Financial Statement School
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Financial Statement School


The word “amortization” refers to the scheduling of payments or charges over time.  There are two types of amortization to which people commonly refer.  One form of amortization is related to lending.  An “amortization schedule” is simply a schedule of loan payments to be made over multiple periods.  The schedule usually details the portion of each payment representing interest as well as the amount of principal being paid.  Since these amounts generally change each period, the amortization schedule separately lists each payment to be made until the loan is repaid.

The other form of amortization is related to intangible assets.  An intangible asset such as a patent may be written off over time (in much the same way that a fixed asset would be depreciated).  Intangible assets are usually amortized on a straight line basis.  The IRS addresses amortization in the instructions to Form 4562-Depreciation and Amortization.

IRS Depreciation

The IRS uses its own rules and methods of depreciating property for income tax purposes.  These rules are too complicated to present here, so you may read the IRS Overview of Depreciation or Publication 946 on Depreciation for further details.  Here are a few definitions and characteristics of IRS depreciation.

The IRS allows something called a “Section 179 Deduction”.  This generally allows you to deduct the entire cost of qualified property in the year that it is acquired.  It can be a good deal for the business owner, but there are limits to the amounts that qualify, and these limits apply to each taxpayer, not necessarily to each business.

The “Modified Accelerated Cost Recovery System” or (MACRS) is the depreciation method used for most property.  The details are complicated.

For example, you will use either the “General Depreciation System” (GDS) or the “Alternative Depreciation System” (ADS) to depreciate property.  You will generally use GDS.  However, you must use ADS if you are specifically required by law to do so, or if you elect to use it.  For example, property used fifty percent or less in a qualified business use or tangible property used predominantly outside the U.S. during the year must be depreciated using ADS.

The IRS stipulates various “conventions” that must be used as well.  For example, the mid-month convention treats all property placed in service or disposed of during the month as placed in service or disposed of at the midpoint of the month.  So, a half-month of depreciation is actually used in the property’s first month and its final month of use.  The IRS also uses mid-quarter and half-year conventions for various types of property.

The IRS uses various depreciation methods as well.  They use the 200% declining balance method, the 150% declining balance method, and straight line deprecation depending on what type of asset is being depreciated.  These methods are similar to those described in earlier posts.

Finally, the IRS requires you to “recapture” (or include as taxable income) any gains on the disposition of property depreciated using MACRS.

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Duration of Lifetime Value (LTV)

LTV is simply the net present value of a stream of future cash flows from a customer.  But, the LTV says little about the timing of the revenues and costs.  To borrow a term from finance, a customer’s LTV also has a “duration”.  Duration is the weighted average of the length of time that it takes for the cash flows to arrive.  So, duration is expressed in units of time, and it measures the timing of the payments.

Duration is important because revenues from customers usually come in over time.  Lifetime revenue streams may even be back-loaded, since new services, cross-selling opportunities, and product improvements happen later.  Ongoing per-unit customer-maintenance costs (which are subtracted to get LTV) may also be higher for a new business.  These factors increase the duration of a customer’s LTV.  Here is an example of how two types of customers with the same LTV can have different durations:

Businesses must address the duration of LTV.  When duration is high, entrepreneurs must be sure to keep enough cash on hand, and more importantly, they need to find ways to accelerate cash flows and shorten the duration.

David Skok recommends that subscription businesses aim to recover CAC in a year or less.  While not explicitly saying it, he is talking about duration.  The timing of the cash flows should be early enough to cover costs in a reasonable period of time.

Lifetime Value (LTV) and Customer Acquisition Cost (CAC)

Another definition of the abbreviation “LTV” is “lifetime value”.  This measurement is often used by internet and software-as-a-service businesses to measure the average lifetime value of a single user or customer.  In this case, LTV represents the sum of all future cash inflows from a customer (net of the regular costs of maintaining the business and customer relationship) all of which are discounted to a single present value.

