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3.CapitalbudgetingI.pptx3. Capital budgeting I: NPV of investment projects
Chapter 2, 9
Capital budgeting: Making investment decisions
Firms face investment opportunities – which to pick?
Solution: compare values
Goal of this lecture: estimating and
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Outline
Accounting basics
Financial statements vs. capital budgeting
From revenue (top) to cash flows (bottom)
Step 1: earnings
Step 2: free cash flows (FCF)
Step 3: NPV
Step 4: sensitivity analysis
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Financial statements
Reports of realized financial performance
Requirement of disclosure by Security Exchange Commission (SEC) on publicly listed firms
Annual report (10-K)
Quarterly report (10-Q)
Edgar – SEC.gov: https://www.sec.gov/edgar/searchedgar/companysearch.html
Three types of reports
Balance sheet: snapshot of firm assets, liabilities, and stockholders’ equity
Income statement: calculation of net income adjusted by expenses and tax
Statement of cash flows: how much cash firm has earned and allocated
Book value vs. market value
Self-estimated vs. market estimated
Periodic (information in the report period) vs. timely updated (new information)
Balance sheet
Assets = liabilities + stockholders’ equity
Assets
Current assets
Investments
Fixed assets
Intangible assets
Other assets
The balance sheet reports the structure of firm’s
assets and debts at the end of fiscal period
Income statement
Estimated total over the reported period
Sale - Cost of good sold = Gross profit
Gross profit - Operating expenses = Operating income
Operating income – Taxes = Net income (or earnings)
Earnings per share (EPS)
EPS = Net income / Shares outstanding
Often used to value firm’s profitability for equity holders
The income statement reports firm’s operations
performance over the past fiscal quarter
Statement of cash flows
Cash flow from three types of activities
Operating
Investing
Financing
Reports change in cash (including cash equivalents) over the
past period, and the resulting cash level
Capital budgeting vs. financial report
What is different between capital budgeting and creating financial reports?
Capital budgeting forecasts project cash flows in the future
Financial reports document firm performance in the past
Capital budgeting and leverage
Here we consider projects fully financed by equity (“unlevered”)
No interest pmt
Leverage does not change nature of business, only amplify risk
Consider debt financing in future
Business example: coffee shop
If you want to open a new coffee shop in our Hub. What types of money flows will you likely experience…
Before its opening?
During its opening?
When shut down or transferred?
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The Capital Budgeting Process
t = 0
t = T
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The Capital Budgeting Process for A Firm
Start with everything we can forecast
Incremental earnings
Free cash flow
NPV
Things are slightly different in the beginning (e.g. capex) and ending period (e.g. liquidation value)
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Step1: Incremental earnings
“Incremental” means within each period
incremental revenues
– cost of goods sold (COGS)
= gross profit
– selling, general, and administrative (SG&A)
– depreciation
= EBIT
– tax (tax = EBIT X tax rate)
= incremental earning
In short,
incremental earnings =
(revenue – COGS – SG&A – depreciation) X (1 – tax rate)
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Forecasting Incremental Earnings - example
Linksys Example
Linksys is considering the development of a product called Homenet
Based on marketing surveys, the sales forecast for Homenet is 50,000 units per year for 5 years
The wholesale price of Homenet will be $260
Production will be outsourced at a cost of $110 per unit
To verify Homenet’s compatibility, Linksys must also establish a lab for testing
Needs to purchase $7.5M of new equipment, which will be depreciated using straight-line method over 5 years
Linksys expects to spend $2.8M per year on rental costs for the lab, as well as on marketing and support for the product
Linksys’s marginal tax rate is 40%
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Forecasting Incremental Earnings - example
Linksys Example
For the next 4 years
Incremental revenues: 50,000 $260 = $13,000,000 = $13M
Incremental costs of goods sold: 50,000 $110 = $5,500,000 = $5.5M
Incremental SG&A: $2.8 M
For the next 5 years
depreciation: $7,500,000 5 = $1,500,000=$1.5M
Tax rate: 40%
| Year | 0 | 1 | 2 | 3 | 4 | 5 |
| Revenues | 13 | 13 | 13 | 13 | 13 | |
| COGS | -5.5 | -5.5 | -5.5 | -5.5 | -5.5 | |
| Gross profit | 7.5 | 7.5 | 7.5 | 7.5 | 7.5 | |
| SG&A | -2.8 | -2.8 | -2.8 | -2.8 | -2.8 | |
| Depreciation | -1.5 | -1.5 | -1.5 | -1.5 | -1.5 | |
| EBIT | 3.2 | 3.2 | 3.2 | 3.2 | 3.2 | |
| Income tax | -1.28 | -1.28 | -1.28 | -1.28 | -1.28 | |
| Incremental earnings | 1.92 | 1.92 | 1.92 | 1.92 | 1.92 |
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Depreciation
Straight-line depreciation
Split evenly across horizon
Accelerated depreciation
Higher depreciation at early times, lower depreciation at later times
Can start depreciation at year 0
Advantage
Save upfront tax bill
Remember TVM? Saving $1 now is better than saving $1 tmr!
