlier years.
—————————————————————————————————————
20
Assume tax rate =30%, discount rate = 15%.
21
Year Accelerated Depreciation
3 Year Annual Depr. Tax Savings Straight
Line
3 Year Tax Savings
1 50% $30,000 $9,000 $20,000 $6,000
2 30% $18,000 $5,400 $20,000 $6,000
3 20% $12,000 $3,600 $20,000 $6,000
PV of Tax Savings @ 15 % ? PV of Tax Savings @ 15 % ?
Suppose the new equipment costs $60,000. There are two depreciation schedules, straight-line depreciation and accelerated depreciation schedules, which one has more tax savings? Assume tax rate is 30% and discount rate is 15%.
Note this accelerated depreciation schedule is hypothetical, just showing that the asset depreciates more rapidly in early years. It is NOT the schedule in MACRS (MACRS is allowed by IRS).
Answer:
First, note that the net effect of depreciation on FCF is tax rate*depreciation (depreciation tax shield), so POSTIVE effect on cash flows.
For both schedules, we will have tax savings for three years. To compare the tax savings, we discount tax savings to Year 0 (today).
Calculation:
For accelerated depreciation.
1.1 Calculate annual depreciation for each year,
60,000 * 50% =$30,000 for Year 1
60,000 * 30% =$18,000 for Year 2
60,000 * 20% =$12,000 for Year 3
1.2 Calculate the tax savings, tax rate (30%)*depreciation
e.g. for year 1, tax savings = $30,000 * 30% = 9000
1.3 Discount the 3-year tax savings to present, so
PV = 9000/1.15 + 5400/1.15^2 +3600/1.15^3 = $14,276
2. Similarly, you can get the PV of tax savings for straight-line depreciation, which is $13,699.
Bottom line: the accelerated depreciation has more tax savings. Because depreciation contributes positively to the firm’s cash flow through the depreciation tax shield, it is in the firm’s best interest to use the accelerated depreciation.
Intuition: in an extreme case, in the next three years, would you prefer to receive the cash flows 6, 0, 0 or 0, 0, 6?
Idea: Sometimes firms explicitly forecast free cash flow over a shorter horizon than the full horizon of a project, then calculate an additional, one-time cash flow at the end of the forecast horizon.
This one-time cash flow is called terminal value. It represents the market value of the free cash flow from the project at all future dates.
PV(all cash flows) = PV(cash flows in the short horizon) + PV(Terminal value)
Caution: remember to discount terminal value.
22
See notes underneath the slide
In this case, we estimate the value of the remaining free cash flow beyond the forecast horizon by including an additional, one-time cash flow at the end of the forecast horizon called the terminal or continuation value of the project.
22
Problem (from textbook page 251)
Base Hardware is considering opening a set of new retail stores. The free cash flow projections for the new stores are shown below (in millions of dollars):
23
See notes underneath the slide
23
Because the future free cash flow beyond year 4 is expected to grow at 5% per year, the terminal value in year 4 of the free cash flows in year 5 and beyond can be calculated as a constant growth perpetuity:
See notes underneath the slide
The free cash flows from year 5 and beyond are 1.3*1.05, 1.3*1.05^2, 1.3*1.05^3, …
Review the slides 32-34 of lecture note 2, if you forgot how to calculate growing perpetuity.
Note that to use the growing perpetuity formula C/(r-g), where the first payment is C. Here in this growing perpetuity 1.3*1.05, 1.3*1.05^2, 1.3*1.05^3, …, the first payment is Year 5 FCF, which is equal to 1.3*1.05. The value of C/(r-g) with C=1.3*1.05 is the value of the cash flow streams at Year 4.
2.
The free cash flows from year 4 and beyond are 1.3, 1.3*1.05, 1.3*1.05^2, 1.3*1.05^3, …
You can also treat this cash flow streams as a growing perpetuity, C/(r-g), where C=1.3. But note this value of C/(r-g) with C=1.3 is the value of the cash flow streams at Year 3.
We can restate the free cash flows of the investment as follows (in thousands of dollars):
Year 4 FCF = 1,300.
FCFs from Year 5 to infinity whose value at Year 4 is 27,300.
Year 0 1 2 3 4
Free cash Flow (years0−4) (10,500) (5,500) 800 1,200 1,300
Continuation value (Year 5 and beyond) Blank Blank Blank Blank 27,300
Free cash flow (10,500) (5,500) 800 1,200 28,600
=$5,597
PV(FCF at Year 4) + PV(Terminal Value)
25
26
Present value of the FCF in year t:
Sum up PV(FCFt), including PV(FCF0)
e.g. NPV =
As a result, the initial capital expenditure is in FCF0.