This LTV is often compared to “CAC” or the average “customer acquisition cost”.  Obviously, LTV must exceed CAC.  The greater the difference between LTV and CAC, and the sooner that customer acquisition costs are covered by net revenues from a customer, the better.  Both the ratio and the timing of the cash flows are important.

Loan to Value (LTV)

Loan to Value = Loan Amount
                           Asset Value

The loan to value ratio is commonly used in lending.  It represents the ratio of a loan amount (or remaining principal balance on a loan) to the market value of the asset pledged as collateral on the loan.  For example, assume that a borrower wishes to purchase a building for $100,000.  If a bank provides a $70,000 mortgage loan against the building, then the loan has a 70% loan to value.

The asset value in the denominator may be exchanged to obtain slightly different measurements.  For example, one might consider the construction cost of a new building in the ratio by measuring “loan to cost.”

Or, a bank might construct a “loan to discounted value” ratio.  Let’s say that a bank makes an asset-based loan to our HVAC business for working capital.  The bank is willing to loan up to 75% of the value of accounts receivable and 50% of the value of inventory on a revolving line of credit.  However, the loan balance is currently only $75,000.  The loan to discounted value is, therefore, 47.5% = 75,000 / (89,000 * 0.75 + 182,000 * 0.50).  The loan to discounted value is often used when a lender wishes to lend at different rates against different assets that secure a single loan.  A loan to discounted value that is equal to or less than 1.0 will fall within the prescribed standards.

Accelerated Depreciation and the Double Declining Balance Method

A variety of "accelerated depreciation" methods have been devised to book relatively higher depreciation amounts earlier in the lives of assets and smaller amounts later.  These methods are meant to more accurately reflect the actual declines in usefulness or values of fixed assets.

One of the most popular methods of accelerated depreciation is the "double declining balance" method.  Under this method, the percentage of the asset's value that is depreciated in the first year is doubled.  Then, in the second year, this same percentage is applied to the remaining balance to calculate depreciation, and so on.

Let's use the same example from the discussion on straight line depreciation.  You buy a vehicle for $20,000.  You believe that it has a useful life of five years and a salvage value of $5,000.  Under straight line depreciation, you would depreciate the asset over five full years; therefore, the annual depreciation represents one fifth or twenty percent of the asset's useful life.

Under the double declining balance method, you would double this twenty percent amount to forty percent.  The depreciation for year one under the double declining balance method would be $8,000 (or 40% of $20,000).  It is important to note that the double declining balance method applies the year-one percentage to the full cost of the asset without deducting any salvage value.

The second year depreciation would be $4,800 or 40% X ($20,000-$8,000).  The third year depreciation expense would be $2,200.  Note that the year-three depreciation calculated by taking forty percent of the remaining balance of $7,200 ($20,000-$8,000-$4,800) would be $2,880.  Remember, however, that the salvage value is $5,000.  We can't depreciate any further than the depreciable basis of $15,000 ($20,000-$5,000).  The remaining depreciation for year three is, therefore, $2,200 (or $7,200-$5,000).

Some accountants switch to straight line depreciation when depreciation under the double declining balance method becomes smaller than that under the straight line method.

Straight Line Depreciation

There are many different ways to depreciate property.  The simplest is the "straight line" method.  First, determine the "useful life" of the asset.  A computer may have a useful life of only five years, while a building may have a useful life of decades.  Second, deduct the "salvage value", or anticipated amount for which the asset can be sold at the end of its useful life, to obtain the depreciable basis.  (For real property, you would subtract the value of the land to arrive at the depreciable basis.)  Divide the depreciable basis by the number of periods (either months or years) over which the item will be depreciated.  The result is the depreciation expense for the asset per period.


An asset or a property is “capitalized” when it is listed on the balance sheet as a fixed asset and depreciated over time.  The periodic charge to the value of the asset is referred to as “depreciation”.  Depreciation represents the “using up” of the asset, and the length of time over which an asset is depreciated very roughly approximates its useful life.