Good for firms with short-term liquidity issues (new, small, fast cash-burning businesses)
Disadvantage
High depreciation means lower residual value in future
1. Have less freedom to adjust tax in the future (e.g. growing firm with increasing revenue likely to pay more tax because of falling in a higher tax bracket)
2. Need to pay more tax on profit for selling the assets at higher price in future (more about liquidation value later)
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Depreciation
MACRS (Modified Accelerated Cost Recovery System) Table
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Depreciation
Linksys Example
MACRS depreciation
Can start at t=0
NPV under straight-line depreciation was $2.862M
NPV under MACRS depreciation is $3.179M
| Year | 0 | 1 | 2 | 3 | 4 | 5 |
| MACRS rate | 20.00% | 32.00% | 19.20% | 11.52% | 11.52% | 5.76% |
| MACRS Depreciation | 1.5 | 2.4 | 1.44 | 0.864 | 0.864 | 0.432 |
| Straight-line Depreciation | 1.5 | 1.5 | 1.5 | 1.5 | 1.5 |
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Tax
https://www.thebalancesmb.com/corporate-tax-rates-and-tax-calculation-397647
Federal + state + sometimes city
Corporate tax is like individual income tax
Amount to pay depends on the corresponding tax bracket
We simplify this by applying an “effective” tax rate on earnings
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Step 2: Determining Incremental Free Cash Flow
Free Cash Flow
= Incremental earnings + Depreciation – Capital expenditure – ∆Net Working Capital
= (Revenue – COGS – SG&A – Depreciation) X (1 –Tax Rate) + Depreciation – Capital expenditure – ∆Net working Capital
Capital expenditure normally only happens at t = 0
Why adding depreciation back?
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Depreciation & Tax
Cash flows depends on “cash” items
Money indeed going in or out of pocket in a specific year
Is revenue a cash item? COGS? SG&A? tax?
Depreciation? No
When calculating incremental earnings, we subtract depreciation solely for accounting and tax purposes
However, depreciation are not really money coming out of pocket during that year!
To get cash flows, we adjust by
adding depreciation back for each year and
take capital expenditure off (mostly happens at t=0)
Depreciation tax shield = Depreciation x Tax rate
Why depreciation method might matter for different firms
Net working captial
Change in net working capital ∆NWC = NWCt – NWCt-1
Net working capital (NWC) = Current assets – Current liabilities
= Cash + Inventory + Receivables – Payables
NWC is basically cash tied up for operational liquidity purposes
Could be used but in fact are not
More NWC, less free cash flow available
Subtract the change in NWC from earnings
Happens commonly at project beginning and end
Important yet assumed zero throughout this course
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Determining Incremental Free Cash Flow
Linksys Example
Convert incremental earnings to incremental free cash flow
Cost of capital is 12%
| Year | 0 | 1 | 2 | 3 | 4 | 5 |
| Incremental earnings | 1.92 | 1.92 | 1.92 | 1.92 | 1.92 | |
| Depreciation | 1.5 | 1.5 | 1.5 | 1.5 | 1.5 | |
| Capex | -7.5 | |||||
| Incremental free cash flow | -7.5 | 3.42 | 3.42 | 3.42 | 3.42 | 3.42 |
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Liquidation / salvage value
Liquidation or salvage value
Assets that are no longer needed can be sold at a resale value
When sold, any capital gain is taxed
After-tax earnings from asset sale = Capital gain (or loss) - tax
Capital gain = Sale price – Book value
Book value = Purchase price – Accumulated depreciation
Linksys example, suppose some event happens in year 4 and managers decide to terminate the business immediately. Instead of keeping equipment for 5 years, we can sell it at the end of 4th year.
| Year | 0 | 1 | 2 | 3 | 4 | 5 |
| Depreciation | -1.5 | -1.5 | -1.5 | -1.5 | -1.5 | |
| Sale price of old equipment | 2 | |||||
| Capital gain | 0.5 | |||||
| Tax on capital gain at 40% | -0.2 | |||||
| Earnings from sale (not cash flow) | 0.3 |
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Step 3: Calculating NPV
How to decide the length of T?
