Economics if Demand falls, Supply will will fall, and employment falls falls Keynes: Sticky prices, so if Expenditures GDP: Consumer Spending, Private Investment, Government expenditures Real GDP = Planned C + I + G + NX
Planned consumption is determined primarily primarily by disposable income. Rise in income allocated to consumption by MPC. NX, net exports, decrease as income rises because imports rise. If Actual Expenditures < Planned Expenditures, Expend itures, then inventory exists, employees will be laid off, output will fall. Thus, investment is the the primary source of instability. If the economy is at less than full employment, then increase spending. If I get an additional $1,000, I spend MPC*$1000 with a group of vendors. This group then spends (MPC*$1000)*MPC and so on. The expenditures multiplier multiplier is thus thus expressed: M = 1 Aggregate spending increases by M*1000 (1 – MPC) LRAS AD2
AD3
SRAS AD1 GDPf At AD1, increased expenditures increase output. At AD2, increased expenditure increases prices. Multiplier shows why small changes in C, I, G have such huge effects. If expansionary fiscal policy is used to thwart recessions, some argue that budget deficits lead to higher interest rates rates and crowd out private investments. investments. Keynesians argue that there are excess loanable funds. Then again, this excess could be from foreign sources which causes the dollar to rise and then raises the value of imports and decrease the value of exports. Classical / Supply-Side: Demand falls then Wages fall, Supply is constant, and Employment is constant Resource Cost-Income Approach: Employee Compensation, Proprietor’s Income, Rents, Corporate Profits, Interest Income, Indirect Business taxes, Depreciation, Net income of foreigners Expansionary fiscal policy such as a tax cut will be saved by consumers in anticipation of a future tax hike. This savings increases the supply supply of loanable funds leaving interest interest rates unchanged.
Automatic stabilizers ensure deficits in a recession and surpluses during booms an d, thus, mitigate policy lags. The three main are Unemployment Unemployment Compensation, Corporate Profit Taxes, Progressive Personal Income Taxes. Supply-siders say that taxes should be cut to stimulate investment and savings, more working, and a reduction in the use of tax shelters. Money & Banking 3 Fed Tools: Fractional Reserve System, Open Market Market Operations (Buy & Sell Treasury Instruments), Discount Rate M1 – currency in circulation, checkable deposits, traveler’s checks M2 – M1 + saving deposits de posits + time deposits (<$100k) + money market mutual fund
Commercial Banks, S&L’s, Credit Unions. Bank reserves – vault cash and deposits held at the Fed. Potential Deposit Expansion Multiplier =
1 Required Reserve Ratio Actual DEM < potential if some decide to hold currency and if banks bank s fail to loan out excess reserves. Expansionary monetary policy: Fed buys T-bonds which raises bond prices and drives down yields (rates). Lower real rates cause more more investments to be profitable, profitable, hence raising investment spending. AD shifts to the right. In the short run, investment, output, and prices increase. Lower real rates depreciate the the dollar which increases exports. Lower rates cause stocks, bonds, and houses to rise in price, thus increasing personal wealth. (Money Supply) * (Velocity) = GDP = (Price) * (Real Output) Thus, if money supply increases while velocity and quantity is fixed, p rices must rise. P = MV/Y In the long run, nominal rates rates rise because expected inflation rises. N = I + R If a policy change is fully anticipated, contracts reflect reflect higher prices. Thus, prices and rates increase, causing no gain in output. Individuals who use adaptive expectations will tend not to anticipate policy changes, thus leading to a change in output over the short-run but only a change in prices over the longrun. Inviduals using rational expectations will tend to anticipate policy changes, thus affecting prices over both the short- and long-run. Problems with monetary or fiscal activism: Recognition Lag, Implementation lag, Impact Lag
Implementation lag is shorter for monetary than it is is for fiscal policy. Tax policy has shortest impact lag. Real Wage = Nominal Wage / Price Level Reduction in real wages occurs if higher prices are unexpected. If higher prices are fully anticipated, individuals demand a higher nominal wage, leaving the real wage unchanged. When actual inflation exceeds expected inflation, unemployment drops below the natural rate and vice versa. Stagflation. Producer Surplus = Σ (Actual Price – minimum acceptable price) Supply curves are elastic when producers can add resources inexpensively. Changes in resource prices: higher costs shift supply curve left (reduce supply and increase prices) Changes in technology: lower cost techniques increase supply (shift curve right) Short run – shifts along the supply curve only Long run – supply curve itself shifts Price Elasticity = Percentage Change in Q / Percentage Change in P Percentage Change = Change in Value / Average Value Perfectly elastic = horizontal demand curve Perfectly inelastic = vertical demand curve Slope of demand curve is not the the price elasticity. Price elasticity is higher at higher prices. Demand generally more elastic in the long run. Unitary price elasticity – total expenditures on a good are constant because a change in price equals the change in quantity demanded at all price levels. For an individual firm, revenue is maximized at UPE. Monopolistic (differentiated, branded commodities) competition differs from pure competition (un-branded commodity markets) in that the monopolistic competitor faces a downward sloping demand curve. Also, in long-run equilibrium, the monopolistic monopolistic competitor does not produce at the the quantity where ATC is minimized. minimized. Monopolistic competitors (price searchers) maximize profits by producing where Marginal Revenue equals Marginal Cost and charges price from the demand curve. In the short run, P>ATC. In the long-run, P = ATC because of low barriers to entry.
Monopolists also set MR=MC but due to high entry barriers, positive economic profits can exist in the long-run. Demand curve must lie above the ATC curve at the optimal quantity point. Monopolists are price searchers with imperfect information information about demand and must experiment with prices. Oligopoly is a small small # of sellers. Interdependence among competitors (decisions made by one firm, affects D, P, Profits of others). Large economies of scale. Significant barriers to entry. Products may be similar or differentiated. Collusion Price increases, output decreases Competition P = LRATC Demand curve facing oligopolist is very elastic or flat so a small decrease in P, leads to a large change in Q. Game Theory: Prisoner’s dilemma Natural Monopoly – Economies of scale are a re so pronounced that Government imposes the price ceiling of Average Cost to ensure normal (zero) economic profit. profit. But this gives the monopolist no incentive to reduce costs and maintain quality. Demand for productive resources is a derived demand since demand for the final good it produces determines demand for the resource. resource. In the short run, if if there are no good substitutes for a resource and demand for the final good is inelastic, then demand for the resource is inelastic. If a resource has few other uses, then it has low resources mobility mobility and a low elasticity of supply…in the short-run. short-run. Demand for a resource also increases as its productivity increases. Marginal Product = MPL = Change in Output / 1 extra unit of labor Marginal Revenue Product = MRPL = Change in Revenue / 1 extra unit of labor If the firm is a price taker: MRPL = MPL * P, where w = Price of Labor, and P = Price of the final good The profit maximizing firm will increase the use of each resource until the MRPL = W of last resource unit. MPA PA
=
MPB PB
=
MPC PC
cost-minimization
For a given firm that holds all other othe r resource inputs constant, a curve depicting the marginal revenue product will be identical to the firm’s demand curve for the resource. Comparative advantage is the ability to produce a good at a lower opportunity cost than others can produce it. Absolute advantage refers to using using the fewest resources to to produce a product.