26
Opportunity Costs
Project Externalities
Sunk Costs
Allocated Overhead
Shut Down Costs
See notes underneath the slide
Some affects incremental revenues and should be included for decision making.
some affects incremental costs and should also be included for decision making.
some should be excluded from decision making.
27
The opportunity cost of using a resource is the value it could have provided in its best alternative use.
e.g. suppose a firm bought a production line which will be placed in a warehouse that the company could have otherwise rented out for $20,000 per year.
Should you include this opportunity cost when calculating free cash flow? – see notes below
Calculation: deduct the opportunity cost from the incremental sales.
28
See notes underneath the slide
A: Yes, because the firm forgoes $20,000 when choosing to place the production in the warehouse instead of having it rented out.
The opportunity cost would reduce the firm’s incremental sales annually by the amount of $20,000
The opportunity cost would reduce the firm’s incremental cash flows annually by this amount:
$20,000× (1 − Tax Rate)
28
Indirect effects of the project that may affect the profits of other business activities of the firm.
Cannibalization is when sales of a new product displaces sales of an existing product.
Release of iphone 11 reduces sales of older versions.
Cross-selling is when a new project generates additional demand for existing or other projects.
A new powerful camera may increase sales of existing lenses.
29
Sunk costs are costs that have been or will be paid regardless of the decision whether or not the investment is undertaken.
Sunk costs should not be included in the incremental earnings analysis.
Past Research and Development Expenditures
Money that has already been spent on R&D is a
sunk cost and therefore irrelevant. The decision to continue or abandon a project should be based only on the incremental costs and benefits of the product going forward.
30
See notes underneath the slide
Note this already spent market research expense is NOT in the calculation of NPV of the project you haven’t undertaken.
Does the market research expense of $10,000 you have already spent affect your decision of the new project?
No. That is a sunk cost.
Should you take the project?
Yes, because the NPV is positive.
What if the NPV of the project is just $1? Again this already spent market research expense is NOT in the calculation of NPV of the project. Should you take the project?
Yes, because the NPV is positive, so PV(benefits) > PV(costs). Note all the costs for this project have been taken out.
30
Typically overhead costs are fixed and not incremental to the project and should not be included in the calculation of incremental earnings.
Firms allocate overhead to projects and business units yet, when making decisions about allocating resources to new projects, only new overhead costs that will be actually incurred due to the project should be included.
31
There are likely to be costs or benefits occurring incrementally at the end of a project that need to be identified and included.
Costs – employee relocation, severance costs …
Benefits – sale of equipment, intellectual property …
32
Steps:
Estimate incremental cash flows in the project.
Determine a cost of capital used for discounting
Calculate NPV
Accept or reject the project
Key: Recognize all cash flow effects (most challenging)
33
capital budgeting
DCF analysis
incremental revenues
change in NWC
unlevered net income
Free Cash Flow (FCF)
marginal tax
depreciation tax shield
accelerated depreciation v.s. straight-line depreciation
terminal value
34
Opportunity Costs
Project Externalities (e.g., Cannibalization)
Sunk Costs
Allocated Overhead
Shut Down Costs
35
As the finance manager of a company, you are presented with the following project. The company is considering the purchase of a new piece of equipment which would cost $210,000. This equipment will have a five-year useful life and have a salvage value of $10,000 at the end of the five-year period. It is estimated that
the new equipment will be able to produce 10,000 shelves per year.
the allocated overhead for running the equipment will be $20,000 per year.
they can sell the shelves for $25 each.
the cost of sales is $15 per shelf.
Net Working Capital requirements for the project are as follows:
Year 0 = $10,000
Year 1 = $15,000
Year 2 = $17,000
Year 3 = $15,000
Year 4 = $10,000
The company has a 30% marginal tax rate and a required rate of return of 15%.
36
Would you accept this project (support your answer with NPV)?
See notes underneath the slide
What contribute(s) to the free cash flows?
What is the annual depreciation?
What is the net working capital at Year 5? (Hint: when you close a coffee shop, you sell all the beans, collect all the receivable, and of course your suppliers will collect their receivable)
Solution is on Blackboard.
Cash flow from equipment sale
Assuming the equipment will be sold at 10,000 at the end of year 5, the cash inflow = 10,000 (sale price) – 0 (tax) = 10,000. The tax is zero because tax is based on the gain on sale, which by definition is sale price minus book value = 10,000 – 10,000 = 0.