One side of a depreciation transaction records the reduction in value of the asset, while the other records depreciation expense.  Depreciation expense is listed on the income statement; however, it does not represent actual cash that is spent by the company.  Instead, depreciation represents the arbitrarily chosen fraction of the useful life of the asset used up during the accounting period.  For this reason, depreciation (and amortization and depletion) are referred to as “non-cash” expenses.

Let’s say you buy a piece of real estate.  For accounting purposes, you must separate the land from the buildings and the equipment.  You may depreciate buildings and equipment, but land is not depreciable.  Many property-owners neglect the extra step that allows them to accelerate depreciation on some assets.  Any equipment, appliances, furniture, tools, and lawn-mowers may be depreciated much more rapidly than the buildings.  Since depreciation is a non-cash expense, you minimize your income taxes by maximizing depreciation without actually spending extra cash.

Some repairs are deductible as expenses, while others must be capitalized and depreciated.  Property-owners usually prefer to write repairs off as expenses, since they receive the full tax benefit right away as opposed to receiving it over multiple years.  So, if you repair the corner of a roof, then you will deduct this as an expense.  However, if you replace the roof, then the value of your property and the length of its life have increased.  Therefore, you must capitalize and depreciate a full roof replacement.

Tax Returns

All business income tax returns are actually just financial statements that have been modified to a format required by the IRS.  The income tax returns required by the IRS are as follows:

Corporation: Form 1120
Subchapter S Corporation: Form 1120S
Partnership: Form 1065
Sole Proprietorship: Form 1040, Schedule C
Limited Liability Company (LLC): may file any of the above

This IRS article provides more detail about which types of businesses file which returns.

The IRS allows businesses to choose some accounting methods used in tax return calculations, such as cash whether to use cash or accrual accounting.  Inventory valuation methods used in tax returns may also differ from business to business based upon the circumstances.  This IRS article describes when various methods may be used.

Other items, such as depreciation and amortization schedules, are often strictly dictated by the IRS.

If you own a business, your banker and your investors will likely require you to send them copies of your tax returns.  This allows them to analyze your financial situation using a statement on which you are not likely to overestimate your income.

Comparison of Value using Gross Rents versus NOI

Consider two properties, the first contains twelve one-bedroom units, and the second consists of six two-bedroom units.  Assume that the two properties have identical potential gross income.  Are the properties really identical in value?

Well, maybe the first property is located just across a municipal border resulting in a higher property tax rate.  With all else being equal, the net operating income, and therefore the value of the property with the higher tax bill will actually be lower.

Whenever gross rents are used to value a property, various property-specific factors are necessarily left out of the equation.  Potential gross income excludes vacancy and bad debt and may also include income that a landlord must actually use to pay for utilities.

Differences in the physical makeup of the units may also lead to differences in the net operating income of two properties.  For example, the building with one-bedroom units may have higher maintenance costs, because it has more appliances and more bathrooms than the building made up of two-bedroom units.  The building with more units may also experience higher advertising and management expenses per dollar of rent as well.

Here is an example of how two properties with identical gross rents can have very different net operating income and appraised values:

Property 1: Property 2: Comments on  

One Bedrooms Three Bedrooms Property 1
Number of Units 12 6
Annual Rent per Unit $7,800 $15,600

Gross Rent $93,600 $93,600
Vacancy and Bad Debt $9,500 $4,500 higher vacancy
Net Rent $84,100 $89,100


Advertising $2,000 $800 more apartments to rent
Bank Charges $100 $100
Insurance $4,500 $4,500
Lawn Care and Landscaping $500 $500
Management Fees $9,360 $9,360
Office Supplies $1,500 $800 more paperwork and supplies
Property Tax $15,500 $13,000 higher tax rate
Professional Fees $1,200 $1,200
Repairs and Maintenance $7,500 $4,500 more appliances to repair
Utilities $2,700 $900 rent includes heat and water
Total Expenses $44,860 $35,660

Net Operating Income (NOI) $39,240 $53,440

NOI divided by 9% Cap Rate $436,000 $593,778

Debt Service $41,000 $41,000
Debt Service Coverage 96% 130%

So, if you’re selling a property and applying a gross rent multiplier leads to a higher value than the conventional method based on NOI, then you might stress that value when talking to potential buyers.  You might also provide an explanation if your historical expenses were out of line or unusual or one-time in nature, so that a buyer or an appraiser can adjust any value based upon NOI upward.