Domestic Supply
P
WorldPrice + Tariff
A
B
C
Quota Supply
A – Domestic Producers Gain B, D – Deadweight Loss A, B, C, D – Consumer Loss C – Government Revenue
D
Domestic Demand Q Quotas are worse than tariffs because government gets ge ts nothing, foreign producers gain from higher prices. Less-developed countries artificially inflate the exchange rate on their c urrency, increasing its costs in exchange markets and adding to the cost of exports. Without exports, a country cannot get foreign exchange for imports. Country’s Balance of Payments BOP = Current Account + Capital Account Acc ount + Official Reserve Account = 0 What will cause a nation’s currency to appreciate? • Slow growth of income relative to one’s o ne’s trading partners will cause imports to lag behind exports • Rate of inflation lower than those of trading partners • Domestic real interest rate that is greater than real interest rates abroad. Current Account is the exchange of merchandise goods, services, investment income, and unilateral transfers (gifts (gifts to and from other nations). All other factors constant, a deficit balance on the current account implies that there is an excess supply of dollars in the Foreign Exchange markets. Hence, the dollar dollar should depreciate. An unanticipated shift to expansionary monetary policy will lead to more (1) rapid economic growth, (2) an accelerated inflation rate, and (3) lower real interest rates. (1) leads to more imports, (2) to fewer exports, and (3) to reduced foreign investments. The weaker $ then leads to more exports more than offsetting the move to deficit in the capital account. An unanticipated shift to a more restrictive fiscal fiscal policy will result result in budget surpluses. Reduced aggregate demand causes an economic slowdown and lower inflation. These discourage imports and encourage exports, resulting resulting in a stronger $. Less demand for borrowing weakens the $. So results conflict. conflict. Expansionary fiscal policy coupled with restrictive monetary policy causes higher real interest rates, net capital inflow, appreciation of currency, and a deficit in the current account. J-curve: When a country’s currency depreciates, the current account may worsen worsen while the country continues to buy the previously contracted for (but now higher-priced) imports instead of domestic goods.
Forward markets are used by traders (import/export) and hedgers (home currency value of foreign-currency denominated assets) to manage currency risk associated with conducting business. Arbitrageurs use them to take advantage of differing interest interest rates. Speculators buy and sell currency and provide liquidity. Spot Quotations Interbank Dealer Quotes: American Terms – USD/FC & European Terms – FC/USD Non-bank Public Customer: Direct Quotes – DC/FC & Indirect Indirect Quotes – FC/DC Banks make money on bid-ask spread, not on commissions on transactions. transactions. It is a function of breadth (number of market participants) and depth (volume of purchases) of the market for the currency as well as the currency’s price volatility. % spread = ask price – bid price (100%) ask price Forward Discount = Forward Rate – Spot Rate = negative Forward Premium = Forward Rate – Spot Rate = positive Forward Rate = Spot Rate + Swap Rate Make sure all quotes are Direct, DC/FC!!!! To annualize a premium for 90-day rate, multiply by 4. Forward differential = Forward Premium / Spot Rate Interest Rate Parity r domestic domestic = r foreign foreign =~ forward exchange rate – spot exchange rate spot exchange rate forward (DC/FC) = spot(DC/FC) [1 + r domestic domestic] [1 + r foreign foreign] 1 – r D – (1+r F)(forward rate) = covered interest differential spot rate If negative: borrow domestic If positive: borrow foreign *Assets are equal risk. *No transaction Costs. *Covered interest differential is zero.
Chebyshev’s Inequality: Inequality: 1 – 1/k 2 = % of sample population within k stdev’s of mean Kurtosis Leptokurtic Normal
Leptokurtic: greater percentage close to the mean or far from the mean (greater risk) than Normal. Platykurtic – flatter than a normal distribution. Relative skewness (sk) = 1 Σ(xi – x)3 N s3 Excess Kurtosis = 1 Σ(xi – x)3 - 3 N s3 S = sample standard deviation Semi-logarithmic scales use an arithmetic scale on the ho rizontal axis and a logarithmic scale on the vertical axis. Then equal vertical movements reflect equal percentage changes. Move from 10 to 20 and 1000 to 2000 would be identical: 100%. Bayes formula is used to update a given set of prior probabilities for a given event eve nt in response to the arrival of new information. Updated Probability = Probability of new information given the e vent Prior Probability Probability of Event * Unconditional Probability of new Info Using Bayes’, we can compute P(B⎥A) given P(B), P(A⎜B), and P(A⎢Bc) Var(x) = σ2(x) = ΣP(xi)[xi - E(x)2] Cov(Ri, Rj) = E{[Ri – E(Ri)]*{Rj – E(Rj)} Cov(Ra, Ra) = var(R A) Stock and put option on a stock have negative Covariance. -1 <= Corr(Ri, Rj) = cov(Ri, Rj) <= +1 σRi * σRj var(x1r 1 + x2r 2) = E{[x1r 1 + x2r 2 – E(x1r 1 + x2r 2)]2} = E{[x1(r 1 – r 1) + x2(r 2 – r 2)]2] = E[x12(r 1 – r 1)2 + x22(r 2 – r 2)2 + 2 x1x2(r 1 – r 1)(r 2 – r 2)] var(x1r 1 + x2r 2) = x12E[(r 1 – r 1)2] + x22E[(r 2 – r 2)2] + 2x1x2E[(r 1 – r 1)(r 2 – r 2)] = x12var(r 1) + x22var(r 2) + 2x1x2cov(r 1, r 2) = x12σ21+ x22σ22+ 2x1x2σ12 = x12σ21+ x22σ22+ 2x1x2ρiσiσ j = w1w1cov(r 1, r 1) + w2w2cov(r 2, r 2) + 2 w1w2cov(r 1, r 2) An n-asset portfolio will have n “wi2Var(Ri)” terms and n(n-1)/2 2Wi@jCov(RjRk)
Labeling: n items that can each receive of k different labels.
n! (n1!)*(n2!)*…*(nk !) !)
