1. Risk Free Rate (7)
1.1. But what makes an asset risk free?
1.1.1. The actual return is always equal to the expected return
1.1.1.1. there can be no default risk
1.1.1.1.1. The only securities that have a chance of being risk free are government securities,
1.1.1.2. there can be no reinvestment risk
1.1.1.2.1. A purist's view of risk free rates would then require different risk free rates for each period and different expected returns.
1.1.1.2.2. Even a 5-year treasury bond is not risk free, since the coupons on the bond will be reinvested at rates that cannot be predicted today.
1.2. With Risk Free Rate to use?
1.2.1. Historical risk premium used in the US should be the excess return earned by stocks over treasury bonds, and not treasury bills, for purposes of long term analysis.
1.2.2. Longer term projects or valuation, the risk free rate should be the long term government bond rate.
1.2.3. Shorter term, the short term government security rate can be used as the risk free rate.
1.2.4. If cash flows are estimated in nominal US dollar terms, the risk free rate will be the US treasury bond rate.
1.2.5. The currency in which the cash flows on the project or firm are estimated determines the risk free rate,
1.2.5.1. If we assume purchasing power parity then differences in interest rates reflect differences in expected inflation rates.
1.2.5.2. In particular, projects and assets will be valued more highly when the currency used is the one with low interest rates relative to inflation.
1.2.5.3. Given that these firms, in spite of their size and stability, still have default risk, you would use a rate that is marginally lower3 than the corporate borrowing rate.
1.3. Real vs Nominal
1.3.1. Under conditions of high and unstable inflation, valuation is often done in real terms.
1.3.2. To estimate of the real risk free rate subtract the expected inflation rate from the nominal interest rate.
1.3.2.1. You also can use the inflation-indexed treasuries.
1.3.2.2. Inmarkets without inflation-indexed default-free securities. There is two main arguments.
1.3.2.2.1. as long as capital can flow freely to those economies with the highest real returns, there can be no differences in real risk free rates across markets.
1.3.2.2.2. if there are frictions and constraints in capital flowing across markets. In that case, the expected real return on an economy, in the long term, should be equal to the expected real growth rate, again in the long term, of that economy, for equilibrium.
1.4. And what do we do when we cannot find such an asset? Emerging Markets case
1.4.1. Look at the largest and safest firms in that market and use the rate that they pay on their long term borrowings in the local currency as a base.
1.4.2. If there are long term dollar-denominated forward contracts on the currency, you can use interest rate parity and the treasury bond rate (or riskless rate in any other base currency) to arrive at an estimate of the local borrowing rate.
1.4.2.1. The biggest limitation of this approach, however, is that forward rates are difficult to obtain for periods beyond a year4 for many of the emerging markets, where we would be most interested in using them.
1.4.3. You could adjust the local currency government borrowing rate by the estimated default spread on the bond to arrive at a riskless local currency rate.
1.4.3.1. The default spread on the government bond can be estimated using the local currency ratings that are available for many countries.
1.4.3.2. EM Risk Free Rate = EM Bond rate - Default Spread
2. Equity Risk Premiums (7)
2.1. Asset Pricing Models Converge on:
2.1.1. Risk in terms of variance in actual returns around an expected return
2.1.2. Risk has to be measured from the perspective of the marginal investor in an asset and that this marginal investor is well diversified.
2.1.3. Is only the risk that an investment adds on to a diversified portfolio that should be measured and compensated.
2.1.3.1. Firm-specific component
2.1.3.2. Market component
2.1.3.2.1. is not diversifiable and should be rewarded
2.2. How to Calculate the Historical Risk Premium?
2.2.1. The actual returns earned on stocks over a long time period is estimated and compared to the actual returns earned on a default-free asset (usually government security). The difference, on an annual basis, between the two returns is computed and represents the historical risk premium
2.2.2. Three reasons for the divergence in risk premiums:
2.2.2.1. Time Period Used:
2.2.2.1.1. The rationale presented by those who use shorter periods is that the risk aversion of the average investor is likely to change over time and that using a shorter and more recent time period provides a more updated estimate. (greater noise in the risk premium estimate, higher standard deviation)
2.2.2.2. Choice of Riskfree Security:
2.2.2.2.1. The riskfree rate chosen in computing the premium has to be consistent with the riskfree rate used to compute expected returns.