Often a finite number with a terminal value representing its worth in the long future
To make it simple, we can ignore NWC and terminal value, and assume either the cash flow lasts forever, or terminate at a finite point
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Example 1
Cameron Industries is purchasing a new chemical vapor depositor in order to make silicon chips. It will cost $5,000,000 to buy the machine and $1,000,000 to have it delivered and installed. The machine is expected to raise gross profits by $4,500,000 per year, starting at the end of the first year, with associated costs of $1 million for each of those years. The machine is expected to have a working life of six years and will be depreciated over those six years. The marginal tax rate is 40%. Derive the incremental cash flows.
Gross profits = 4.5, Costs = -1, CAPEX = -5-1 = -6, Depreciation = CAPEX / 6 = -1
Incremental Earnings = (4.5-1-1) x (1-0.4) = 1.5 from t=1 to t=6
Treat NWC = 0 if not mentioned; naturally, change in NWC will also be zero.
Example 1
| Year | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| Gross profits | 4.5 | 4.5 | 4.5 | 4.5 | 4.5 | 4.5 | |
| Costs | -1 | -1 | -1 | -1 | -1 | -1 | |
| Depreciation | -1 | -1 | -1 | -1 | -1 | -1 | |
| Tax at 40% | -1 | -1 | -1 | -1 | -1 | -1 | |
| Incremental earnings | 1.5 | 1.5 | 1.5 | 1.5 | 1.5 | 1.5 | |
| Depreciation | 1 | 1 | 1 | 1 | 1 | 1 | |
| Capex | -6 | ||||||
| Change in NWC | |||||||
| Incremental free cash flow | -6 | 2.5 | 2.5 | 2.5 | 2.5 | 2.5 | 2.5 |
Example 2
CathFoods will release a new range of candies which contain antioxidants. New equipment to manufacture the candy will cost $2 million, which will be depreciated by straight-line depreciation over four years. In addition, there will be $5 million spent on promoting the new candy line. It is expected that the range of candies will bring in revenues of $4 million per year for four years with production and support costs of $1.5 million per year. If CathFood's marginal tax rate is 40%, calculate the incremental free cash flows.
Capex = 2, depreciation = 2 / 4 = 0.5, rev = 4, COGS = 1.5
Promoting cost = 5 at t=0
Example 2
| Year | 0 | 1 | 2 | 3 | 4 |
| Gross profits | 4 | 4 | 4 | 4 | |
| Operating expenses | -5 | -1.5 | -1.5 | -1.5 | -1.5 |
| Depreciation | -0.5 | -0.5 | -0.5 | -0.5 | |
| Tax at 40% | 2 | -0.8 | -0.8 | -0.8 | -0.8 |
| Incremental earnings | -3 | 1.2 | 1.2 | 1.2 | 1.2 |
| Depreciation | 0.5 | 0.5 | 0.5 | 0.5 | |
| Capex | -2 | ||||
| Incremental free cash flow | -5 | 1.7 | 1.7 | 1.7 | 1.7 |
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Step 4 (often times): Analyzing Projects: More Than Computing NPV
Sensitivity analysis!!!
How does your estimate of NPV vary when relaxing the underlying assumptions?
Which assumptions are more “important” than others, i.e., NPV is more sensitive with?
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Summary
Capital budgeting process
Revenues to earnings to FCF to NPV
Understanding of each important item
Depreciation
Calculated from capital expenditure
Subtracted to get earnings and tax, then added back to get cash flow
Depreciation method
Tax
Simplified rate
Carryback or carryforward
No interest payment so far
Salvage value (capital gain subject to tax)
Sensitivity analysis
Tools: financial calc & Excel
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Next…
A comprehensive excel spreadsheet example
Investment decision rules
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