Ex: Portfolio of 8 stocks 4 should be “long-term holds,” 3 “short-term holds,” 1 “sell” There are 8! = 40,320 total possible sequences that can be followed to assign the 3 labels to the 8 stocks. Since it does not matter which of the three stocks labeled “long-term” is the first to be labeled. Thus, number of ways to label the 8 stocks is 8! 4!*3!*1! If number of labels, k=2, then use u se the binomial formula, nCr = n! = # of ways to select r items from a set of n items when the order of (n-r)!*r! selection is not important. Ex: How many ways can 3 stocks be sold from an 8 stock portfolio? po rtfolio? nCr = n! = 56 (n-r)!*r! Permutation Formula: rPr = 1. 2. 3.
4. 5.
n! (n-r)! Multiplication rule of counting is used when there are two or more groups. The key is that only one item may be selected from each group. Factorial is used used with no groups. Only arrange n items n! ways. Labeling applies to 3 or more more sub-groups of pre-determined size. size. Each element of the group must be assigned a place, or label, in one of the three or more subgroups. Combination formula applies to only 2 groups of predetermined size. Look for the word “choose.” Permutation formula applies to only 2 groups of predetermined predetermined size. Look for a specific reference or order.
Binomial Distribution Binomial RV: # of successes in a given # of trials whereby the outcome is “success” or “failure.” The Binomial Distribution defines the probability of “x” success in “n” trials. p(x) = P(X=x) = # of ways to choose c hoose x from n, px(1-p) x where # of ways to choose x from n = nCr = n! = (n) “n choose x” (n-x)!*x! (x) p = probability of success on each trial E(x) = expected # of successes = np Var(x) = expected # of successes = np(1-p) Continuous Uniform Distribution P(x1≤X≤x2) = (X2 – X1)/(b-a) where a, b are lower and upper limits of the range. Probability density function for a continuous uniform distribution is f(x) = P(a=b
Standard Normal Distributions Z = observation – population mean = X - µ Standard deviation σ A lower combination of normally distributed random variables is normally distributed as well. Use a multivariate normal distribution. N means, n variances, ½ n(n-1) pair-wise correlations Shortfall-risk: portfolio falls short of a threshold. Safety-first rules monitor and control shortfall risk. 1. Minimize P(Rp < R L) 2. Maximize Sharpe Ratio: excess return over threshold return per unit of risk Y = ex where X~N(µ,σ2), e = 2.718 Lognormal Distribtuion
E(Y) = eE(X) + VAR(X)/2 , VAR(Y) = e2E(X)+VAR(X) - (eVAR(X) – 1) Continuously compounded HPR: r 0,1 0,1 = ln(1+R 0,1 0,1) = ln(S1/S0) Simple Random Sample Sampling error = sample mean – population pop ulation mean = x(bar) - µ 2 Where x(bar) ~ (µ,σ /n) for n ≥ 30 (Central Limit Theorem) is an unbiaxed estimator, consistent if σ2/n is minimized Stratified Random Sampling Population is stratisfied into subgroups, then a random sample is drawn from the subgroups based on the size of the subgroup relative to the population Zα/2 = 1.96 for 95% confidence intervals X(bar) ± Zα/2 * σ/√n, σ/√n = standard error Use student’s t-distribution when constructing confidence intervals based on small samples (n<30) from populations with unknown variance and (nearly) normal distributions. 1. defined by degrees of freedom, n-1, # of trials – 1 2. approaches ~N as n gets larger 3. less peaked than ~N with fatter tails 4. Confidence Interval: X(bar) ± tα/2 * s/√n
tα/2 = 2.045, for α = 5% or 95% confidence intervals and n-1 = 29 If the distribution is non-normal, but the variance is known, the z-statistic can be used as long as the sample size is large (n ≥ 30) If the distribution is non-normal, and the variance is unknown, the t-statistic can be used as long as the sample size is large (n ≥ 30) Beware biases that render samples non-random: Data-Mining, Sample Selection (Survivorship), Look-ahead, Time-Period Hypothesis Testing H0: µ ≥ 0 2-tailed (µ = 0, µ ≠ 0) Ha: µ > 0 State the Hypothesis Select the appropriate test statistic Specify the level of significance State the decision rule re: hypothesis Collect the sample and calculate sample stats Make a decision re: hypothesis Make a decision based on tests When the null hypothesis is discredited, the implication is that the alternative hypothesis is valid Test statistic = sample statistic – hypothesis value Standard error 2-tailed: Reject H0 if +1.96 < test statistic < -1.96 significance level = probability of a Type I error = 1-P(Type II) Type I error: rejection of the null hypothesis when it is actually true Type II error: failure to reject the null hypothesis when it is actually false One-tailed Reject H0 if test statistic > 1.645 = Z.05 p-value = Z-2.67 = .0038 < .05 = α, reject H0 To reject the null hypothesis, look for big test statistics and small p-values p-value is the probability that lies above (below) the computed test statistic for upper (lower) tail tests t-distribution is more conservative and thus more difficult the reject the null hypothesis than the z-. Use the t- if the population variance is unknown and 1. sample is large large (n≥30) 2. sample is small but distribution is ~N tn-1 = X(bar) - µ0 s/√n
z-statistic = X(bar) - µ0 for unknown population variance and large size, else standard deviation is σ s/√n Tests of differences between means (used when samples are independent) H0: µ1 - µ2 = 0 vs Ha: µ1 - µ2 ≠ 0 H0: µ1 - µ2 ≤ 0 vs Ha: µ1 - µ2 > 0 H0: µ1 - µ2 ≥ 0 vs Ha: µ1 - µ2 < 0 Use t-tests for each population Type I Error: Reject the null hypothesis when it is actually true Type II Error: Fail to reject the null hypothesis when it is actually false Significance level (α = .05) is the probability of making a Type I Error. Power of the test = 1 – P(Type II) error ↓P(Type I Error) ↑P(Type II error) Power of the test declines Unknown Variances: Assumed Equal t = (x1 – x2) – (µ1 - µ2) where s p2 = (n1 – 1)s12 + (n2 – 1)s22 (s p2/n1 + s p2/n2)½ n1 + n2 - 2 Unknown Variances: Not Assumed Equal t = (x1 – x2) – (µ1 - µ2) where df = (s12/n1 + s22/n2)2 (s12/n1 + s22/n2)½ (s12/n1)2 + (s22/n2)2 n1 n2 Paired differences: Tests of Mean Differences H0: µd = µd0 vs. Ha: µd ≠ µd0 Where µd = mean of population of paired differences µd0 = hypothesized mean (commonly zero) t = d(bar) - µ d0 where d(bar) = sample mean difference = (1/n)Σdi sd(bar) sd(bar) = standard error = s d/√n sd = sample standard deviation = [Σ(di – d)2]½ n–1 Used when samples are not independent but allow paired comparisons Hypothesis testing for a single population variance H0: σ2= σ20 vs. Ha: σ2≠ σ20 Chi-Square test statistic χ 2n-1 = (n-1)s2
σ2 0
Equality of Variance of 2 independent, ~N distributed populations H0: σ2= σ20 vs. Ha: σ2≠ σ20 F = s12/s22 where s1 > s2, so F > 1 Use n1 – 1 and n2 – 1 for degrees of freedom.