2.2.2.3. Arithmetic and Geometric Averages:
2.2.2.3.1. If annual returns are uncorrelated over time an our objectives were to estimate the risk premium for the next year, the arithmetic average is the best unbiased estimate of the premium. However,empirical studies seem to indicate that returns on stocks are negatively correlated over time. Consequently, the arithmetic average return is likely to overstate the premium. Also while asset pricing models may be single period models, the use of these models to get expected returns over long periods (such as five or ten years) suggests that the single period may be much longer than a year. In this context, the argument for geometric average premiums becomes even stronger.
2.2.3. How to Calculate in Other Markets
2.2.3.1. Historical risk premiums for markets outside the United States cannot be used in risk models
2.2.3.1.1. Short Historical Time Serie
2.2.3.1.2. Volatile Histories
2.2.3.1.3. Dominated by a few large companies
2.2.3.1.4. Standard errors on these historical time series make them close to useless
2.2.3.2. Equity Risk Premium = Base Premium for Mature Equity Market + Country Premium
2.2.3.2.1. The US equity market is the mature market because there is sufficient historical data in the United States to make a reasonable estimate of the risk premium.
2.2.3.2.2. Should there be a country premium, and if so, how do we estimate the premium?
2.2.3.2.3. Can country risk be diversifiable?
2.3. Implied Equity Premium
2.3.1. Simple Valuation Model for Stocks
2.3.1.1. Expected Growth Rate in Dividends
2.3.1.2. Required Return on Equity
2.3.1.2.1. This is the only unknown variable
2.3.1.2.2. If you subtract the risk free rate you get the impli
2.3.1.3. Current level of the market Value
2.3.2. Disadvantage: it varies a lot over time, much more than historical premiums
3. Valuation (2)
3.1. Discounted Cash Flow
3.1.1. Equity Valuation
3.1.1.1. The value of equity is obtained by discounting expected cashflows to equity, i.e., the residual cashflows after meeting all expenses, reinvestment needs, tax obligations and net debt payments (interest, principal payments and new debt issuance), at the cost of equity, i.e., the rate of return required by equity investors in the firm.
3.1.1.2. PV of Equity = PV of Firm – Market Value of Debt
3.1.2. Firm Valuation
3.1.2.1. The value of the firm is obtained by discounting expected cashflows to the firm, i.e., the residual cashflows after meeting all operating expenses, reinvestment needs and taxes, but prior to any payments to either debt or equity holders, at the weighted average cost of capital, which is the cost of the different components of financing used by the firm, weighted by their market value proportions.
3.1.2.2. WACC = Cost of Equity (Equity / (Debt + Equity)) + Cost of Debt (Debt/(Debt+Equity))
3.1.3. Adjusted Present Value (APV)
3.1.3.1. We begin by valuing equity in the firm, assuming that it was financed only with equity. We then consider the value added (or taken away) by debt by considering the present value of the tax benefits that flow from debt and the expected bankruptcy costs.
3.1.3.2. Value of firm = Value of all-equity financed firm + PV of tax benefits + Expected Bankruptcy Costs
3.1.3.3. In fact, this approach can be generalized to allow different cash flows to the firm to be discounted at different rates, given their riskiness.
3.1.4. Notes:
3.1.4.1. If the cash flows that are being discounted are after interest expenses (and principal payments), they are cash flows to equity and the discount rate that should be used should be the cost of equity. If the cash flows that are discounted are before interest expenses and principal payments, they are usually cash flows to the firm.
3.1.4.2. In excess return (and excess cash flow) models, only cash flows earned in excess of the required return are viewed as value creating, and the present value of these excess cash flows can be added on to the amount invested in the asset to estimate its value.
3.1.4.2.1. Value of asset = Present value of excess return + Investment in the asset
3.1.4.2.2. Excess return = Cash flow earned – Cost of capital * Capital Invested in asset
3.1.4.3. There are some cases where the DCF is not good:
3.1.4.3.1. Firms in trouble
3.1.4.3.2. Cyclical Firms
3.1.4.3.3. Firms with unutilized assets
3.1.4.3.4. Firms in the process of restructuring
3.1.4.3.5. Firms involved in acquisitions
3.1.4.3.6. Private Firms
3.1.4.3.7. Firms with patents or product options
3.2. Relative
3.2.1. In relative valuation, the value of an asset is derived from the pricing of 'comparable' assets, standardized using a common variable such as earnings, cashflows, book value or revenues.
3.2.2. we assume that the market is correct in the way it prices stocks, on average, but that it makes errors on the pricing of individual stocks.
3.2.3. Cross Sectional Comparisons
3.2.4. Comparisons across time
3.3. Contingent Claim
3.3.1. In some cases the value of an asset may not be greater than the present value of expected cash flows if the cashflows are contingent on the occurrence or non-occurrence of an event.