If you’re buying a property, keep in mind that using a gross rent multiplier may fail to account for a situation where the current rents being charged by the seller fall short of market rents.  In this case, there may be room for improvement, and the artificially low rents may be leading to a low valuation when a gross rent multiplier is applied.  In this case, you may adjust potential gross income upward to get a better value.

Gross Rent Multiplier

Gross Rent Multiplier = Sale Price / Potential Gross Income

The higher the Gross Rent Multiplier, the better, if you are the seller of a property.  Be sure to use annual income in this calculation.  You may also need to make an adjustment if the owner of the subject property pays for utilities.  Subtract amounts paid for utilities from income before constructing the ratio, so you’ll be able to make apples-to-apples comparisons among different properties.

Another way to look at the same ratio is:

Sale Price = Gross Rent Multiplier x Potential Gross Income

You may ask about the going rate for the gross rent multiplier in your area.  You can then apply this rate to your own rents and very roughly gauge the value of your property.  But be careful, we’ll see that basing a price on gross rents is not necessarily the best method of determining value.

Cap Rate from the Investor’s Perspective

Cap Rate = Net Operating Income / Price

Investors often use a derivation of the exact same income approach formula used by appraisers, but instead they solve for the cap rate.

Another way to look at the cap rate is that it represents the annual rate at which the property or investment pays for itself.

Cap Rate from the Appraiser's Perspective

Using the income approach, an appraiser solves the previous formula to determine the value of a property.  To solve for the value, the appraiser needs an appropriate capitalization rate.

The capitalization rate or “cap rate” used by an appraiser is constructed from a mortgage constant and an equity rate of return.  The best way to obtain an accurate cap rate for your locale or type of property is to call an appraiser and ask for it.  You may also ask your banker what cap rates are being used in local appraisals.

You may calculate a cap rate yourself using the following method.  Start by determining typical percentages of equity investment and debt financing for similar investments.  The combined percentage of equity and debt must equal one hundred percent.  For example, you might assume twenty-five percent equity and seventy-five percent debt financing:

Cap Rate = 25% x Equity Rate of Return + 75% x Mortgage Constant

The “equity rate of return” represents an estimate of the required rate of return by investors in similar projects.  The mortgage constant simply represents total annual debt service divided by the loan amount.

Cap rates are usually calculated based upon prevailing market rates of return, interest rates, loan to value ratios, and mortgage amortizations for similar properties.  The specific numbers that appraisers plug into the cap rate formula are often determined by judgment calls.  Because of this, it is important to learn why appraisers use certain values and whether different appraisers in your area might make different assumptions.

Real Estate Valuation using the Income Approach

Property Value = Net Operating Income / Capitalization Rate

The “income approach” is the primary method used by real estate appraisers to value investment properties.  Although they consider cost and market comparables as well, appraisers typically give the most weight to the income approach when valuing commercial property.

If the appraiser believes that market rents differ from the actual rents of the property, then he or she may substitute them.  Similarly, if a property requires a great deal of maintenance that has been deferred or if capital improvements will be necessary in the future, then the NOI or the value may be adjusted downward by the appraiser to reflect the situation.

Real Estate Income Statement

The statement of income that is used for real estate properties differs from that of conventional businesses.  A typical real estate income statement looks something like this:

Potential Gross Income (or PGI)
Plus: Other Income
Less: Vacancy and Bad Debt Expense
Equals: Effective Gross Income (or EGI)

Less: Operating Expenses
Equals: Net Operating Income (or NOI)

Less: Debt Service
Equals: Before-Tax Cash Flow

Less: Income Tax

Equals: After-Tax Cash Flow

Potential gross income represents a full year of rents assuming that the property involved is fully occupied.  Other income might include payments for parking, laundry facilities, or fees.