0 2.98 2.5% = for a 5% 2-tailed test test (only use 1 tail) tail) since F-test bounded by zero Compounding FV = PV(1+r/m)m where m = payments per year and r = annual interest rate FV = PVert, for continuous compounding EAR = (1 + periodic rate)m – 1 Testing for significance of correlation coefficient H0: ρ = 0 vs. Ha: ρ ≠ 0 t = r √n-2 where r = sample correlation df = n-2 √1-r 2 Correlation captures the strength of linear relationships between 2 variables Least-Squares Regression Line Yi = b0 + b1Xi + εi explained by Y i = b0 + b1Xi SSE = Σ(Yi – Y )2 = Σ(Yi – b0 - b1Xi)2 = Σεi2 b1 = cov(X, Y) ; b0 = Y i - b1Xi Independent Variable is uncorrelated with error term. E(εi) = 0, homoskedastic (constant variance) Error terms are independently distributed and not auto-correlated SEE: Standard Error of the Estimate MSE = mean square error SEE = √Se2 = √(SSE/(n-k-1)) = √MSE Coefficient of Determination: % of total variation in the dependent variable is explained by the independent variable. R 2 = r 2 for one independent variable Total variation = Σ(Yi – Y(bar))2 = SST Unexplained variation = Σ(Yi – Y i)2 = SSE Explained variation = Σ(Y i – Y(bar))2 = SSR Variance = variation/(n-1) SST = SSE + SSR R 2 = SSR/SST = 1 – SSE/SST Hypothesis testing of Regression Coefficients a. Confidence Intervals using t-test df = n-k-1 where k is the # of independent variables b1 ± tcsb1 = confidence interval where sb1 = standard error of the coefficient t = b1 - b1
sb1 Confidence Intervals for Predicted Values Y ± tcs f = Y(hat) - tcs f < Y < Y(hat) + tcs f Where df = (n-2) and s f = standard error of the forecast (difficult to calculate) F-statistic H0: b1 = b2 = b3 = …. = b = bk = 0, Ha: at least 1 bi ≠ 0 F = mean square regression, MSR = SSR/k Mean square error, MSE = SSE/(n-k-1) F-test, goodness-of-fit test, whether at least one independent variable in the set of independent variables explains a significant portion of the variation of the dependent variable. With only one independent variable, F-statistic equals t-statistic. Non-stationarity: regression relations change over time. Adjusted R 2: R a2 = 1 – [(n – 1)/(n – k – 1) * (1 – R 2)] Breusch – Pagen chi square test for heteroskedasticity: BP = n*R2 Durbin – Watson for serial correlation: DW = Σ(εt - εt-1)2 / Σε2t = 2(1 – r) Nominal risk-free rate = (1 + real r f f)*(1 ) *(1 + inflation) – 1 Nominal risk-free rate ~> real r f f + i (+ risk premium = 0) 1+ nominal required rate = (1 + real rate) * (1 + expected inflation) * (1 + risk premium) Systematic Beta Risk cannot be diversified away. Security Market Line E(R) = Rf + β(Rm – Rf), β = systematic risk 1. Movements along the line mean the security’s risk has changed 2. Change in the slope of the SML means that investors have changed their risk premium per unit of market risk. If an increase in the premium, the SML will rotate counterclockwise about the risk-free rate. 3. Change in capital market conditions and the rate of inflation will cause the SML to experience a parallel shift. Upward for increasing inflation. inflation. Downward for decreasing. Asset Allocation Policy: Asset Classes Policy: Weighting Timing: How far can the manager deviate de viate Selection: of securities
σ12 = cov(r 1, r 2) = Σ pi(R i,1 i,1 – E[R 1]) * (R i,2 i,2 – E[R 2]) = Σ(R t,1 t,1 – R 1(bar)) * (R t,2 t,2 – R 2(bar))
N var(x1r 1 + x2r 2) = x1 E[(r 1 – r 1) ] + x22E[(r 2 – r 2)2] + 2x1x2E[(r 1 – r 1)(r 2 – r 2)] = x12var(r 1) + x22var(r 2) + 2x1x2cov(r 1, r 2) = x12σ21+ x22σ22+ 2x1x2σ12 = x12σ21+ x22σ22+ 2x1x2ρiσiσ j = w1w1cov(r 1, r 1) + w2w2cov(r 2, r 2) + 2 w1w2cov(r 1, r 2) 2
2
Introduction of a risk-free asset changes the Markowitz efficient frontier from a curve into a straight line called the Capital Market Line. r c = wr p + (1 – w)r f f ; E(r c) = wE(r p) + (1 – w)r f f = r f f + w[E(r p) - r f f ] E(r p) - r f f is the risk premium σc = wσ p since σf = 0 E(r c) = r f f + σc[E(r p) - r f f]
σ p
(Jensen’s) α = (r I - r f f ) - βi(R M - r f f) Security Market Line: α = Rs – (Rf + β(R M) ) E(Ri) = Rf + (E(Rm) – Rf)* βi Asset with E(R) (given our forecasts of future prices and dividends) to identify undervalued assets and create the appropriate trading strategy βI = covi,m = (σ1) * ρi,m
σ2m
σm
1. Costs can’t be estimated Completed Contract (conservative, less stable earnings) 2. Incomplete Earnings Process and costs can be estimated Percentage of Completion Method (approximates sales basis) 3. Use Cost-Recovery for sales complete with contingencies and revenue either assured or not. Similar to Completed Contract in in that income and revenue are recognized when the contract is complete 4. Installment Sales: Use when earnings process is complete but revenue is not assured. 5. Sales Basis: Goods provided upfront and collection very likely. Change prior years’ financial statements if: a. Change from LIFO to another method b. Change to or from the Full-Cost Method c. Change to or from the Percentage-of-Completion Pe rcentage-of-Completion Method d. Any change just prior to an IPO e. Distinct operation is discontinued, changes occur below b elow the line Percentage of completion capitalizes “Construction in Progress” = Construction in Progress – Cumulative Advance Billings 0 Asset, < 0 Liability Liabilities will most likely be greater under the completed contract method compared to the percentage of completion method. Cash collections = sales – increase in A/R Cash Inputs = COGS + Increase in Inventory – Increase in A/P
Direct Method
Cash Expenses = Wages – Increase in Salaries Payable Cash Interest = Interest – Increase in Interest Payable Cash Taxes = Taxes – Increase in Taxes Payable – Increase in Deferred Taxes Indirect Method NI + Depreciation – Gain from Sale of PPE + Increase in A/R + Increase in Inventory – Increase in A/P – Increase in Salaries Payable – Increase in Interest Payable – Purchase of PPE (+ Sale of PPE) + Debt Issue + Stock Issue – Dividends Dividend s + Increase in Dividend Payable + Increase in Deferred Taxes FCF = Cash Flow from Operations – Capital Spending + Sale of o f fixed assets Basic EPS= net income – preferred dividends Weighted average # of common shares outstanding Weighted Average # of shares outstanding (at year-end) = = (# of shares at the beginning of the year)*(12 months)*(1+% stock dividend) + (# of shares issued at time x [before stock dividend]) * (12-x months)* (1+% stock dividend) - (# of shares repurchased at y) * (12 – y months) If strike price of the warrants < average share share price, warrants are dilutive. dilutive. Complex EPS denominator increases by (# of warrants) * (1 – Strike Price) Price) Avg Market Price # of shares issued to satisfy warrants proceeds used to repurchase shares Use LIFO when examining profitability or cost ratios and FIFO values when examining asset or equity ratios. Capitalize interest on debt used to purchase an asset. Add weighted average of interest on other non-asset specific debt on any cost not covered by asset-specific debt used in purchase. Analyst should expense interest and deduct it from depreciation expense of prior years. No CF impact.