3.3.2. An option can be valued as a function of the following variables (Black and Scholes)
3.3.2.1. The current value
3.3.2.2. The variance in value of the underlying asset
3.3.2.3. The strike price
3.3.2.4. The time to expiration of the option
3.3.2.5. The riskless interest rate
3.3.3. An asset can be valued as an option if the payoffs are a function of the value of an underlying asset.
3.3.3.1. It can be valued as a call option if the payoff is contingent on the value of the asset exceeding a pre-specified level.
3.3.3.2. It can be valued as a put option if the payoff increases as the value of the underlying asset drops below a pre-specified level.
3.3.4. Categorizing Option Pricing Models
3.3.4.1. Financial asset: Traded Security
3.3.4.2. Real asset: Non traded
3.3.5. Assets that share several option characteristics.
3.3.5.1. Equity
3.3.5.1.1. Can be viewed as a call option on the value of the underlying firm, with the face value of debt representing the strike price and term of the debt measuring the life of the option.
3.3.5.2. Patent
3.3.5.2.1. Can be analyzed as a call option on a product, with the investment outlay needed to get the project going representing the strike price and the patent life being the time to expiration of the option.
3.4. Asset Based Valuation Models
3.4.1. Liquidation value
3.4.1.1. Which is obtained by aggregating the estimated sale proceeds of the assets owned by a firm.
3.4.2. Replacement cost
3.4.2.1. Where you evaluate what it would cost you to replace all of the assets that a firm has today.
4. Financial Statements (3)
4.1. Four Big Questions:
4.1.1. How valuable are the assets of a firm?
4.1.1.1. Assets with long lives
4.1.1.1.1. land and buildings...
4.1.1.2. Assets with shorter lives
4.1.1.2.1. inventory...
4.1.1.3. Intangible assets
4.1.1.3.1. patents and trademarks...
4.1.2. How did the firm raise the funds to finance these assets?
4.1.2.1. owners (equity)
4.1.2.2. borrowed money (debt)
4.1.3. How profitable are these assets?
4.1.3.1. return greater than the hurdle rate
4.1.4. How much uncertainty (or risk) is embedded in these assets?
4.2. Accounting Principles
4.2.1. Historical Cost
4.2.1.1. Is the original cost of the asset, adjusted upwards for improvements made to the asset since purchase and downwards for the loss in value associated with the aging of the asset.
4.3. Investments and Marketable Securities
4.3.1. Minority, Passive Investments
4.3.1.1. Securities or assets owned in another firm represent less than 20% of the overall ownership of that firm
4.3.1.1.1. Held to Maturity
4.3.1.1.2. Held for Trading
4.3.1.1.3. Available for Sale
4.3.2. Minority, Active Investments
4.3.2.1. Securities or assets owned in another firm represent between 20% and 50% of the overall ownership of that firm
4.3.2.1.1. While these investments have an initial acquisition value, a proportional share (based upon ownership proportion) of the net income and losses made by the firm in which the investment was made, is used to adjust the acquisition cost. In addition, the dividends received from the investment reduce the acquisition cost. This approach to valuing investments is called the equity approach.
4.3.2.1.2. The market value of these investments is not considered until the investment is liquidated, at which point the gain or loss from the sale, relative to the adjusted acquisition cost is shown as part of the earnings under extraordinary items in that period.
4.3.3. Majority, Active Investments
4.3.3.1. Securities or assets owned in another firm represent more than 50% of the overall ownership of that firm
4.3.3.1.1. In this case, the investment is no longer shown as a financial investment but is instead replaced by the assets and liabilities of the firm in which the investment was made. This approach leads to a consolidation of the balance sheets of the two firms, where the assets and liabilities of the two firms are merged and presented as one balance sheet. The share of the firm that is owned by other investors is shown as a minority interest on the liability side of the balance sheet.
4.3.3.1.2. Here again, the market value of this investment is not considered until the ownership stake is liquidated. At that point, the difference between the market price and the net value of the equity stake in the firm is treated as a gain or loss for the period.
4.4. Long Term Debt
4.4.1. Long-term loan from a bank or other financial institution
4.4.1.1. For bank loans, the present value of payments due on the loan or bond at the time of the borrowing will be equal to the nominal value of the loan.
4.4.2. Long-term bond issued to financial markets
4.4.2.1. Bonds are issued at par value
4.4.2.1.1. The value of the long-term debt is generally measured in terms of the nominal obligation created, in terms of principal (face value) due on the borrowing.