36
1
()
(1)(1)
t
tt
tt
tyear discount factor
FCF
PVFCFFCF
rr
=
==´
++
123
Using a Spreadsheet
Program
Here we highlight a few best practices when developing your own capital budgets.
All capital budgeting analyses begin with a set of assumptions regarding future revenues and
costs associated with the investment. Centralize these assumptions within your spreadsheet in
a project dashboard so they are easy to locate, review, and potentially modify. Here we show an
example for the HomeNet project.
In spreadsheet models, use a blue font color to distinguish numerical assumptions from formulas.
For example, HomeNet’s revenue and cost estimates are set to a numerical value in year 1,
whereas estimates in later years are set to equal to the year 1 estimates. It is therefore clear which
cells contain the main assumptions, should we wish to change them at a later date.
In the HomeNet dashboard, note that we state all assumptions on an annual basis even if we
expect them to remain constant. For example, we specify HomeNet’s unit volume and average
sale price for each year. We can then calculate HomeNet revenues each year based on the
corresponding annual assumptions. Doing so provides flexibility if we later determine that
HomeNet’s adoption rate might vary over time or if we expect prices to follow a trend, as in
Example 8.3.
So that your assumptions are clear and easy to modify, reference any numerical values you need
to develop your projections in the project dashboard. Never “hardcode,” or enter numerical val-
ues directly into formulas. For example, in the computation of taxes in cell E34 below, we use the
formula “ = – E21*E33< rather than “ = - 0.40*E33<. While the latter formula would compute
the same answer, because the tax rate is hardcoded it would be difficult to update the model if
the forecast for the tax rate were to change.
following topics:
• Free cash flow
• Sensitivity analysis and scenario analysis
in the Lecture 6 folder, which provides the basis for this case. You need to finish both lectures 6
and 7 to be able to complete the case study.
and weatherability of cement-based materials. After spending $500,000 on the research of the
potential market for the new chemical, Canyon Buff is considering a project that requires an initial
investment of $9,000,000 in manufacturing equipment.
the equipment is subject to a 5-year straight-line depreciation schedule, with a projected zero
salvage value. For simplicity, however, we will continue to assume that the asset can actually
be used out into the indefinite future (i.e., the actual useful life is effectively infinite).
that, the sales will grow at the estimated 2% annual rate of inflation in perpetuity.
are expected to be 15% of the next year sales, inventory is expected to be 20% of the next
year’s cost of goods sold and accounts payable are expected to be 15% of the next year’s
cost of goods sold.
is not accepted.
the pro forma income statements and calculate the incremental unlevered net income. You should
include ONLY the factors that will affect your capital budgeting decision. Revise the template
if necessary.
can be easily changed to identify the sensitivity of your calculations to these assumptions. Never
hardcode in excel (see the pdf “Using Excel in Capital Budgeting” on blackboard).
two sheets for questions 5 and 6.
your numbers.
unlevered net income for the first six years.
expenses mentioned in the case? If not, what expenses should we exclude and why?
Clearly and concisely state your reasons in the cell E9 of the excel template. If you
just forecast the unlevered net income but don’t given any explanations on why you
exclude certain expenses, a penalty of 30 points will deducted from your grade for
the case study.
the income statement and depreciation, changes in net working capital, and capital
expenditures or dispositions.
Pay attention to the timing of NWC.
rate of 2%/year into the indefinite future. Calculate PV(terminal value that captures the
value of future free cash flows in Year 6 and beyond). That is, calculate the terminal value
first, then find its value in Year 0 (today).
We went over this in Lecture Note 6, so let me briefly review the key points:
a. Assuming the cash flows grow at a constant rate g after Year N+1, then
Year N TV = (Year N+1 CF)/(r−g) (from growing perpetuity formula).
where r is discount rate
6 FCF/(r-g).
FCF/(r-g).
Sales in Year 1 $30,000 $27,000 $33,000
NPV
Sales Growth through Year 6 6% 0% 10%
NPV
Cost of Goods Sold (% of Sales) 72% 77% 67%
NPV
Cost of Capital 20% 23% 17%
NPV
case $33,000, holding all the other parameters fixed (at the level of initial assumptions).
Then fill in the highlighted blank boxes for NPV in Excel (the sheet “Sensitivity Analysis”)
the assumption on ONLY ONE of the above four parameters, which one should you choose
and why? Clearly state the reason. Write your answer in Excel.
through Year 6
Goods Sold NPV
Scenario 2 6% 72%
Scenario 3 8% 73%
Scenario 4 9% 74%