Analysis of Inventories GAAP requires inventory valuation at lower of cost or market. COGS = purchases + beginning inventory – ending inventory Rising Prices: LIFO COGS > FIFO COGS LIFO NI < FIFO NI & LIFO Inventory < FIFO Inventory LIFO Current Ratio (CA/CL) < FIFO Current Ratio (CA/CL) LIFO Inventory Turnover (COGS/Avg Inventory) < FIFO By decreasing inventory to levels below normal, firm can proclaim high profit in a LIFO liquidation. FIFO provides the most useful estimate of the inventory value and LIFO the most useful estimate of COGS. LIFO reserve = InvF – InvL 1. COGSF = COGSL – change in the LIFO reserve 2. purchases = EIL – BIL + COGSL EIF = EIL + LIFO reserveE BIF = BIL + LIFO reserveB COGSF = purchases + BIF – EIF
Depreciable Lives and Salvage Value
Earnings can be manipulated via useful life and salvage value estimates e stimates as follows: • The utilization of a longer useful life will result in higher net asset value, lower depreciation expense and increased net income over the years being applied. Management can then write- down the overstated assets in a restructuring. • Management might also write down assets, taking an immediate charge against income, and then record less future depreciation expense ex pense based upon the written-down assets. This results in higher future net income in exchange for a one-time charge to current net income. • A company estimates the salvage value of an asset at the time the asset is placed into service. For the SL and SYD methods, salvage value is deducted from the purchase price to calculate ar 4 the amount that is depreciated each year. The higher the salvage value, the lower the amount of depreciation expense that is being applied each year. Consequently, management can increase reported income by estimating higher salvage values for its assets. This will also result in an overstatement of loss when the asset is retired. Pensions and other Employee Benefits Calculation of Compensation Expense 1. Intrinsic Value Method (APB#25): Stock Compensation Expense = Market Price – Exercise Price on measurement date SCE expensed equally over the service period of the stock options, ie, the time between the grant date and the vesting date.
2.
Fair Value Method (SFAS #123) uses an option pricing model to determine compensation expense on the grant date. The CE is expensed over the service period.
Tax Savings from the effect of expensing e xpensing options in prior years should be recorded as a deferred tax asset offset by a reduction in retained earnings and an increase in paid-incapital. Adjust the # of shares outstanding to reflect any dilution from the exercise of the options that are at- or in-the-money. Because firms do not recognize compensation expense related to granting options, they record a tax deduction related to their exercise directly to the shareholder’s equity account. This tax benefit is also also included as a component in the operating operating Cash Flows. Cash Flow is not immediately affected by the granting of options. Analysis of Intercorporate Investments Recognize dividends and interest in the the year they are earned. Carrying values are different under three different accounting treatments: a. Cost Method recognizes changes in the market values v alues upon sale of securities b. Market Method recognizes changes in the market values in the period in which they occur c. Lower of cost or market method recognizes declines in market value in the period in which they occur
3 categories of securities secu rities classification a. Debt securities held-to-maturity are securities that a company ahs the positive intent and ability to hold to maturity. These securities are carried at amortized cost and cannot be sold prior to maturity except under unusual circumstances. b. Debt and equity securities available-for-sale may be sold to address the liquidity and other needs of a company. They are carried at fair market value. Unrealized gains and losses are excluded from income but reported (net of deferred income tax) as a separate component of shareholders’ equity (other comprehensive income). c. Debt and equity trading securities are securities acquired for the purpose of selling them in the near term. term. These are measured measured at fair fair market value. Unrealized gains and losses, as well as interest income and dividends, are reported in income. Management can re-classify securities between classifications at current fair market value and can recognize any unrealized gains or losses in income.
B/S (carrying) value
Recognized as income
Security Classification Trading Available-for-Sale Fair Market Value Fair Market Value with unrealized G/L in equity • Dividends • Dividends • Interest • Interest • Realized G/L • Realized G/L • Unrealized G/L
Held-to-Maturity Amortized Cost
• Interest • Realized G/L
Although the pre-tax income for available-for-sale and held-to-maturity securities is the same, the book rate of return varies because unrealized gains and losses are included in the carrying value of the securities under the available-for-sale method, while the cost of the securities is used under the held-to-maturity method.