Operating expenses include property taxes, management fees, (and a replacement reserve when used for an appraisal).  Debt service includes both principal and interest payments.

Note that operating expenses exclude depreciation.  In fact, deprecation does not appear anywhere within this form of income statement.  (Depreciation expense is, however, considered when calculating the income tax requirement.)  Because this type of statement excludes depreciation and includes principal payments, the bottom line represents cash flow as opposed to “net income”.

Return on Capital (ROC)

Return on Capital =       Net Operating Profit – Income Tax
                                       Total Long-Term Debt + Equity Capital

The Return on Capital Ratio is also known as “Return on Invested Capital” (or ROIC), and it measures a company’s efficiency at turning its total capital into profits.

This CFO article argues that ROC better measures company value than other efficiency ratios such as ROE.

PEG Ratio

PEG Ratio =                   P/E Ratio
                         Expected Annual EPS growth

We have already learned that when companies are expected to grow rapidly in the future, they generally exhibit high P/E multiples.  Investors are willing to pay more for a stock now if they expect to profit from increasing earnings in the future.  The anticipated earnings growth justifies the higher stock price relative to current earnings.

In order to compare apples to apples regarding companies with different growth models, the PEG Ratio was created.  This ratio attempts to even the score by dividing company P/E Ratios by their expected growth rates.

A problem with this ratio involves the fact that the growth rate is a prediction; it’s not a hard number.  The problem may be compounded when using “forward” earnings to construct the P/E Ratio.  In this case, two variables in the PEG equation are actually estimates.  A low PEG Ratio may result when the outlook for a company is too rosy, providing the misleading implication that the stock is underpriced.

P/E 10

For some reason, human beings tend to be relatively short-sighted when it comes to investing in stocks.  Instead of making long-term investment decisions, people often focus on relatively minor or short-term occurrences or temporary changes in earnings.  One result of this phenomenon is the fact that the traditional P/E ratio, which uses only one year of earnings in its calculation, is a very popular measure used in stock buy and sell decisions.  Many investors react aggressively to changes in a single quarter or a year of earnings or in anticipation of future earnings.

In his popular book, Irrational Exuberance, Robert J. Shiller instead recommends using an inflation-adjusted P/E covering the past ten years to support decisions about whether to buy or sell stocks.  This ratio is referred to as the P/E 10.

Since, the P/E Ratio can also be measured for a bundle of stocks, Shiller illustrates his point using the S&P 500.  During the times preceding a market crash, the S&P 500 has become overvalued, exhibiting a very high P/E 10.  The P/E 10 rose all the way to the low forties in 1999 and 2000 just before the tech bubble, and it reached high twenties again just prior to our current economic turmoil.

Shiller keeps an updated and ongoing spreadsheet of the P/E 10 calculation for the S&P 500 all the way back to 1871 here.

Price/Earnings or “P/E” Ratio

    P/E Ratio =     Stock Price
                          Earnings per Share

The P/E Ratio represents the multiple of a stock’s price over its earnings per share.  A stock with a high P/E (of around twenty or above) usually has high expected earnings growth as well.  The future earnings expectations are necessary to justify the high price relative to current or historical earnings.

A lower P/E (for example, a number closer to ten) may indicate that a stock is a bargain; although, it may also indicate some serious problem that is keeping the stock price down.

If earnings are particularly high or low due to some passing or one-time event, then the P/E may be thrown off or need adjustment.  If the stock price remains about the same, then you may attempt to adjust the financial effect of the unusual event out of EPS.  You can then use the adjusted EPS to calculate a more meaningful P/E.

Other times, the stock price will actually adjust to an anomalous change in earnings per share.  When this happens, the stock may become a relative bargain or become overly expensive.

EPS and P/E are widely used measures of stock performance and value.  The fact that an individual event or a single year of earnings may so drastically alter these ratios (and therefore the stock price) can be problematic.  It does not necessarily make sense to base the price of a stock on just one year of earnings.

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