4.4.2.2. Bonds issued at a discount/ Premium on par value
4.4.2.2.1. The bonds are recorded at the issue price, but the premium or discount to the face value is amortized over the life of the bond.
4.4.2.2.2. The difference between the issue price and the face value is amortized each period and is treated as a non-cash interest expense that is tax deductible.
4.4.2.3. Notes
4.4.2.3.1. In all these cases, the book value of debt is unaffected by changes in interest rates during the life of the loan or bond.
4.4.2.3.2. This updated market value for debt is not shown on the balance sheet. If debt is retired prior to maturity, the difference between book value and the amount paid at retirement is treated as an extraordinary gain or loss in the income statement.
4.4.2.3.3. Companies which have long term debt denominated in non-domestic currencies have to adjust the book value of debt for changes in exchange rates. Since exchange rate changes reflect underlying changes in interest rates, it does imply that this debt is likely to be valued much nearer to market value than is debt in the home currency.
4.5. Equity
4.5.1. Original proceeds received by the firm when it issued the equity, augmented by any earnings made since (or reduced by losses, if any) and reduced by any dividends paid out during the period.
4.5.1.1. This is the book value of equity
4.5.2. Other itens that affects
4.5.2.1. treasury stock
4.5.2.1.1. When companies buy back stock for short periods, with the intent of reissuing the stock or using it to cover option exercises, they are allowed to show the repurchased stock as treasury stock, which reduces the book value of equity.
4.5.2.2. Firms that have significant losses over extended periods or carry out massive stock buybacks can end up with negative book values of equity.
4.5.2.3. Unrealized gain or loss in marketable securities
4.5.2.3.1. Any unrealized gain or loss in marketable securities that are classified as available-for-sale is shown as an increase or decrease in the book value of equity in the balance sheet.
4.6. Nonrecurring items
4.6.1. Unusual or Infrequent items
4.6.1.1. Such as gains or losses from the divestiture of an asset or division and write-offs or restructuring costs. Companies sometimes include such items as part of operating expenses.
4.6.2. Extraordinary items
4.6.2.1. Which are defined as events that are unusual in nature, infrequent in occurrence and material in impact.
4.6.3. Losses associated with discontinued operations
4.6.3.1. Which measure both the loss from the phase out period and the estimated loss on the sale of the operations. To qualify, however, the operations have to be separable separated from the firm.
4.6.4. Gains or losses associated with accounting changes
4.6.4.1. Which measure earnings changes created by accounting changes made voluntarily by the firm (such as a change in inventory valuation and change in reporting period) and accounting changes mandated by new accounting standards.
5. Basics of Risk (4)
5.1. Promised cash flows
5.1.1. Risk Free + Default Spread
5.1.1.1. Determinants of the default spread:
5.1.1.1.1. Firm’s capacity to generate cash flows from operations
5.1.1.1.2. Firm’s capacity to pay its interest and its principal payments.
5.1.2. How do we measure default risk?
5.1.2.1. Can be measured by ratings agencies
5.2. No promised cash flows, but there are expected cash flows
5.2.1. How do we measure equity risk?
5.2.1.1. The variance in actual returns around an expected return. The greater this variance, the more risky an investment is perceived to be.
5.2.1.2. There is risk that can be diversified away by investors and risk that cannot
5.2.1.2.1. Marginal Investor
5.2.1.2.2. Firm-specific risk
5.2.1.2.3. Market risk
5.2.1.2.4. Portfólio
6. Earnings (9)
6.1. Need to ajust:
6.1.1. Operating lease expenses (that are financial expenses)
6.1.1.1. 1. Discount future operating lease commitments back at the firm’s pre-tax cost of debt
6.1.1.2. 2. Add the present value of the operating lease commitments to the conventional debt of the firm to arrive at the total debt outstanding.
6.1.1.2.1. Adjusted Debt = Debt + Present Value of Lease Commitments
6.1.1.3. 3. When you convert operating leases into debt, you also create an asset to counter it of exactly the same value.