Unrealized Gains Sales/Avg WC Sales/Avg Tot Asset Unrealized Losses Sales/Avg WC Sales/Avg TC
Unrealized Gains CA/CL
Trading
Activity Ratio Effects Available-for-Sale
Lower Lower
Lower Lower
Higher Higher
Higher Higher
Higher Higher
Lower Lower
Trading
Liquidity Ratio Effects Available-for-Sale
Higher
Higher
Held-to-Maturity
Held-to-Maturity Lower
Unrealized Losses CA/CL
Unrealized Gains Assets Equity Debt/Tot Capital Debt/Equity Unrealized Losses Assets Equity Debt/Tot Capital Debt/Equity
Lower
Lower
Higher
Trading
Leverage Ratio Effects Available-for-Sale
Higher Higher Lower Lower
Higher Higher Lower Lower
Lower Lower Higher Higher
Lower Lower Higher Higher
Lower Lower Higher Higher
Higher Higher Lower Lower
Profitability Ratio Effects Trading Available-for-Sale Unrealized Gains Pretax margin Profit margin Return on Assets Return on Equity Unrealized Losses Pretax margin Profit margin Return on Assets Return on Equity
Held-to-Maturity
Held-to-Maturity
Higher Higher Higher Higher
Higher Higher Higher Higher
No change No change No change No change
Lower Lower Lower Lower
Lower Lower Lower Lower
No change No change No change No change
Mark-to-Market Investment Return Market Valuation Adjustment = Cost of Portfolio – FMV (Portfolio) Unrealized holding gains and losses = MVA Change in MVA = MVA (Current Period) – MVA (Prior Period) Mark-to-Market Investment Return = (Current Period) Realized Gains/Losses/Dividends/Interest + Change in MVA
Ownership Less than 20% 20-50% Greater than 50%
Criterion (degree of influence) No significant Influence Significant Influence Control
Method Cost or market Equity Consolidation
Joint Venture Joint Venture Participant Proportionate Consolidation Under the equity method, the proportionate share of the investee’s income is included in the parent’s income. The parent receives dividends (cash) and lowers lowers the investment account by a like amount. The parent’s reported income is not affected by changes in the market value of the investee, unless the value decline is considered permanent, or realized losses are incurred incurred upon sale of the investment. The parent also reports a proportionate share of the investee’s investee’s net assets. Capital gain on sale is based on cost for tax purposes. The portion of the investee’s income owned by the parent increases the parent’s investment in investee. Investment in Sub = Σ(Investments in Sub) + Σ(share of sub’s income) – Σ(share dvdnds) In consolidated reporting, two firms are presented as one economic entity with all income of the affiliate (less any minority interests) is reported on the parent’s income statement. Income is higher under the equity method than under the cost or market market method. The remainder owned by other investors is accounted for as a liability by use of the minority interest account and is computed as (1 – parent’s ownership) times subsidiary’s net worth. Each account consists of the sum sum of the corresponding accounts from from each of the individual firms, less any intercompany transactions (revenues and COGS are bo th lowered by the proportionate value of intercompany transactions and A/R and A/P are adjusted). Do not add the equity accounts together. Current Assets = Parent’s CA + Parent’s share of Sub’s CA - year’s investment in S ub Total Assets = Parent’s TA + Parent’s share of Sub’s TA - year’s investment in Sub Net Income = Parent’s NI + Sub’s NI – Minority Income Interest COGS = Parent’s COGS + Parent’s share of sub’s COGS – Parent’s share of sub’s intercompany revenues Consolidation and the equity method both result in the same net income and the same net worth. If the subsidiary is profitable, the equity method reports better results. results. Proportionate Consolidation “Equity in JV” is a Revenue Account equal to (ownership share) * (JV’s net income) “Investment in JV” is a B/S Account equal to (ownership share) * (JV’s equity) Reportable segment is a component of an enterprise that has at least 10 percent of one of the following Revenues, operating profit or loss, combined co mbined identifiable assets of the enterprise as a whole. Include operating profit, identifiable identifiable assets, intersegment sales sales and sales to unaffiliated customers, interest income and expense, expenses related to depreciation, amortization, or depletion, unusual or extraordinary items, income tax expense, capital expenditures. Earnings of the the segments (after (after eliminating intersegment intersegment transactions) can be added up to get the earnings of the consolidated firm. firm. Limitations of segment cash flow data include lack of detailed information on liabilities and on cash ca sh flow data, and operating income is calculated before interest payments and includes intercompany transfers which may include transfer pricing. ANALYSIS OF BUSINESS COMBINATIONS The Purchase Method The key attributes of the purchase method are:
• The transaction is structured so that the liabilities and a ssets of one company are assumed another company. • The purchase price paid must be equated to the fair market value va lue of the assets acquired less the fair market value of the liabilities assumed. If the value of the tangible assets minus the fair market value of the liabilities is less than the purchase price, then the excess purchase price is attributed to intangible assets. In most cases goodwill (an intangible asset) is also created. • The operating results of the acquired company are included in the income statement of the purchaser from the date of acquisition ac quisition onward. Operating results occurring before the acquisition are not restated, resulting in pre-and post-acquisition cash flows that are nor comparable. The Pooling of Interests Method The pooling of interests method combines the ownership interests of two companies, and V the participants as equals—neither firm acquires the other (intuitively, you can think of the purchase method as an acquisition and the pooling method as a merger). The pooling method similar to the consolidation method discussed in the previous topic review. Assets and liabilities of the two firms are combined (and any intercompany accounts are eliminated). Major attributes of the pooling method are: • The two companies are combined using historical cost accounting values. • Operating results for prior periods are added together. • Ownership interests continue, and former accounting bases are maintained. Note that fair market values play no role in accounting for a business combination using the pooling method—the actual price paid is suppressed from the balance sheets and income statements. Target’s common equity is eliminated. Post-acquisition value of common equity of acquirer = pre-acquisition value + equity issued to finance transaction (- amount attributed to expensed R&D) US GAAP Results for the consolidated firm reflect combined results of the combination d ate Recognize target intangible assets of target such as software development costs, licenses, in-process R&D. Then, amortize these (except R&D for US GAAP) on income statement. Goodwill is not amortized under US GAAP. Increase in inventory is expensed in COGS. IPR&D and goodwill are amortized over 4 & 10 years respectively under IASB GAAP. Sales growth is smaller under pooling because past results are re-stated as if the combination had existed all along. Shareholders of the acquired company do not recognize a gain or loss on the exchange of shares. They use the old basis in the shares of the acquired acquired company as the basis for the shares they receive.
Under IASB Purchase Method depreciate FMV of PPE over its remaining useful life. Interest expense related to acquired company’s long-term debt will increase if the debt’s market value is lower than book, because the difference between FMV of the long-term debt and its par value must be amortized as interest expense. Defined Contribution Plan Liability accrues to the employing firm. Defined Benefit Plan More complex, because management must calculate the value of plan assets and liabilities based on estimated of the future changes in the relative values of the plan assets and liabilities are reflected on the firm’s financial statements, typically as a net pension expense on the income statements and a net pension liability or asset on the balance sheet. A. Pay Related vs. Non-Pay Related Pension Plans 1. Non-Pay, benefits not based on compensation 2. Pay based on employee’s future compensation or average compensation over career. B. Pension Benefit Obligation Measures 1. Projected Benefit Obligation (PBO) is the PV of all future pension benefits earned to date, based on expected future salary increases. 2. Accumulated Benefit Obligation (ABO) is the PV of all future benefits based on current salary levels, ignoring future increases. This is relevant if the company expects to liquidate and pay off its obligations. 3. Vested benefit obligations (VBO) is the amount of the ABO to which the employee is entitled based on the company’s vesting schedule. Pension Fund Terminology Service Cost – change in the PBO attributed to employee efforts during the year (i.e., the actuarial present value of pension benefits earned during the year). Recurring expense which increases plan obligations. Interest Cost – Increase in the PBO due to the passage of time. Beginning PBO * Discount Rate Actual Return on Plan Assets -- determined by the dividend and interest income and capital gains and losses of the investments held by b y the plan. Expected Return on Plan Assets – assumed rate of return that will be earned in the long run. Prior service cost and related amortization: change in PBO that results from an amendment to the pension play. result from Net gains and losses and related amortization amor tization: Liability gains and losses result changes in actuarial assumptions (changes in the discount rate and rate of compensation increase) or the composition of plan participants (eg, an increase in the expected post-
retirement life span span increases the PBO). Asset gains and losses result from differences differences between the actual and expected return on plan assets. Transition Liability and Related Amortization: asset or liability amount that was created when FAS No. 87 8 7 was first applied, usually 1987. Contributions are payments made by company or participants into the pension account. Benefits paid are payments made from the pension account to retirees. Both the plan’s obligations and assets decrease when the firm pays out benefits. Accumulated post-retirement benefit obligation (APBO) is the actuarial PV of all future non-pension post-retirement benefit (mainly healthcare) payments earned to date. Usually not related to employee salaries.
3 key assumptions: discount rate, rate of compensation compensation increase, E(R) on plan assets Summary of Off-Balance Sheet Impact of Pension Plan Assumptions Effect on… Higher Discount Lower Compensation Higher Expected Rate Rate Increase Return on Assets FMV of plan assets No effect No effect No effect PBO Decrease Decrease No effect Funded status Favorable Favorable No effect ABO Decrease No effect No effect Summary of Income Statement Impact of Pension Plan Assumptions Effect on… Higher Discount Lower Compensation Higher Expected Rate Rate Increase Return on Assets Service Cost Decrease Decrease No effect Interest Cost Increase No effect No effect Expected Return No effect No effect Increase Net Pension Cost Decrease Decrease Decrease A higher discount rate improves reported results by lowering PBO a nd service cost (though it does increase the interest cost) which lowers pen sion expense. Lower rate of compensation increase improves reported results by lowering future pension payments and, hence, PBO, and lowering service and interest cost. Higher expected return on plan assets will improve reported results by not affecting PBO/ABO, result in higher expected future pension assets and reducing net pension liability, and resulting in a lower pension expense. Lower Healthcare Inflation Rate improves reported results because it decreases the APBO and post-retirement benefit expense.
Funded Status = PBO – FMV Pension Plan Assets Net Pension Liability/Asset = PBO – Reported Value Pension Plan Assets FMV Plan Assets at end of the year = FMV Plan Assets at Beginning of the year + Employer Contributions + Plan Participant Contributions - Benefits paid to retirees during the year PBO at end of the year = PBO at Beginning of year + Service Cost + Interest Cost ± Amortization of actuarial losses or gains & plan amendments - Benefits paid to retirees during the year Net Pension Liability = Funded Status + Unrecognized actuarial losses (– Unrecognized actuarial gains) + Unrecognized prior service cost + Unrecognized prior transition obligation OR (- Unrecognized prior transition asset) ± Amortization of actuarial losses or gains & plan a mendments Pension Expense reporting is smoothed (made less volatile) by delaying recognition of plan amendments and losses and computing it on an expected rate of return rather than actual rate of return. To partially compensate for this smoothing, FASB requires requires that if the ABO exceeds the FMV of o f plan assets, at least that difference must show on the B/S as a liability. The existing pension asset or liability balance must be adjusted to this liability liability value by recording an additional pension liability called the minimum liability allowance. Any difference between the actual return on plan assets and the expected return is deferred and accumulated. Similarly with any liability gains and losses. This net amount is deferred to future years and is amortized when it exceeds the corridor amount of 10 percent of the greater of PBO or plan assets. If unamortized deferred and accumulated amount falls below the corridor amount, the amortization stops until the corridor amount is exceeded in a future year. Market-related value of the plan assets is an “average” asset value given by amortizing the differences between actual and expected return over a period of five years. Ending Market-Related Value = Beginning Market-Related Value + Expected Return on Plan Assets + Employer Contributions - Benefits Paid ± 20% of deferred asset gains/losses over past 5 years
Reported Pension Expense = Service Cost + Interest Cost – E(R) on Plan Assets + Amortization of unrecognized prior service costs + Amortization of deferred actuarial and investment losses
OR (- Amortization of deferred actuarial and investment gains) If we assume that deferred taxes will be reversed in the future, an increase in pension liability (or a decrease in a pension asset) will result in offsetting declines in deferred tax liabilities and equity. If we instead assume that the deferred taxes will not be reversed in the future, there will be no effect on deferred taxes and an increase in pension liability (or a decrease in a pension asset) will result in a decline in equity. Net Pension Liability – Funded Status = Increase in Liabilities Decrease in Deferred Taxes = Increase in liabilities * avg tax rate Decrease in Equity = Net Pension Liability – Decrease in Deferred Taxes Adjusted Operating Income = Reported Operating Income + Reported Pension Expense – Service Cost Adjusted Income Before Taxes = Reported Income Before Taxes + Reported Pension Expense – Adjusted Pension Expense Adjusted Pension Expense = Service Cost + Interest Cost – E(R) on Plan Assets Adjusted Income Before Taxes = Reported Income Before Taxes + Reported Pension Expense – Economic Pension Expense Economic Pension Expense = Service Cost + Interest Cost – Actual Return o Plan Assets