6.1.1.4. 4. You need to ajust the Operating Income to the lease expenses and depreciation of created leased asset
6.1.1.4.1. Adjusted Operating Income = Operating Income + Operating Lease Expenses – Depreciation on leased asset
6.1.2. Research and development expenses (that are capital expenses)
6.1.2.1. How to Capitalize?
6.1.2.1.1. How long it takes for research and development to be converted, on average, into commercial products? (this is the amortizable life)
6.1.2.1.2. If the amortizable life is 5 years, get the last 5 years data to create the R&D asset
6.1.2.1.3. Need to ajust the Book Value of Equity
6.1.2.1.4. Need to ajust de Net income
6.1.3. Extraordinary items
6.1.3.1. See the frenquency that this itens appear, and se if there is any patterns
6.1.4. One-time charges
6.2. Free Cash Flow
6.2.1. Free cash flows to the firm
6.2.1.1. after-tax operating earnings
6.2.2. Free cashflow to equity
6.2.2.1. net income
6.3. Key Financial Questions
6.3.1. Assets in Place
6.3.1.1. What are the assets in place?
6.3.1.2. How valuable are these assets?
6.3.1.3. How risky are these assets?
6.3.2. Growth Assets
6.3.2.1. What are the growth assets?
6.3.2.2. How valuable are these assets?
6.3.3. Debt
6.3.3.1. What is the value of the debt?
6.3.3.2. How risky is the debt?
6.3.4. Equity
6.3.4.1. What is the value of the equity?
6.3.4.2. How risky is the equity?
6.4. Techniques for Managing Earnings
6.4.1. Planning ahead:
6.4.2. Revenue Recognition:
6.4.3. Book revenues early:
6.4.4. Capitalize operating expenses:
6.4.5. Write offs:
6.4.6. Use reserves:
6.4.7. Income from Investments:
6.5. Warning Signs in Earnings Reports
6.5.1. Is earnings growth outstripping revenue growth by a large magnitude year after year?
6.5.2. Do one-time or non-operating charges to earnings occur frequently?
6.5.3. Do any of the operating expenses, as a percent of revenues, swing wildly from year to year?
6.5.4. Does the company manage to beat analyst estimates quarter after quarter by a cent or two?
6.5.5. Does a substantial proportion of the revenues come from subsidiaries or related holdings?
6.5.6. Are accounting rules for valuing inventory or depreciation changed frequently?
6.5.7. Are acquisitions followed by miraculous increases in earnings? An
6.5.8. Is working capital ballooning out as revenues and earning surge?
7. Terminal Value (12)
7.1. Stable Growth (sustained in perpetuity)
7.1.1. Determinants
7.1.1.1. Firm’s size, relative to the market that it serves
7.1.1.2. Current growth rate
7.1.1.3. Competitive advantages
7.1.2. Need to consider
7.1.2.1. domestic vs multi-nationally operations
7.1.2.2. Nominal or real terms
7.1.2.3. Currency is being used
7.1.3. Can it be negative?
7.1.3.1. may be the right choice to make when valuing firms in industries that are being phased out because of technological advances, or where an external and critical customer is scaling back purchases for the long term.
7.1.4. Characteristics
7.1.4.1. less risky
7.1.4.2. more debt
7.1.4.3. lower excess returns
7.1.4.4. reinvest less
7.1.5. Variables to adjust
7.1.5.1. Equity Risk
7.1.5.1.1. high growth = higher betas
7.1.5.2. Project Returns
7.1.5.2.1. In stable growth, it becomes much more difficult to sustain excess returns
7.1.5.3. Debt Ratios and Costs of Debt
7.1.5.3.1. As firms mature, their debt capacity increases.
7.1.5.4. Reinvestment and Retention Ratios
7.1.5.4.1. Stable growth firms tend to reinvest less than high growth firms
7.1.5.4.2. Expected Growth Rate = Retention ratio * Return on Equity
7.1.5.4.3. Expected Growth rate = Reinvestment rate * ROIC
7.1.5.5. Return on Equity
7.1.5.5.1. Return on equity equal to the cost of equity in stable growth
7.1.6. Fórmula
7.1.7. Periods
7.1.7.1. Two Stage
7.1.7.1.1. The firm will be maintain its high growth rate for a period of time and then become a stable growth firm abruptly
7.1.7.2. Three Stage
7.1.7.2.1. The firm will maintain its high growth rate for a period and then have a transition period where its characteristics change gradually towards stable growth levels
7.1.7.3. n-Stages
7.1.7.3.1. The firm’s characteristics change each year from the initial period to the stable growth period; this can be considered an n-stage model.
7.2. Liquidation Value
7.2.1. Book value of the assets, adjusted for any inflation during the period
7.2.2. Earning power of the assets
7.2.2.1. The estimated value of debt outstanding in the terminal year has to be subtracted from the liquidation value to arrive at the liquidation proceeds for equity investors.
7.2.3. Cash Burn Ratio
7.2.3.1. Estimated as the cash balance of the firm divided by its earnings before interest, taxes and depreciation (EBITDA).
7.2.4. Probability of Distress
7.2.4.1. The other way of estimating the probability of default is to use the bond rating for the firm, if it is available.