VARIABLE INTEREST ENTITY: partnerships, LLC’s, trusts, etc. that conduct business or hold assets, often passively (receivables or real estate), or as entities that service (R&D) for other companies. VIE is distinguished as a legal entity if: if: 1) Equity investors have no voting rights 2) Equity investors do not provide sufficient capital (<10%) to support the entity’s activities Variable interests are those that change with changes cha nges in the value of assets of the VIE. For example, management service contracts, leases, subordinated debt, equity, and options to purchase assets. VIE must be consolidated by the primary beneficiary if either: 1) A majority of the risk of loss from the VIE’s activities is borne by the company 2) A majority of the residual returns from the VIE are claimed by the company In situations where one interest receives a majority of the income and/or gains, while another is exposed to a majority of losses, the interest exposed to the losses must consolidate the VIE. The Primary Beneficiary consolidates VIE’s Assets, Liabilities, and non-consolidated interests at FMV. Assets transferred from from PB to VIE are at carrying value. Primary Beneficiary must disclose: 1) VIE’s nature, purpose, size, and activities 2) Collateral of the VIE, including the classification and carrying amount of the consolidated assets 3) Whether the creditors of the VIE have recourse rec ourse to the general credit of the consolidating primary beneficiary. Non-Primary Beneficiaries with significant interest must disclose the: 1) VIE’s nature, purpose, size, and activities 2) Date of initial involvement in the VIE 3) Nature of its involvement with the VIE 4) Enterprise’s maximum exposure to loss
Analysis of Multinational Operations Exchange rates can impact the reporting firm’s financial statements in two ways: 1) flow effects: those changes on flow variables such as a s revenue 2) Holding effects: those changes on assets and liabilities held Functional currency is that of the primary economic environment in which the foreign subsidiary generates and expends cash. Current rate is the exchange rate as of the b/s date. Average rate is the average exchange rate over the reporting period. Re-measurement is the translation of local currency transactions into the functional currency using the temporal method, with gains and losses flowing to the I/S. Translation is the conversion of the functional currency of a subsidiary into the reporting currency uses the all-current method with gains and losses flowing to the B/S. Temporal Method 1. Cash, Accounts Receivable, Accounts Payable, and long-term debt (defined as monetary assets and liabilities) are translated using the current rate. 2. All other assets and liabilities (non-monetary assets and liabilities) are translated at the historical rate. Hence, a major drawback of the temporal method is that you need to keep track of many different historical exchange rates. 3. Revenues and expenses are translated at the average rate. 4. Purchases of inventory and fixed assets are re-measured a t the historical rate as of the date of purchase. 5. Translation gain or loss is shown on the income statement. Under FIFO, inventory is at the exchange rate at which the purchases were made. Under LIFO, inventory is valued at the historical rate. To calculate COGS, use COGS = Beginning Inventory + purchases – ending inventory by converting these to the reporting currency FIFO LIFO Depreciating Local Higher Cogs Lower COGS Currency Lower Ending Inventory Higher Ending Inventory Appreciating Local Lower COGS Higher COGS Currency Higher Ending Inventory Lower Ending Inventory
All-Current Method (much easier to apply) 1. All income statement accounts are translated at the average rate. 2. All balance sheet accounts are translated at the current rate except for common stock, which is translated at the appropriate historical rate that applied when the equity was issued 3. Dividends are translated at the rate that applied when they were paid. 4. Foreign currency adjustment is included on the b/s in the equity section
The method used depends on the choice of functional currency. 1. The results of operations, financial position, and cash flows of all foreign operations must be measured in the designated functional currency. 2. Self-contained, independent subsidiaries whose O/I/F activities are primarily local will use the local currency as the functional currency. Subsidiaries whose operations are well integrated with the parent will use the parent’s currency as the functional currency. Subsidiaries that operate in highly inflationary (100%) environments will use the parent’s currency as the functional currency. 3. If the functional currency is the local currency, use the all-current method (translation). Else, use the temporal method (re-measurement). 4. Finally, a third currency may serve as the functional currency when a subsidiary is operating relatively independently in a market where the local currency, prices, and some costs are controlled or restricted. Either method may be used.
Account Nonmonetary assets Nonmonetary liabilities Common Stock Equity (taken as a whole) Revenues and SG&A Cost of Goods Sold Depreciation Net income
Rate used to translate Temporal Method Historical Rate Historical Rate Historical Rate Mixed* Average Rate Historical Rate Historical Rate Mixed*
Temporal Method Remeasure the B/S (Retained Earnings is a Plug) Derive the COGS using avg rate on purchases in (BI + P – EI) Derive Net Income Derive the I/S and translation G/L
account using the… All-Current Method Current Rate Current Rate Historical Rate Current Rate Average Rate Average Rate Average Rate Average Rate
All-Current Method Derive the I/S using the current rate
Derive Retained Earnings = Beginning Retained Earnings + NI – Dividends Compute the B/S, translation adj (PLUG) Translation adjustment is part of equity act
In a net asset position, the assets that are translated at the current rate exceed the liabilities that are translated at the current rate (since equity > 0). In a net liability position, the liabilities that are exposed to the current rate exceed the assets that are exposed to the current rate. Under the temporal method, A/P and longterm debt are translated at the current rate, but only cash and A/R are on the asset side. If you hold a net asset position, a depreciating foreign currency reduces the USD value of that net asset position. Thus, the translation adjustment adjustment will be negative. If you hold a net liability position, a depreciating foreign c urrency increases the USD value of the position. position. Hence, a positive translation translation adjustment.
1. In the all-current method, ratios are unaffected if the numerator and denominator are both derived from either the B/S or I/S because multiplying both by the exchange rate cancels out. 2. The all-current method results in small changes in ratios combining income statement and balance sheet data. 3. Temporal method results in ratios that are materially different. 4. An appreciating (depreciating) local currency creates the illusion of higher (lower) sales and earnings of foreign subsidiaries. 5. Translated sales, SG&A, and expenses are the same under both methods; COGS, depreciation, and net income income are not. Since COGS and depreciation are translated at the average av erage rate in the all-current method and at the historical rate in the temporal method, COGS and depreciation are lower, and profitability margins are higher, under the all-current method. 6. Translation gain increases the net profit margin under the temporal method, though less so than under the all-current method. 7. All-current method results in lower total assets and a higher total asset and inventory (due to measuring COGS at an average rate, rather than the historical rate, which is higher as a result of the depreciating currency) turnover than the temporal method. 8. If the local currency is depreciating, than COGS and depreciation will be lower in the all-current method. 9. Debt/total capital and debt/equity ratios are lower under remeasurement if the foreign currency depreciates. Total debt is converted at the the same rate under both methods. Lower COGS and depreciation expense under the all-current method result in higher net income. Incremental net income is more than offset by the translation adjustment to the equity account. 10. If a local currency is appreciating, the foreign subsidiary’s performance will have a greater impact on the consolidated data.
Financial Shenanigans – Deception Strategies Inflate reported current-period earnings by inflating reported current-period revenue and gains or by deflating reported current-period current-period expenses. Deflating reported current-period current-period earnings by deflating reporting current-period revenue and gains or by inflating reported current-period expenses. 1. Recording Revenue 2. Recording Fictitious revenues 3. Shifting current expenses to a later period 4. Boosting income with one-time gains 5. Failing to record or disclose all liabilities 6. Shifting current income to a future period 7. Shifting future expenses to the current reporting period High growth (high P/E makes stock prices vulnerable v ulnerable to declines in earnings), very weak, private (not audited), and newly public companies c ompanies are most prone to shenanagins. 3. Shifting current expenses to a later period By (1) capitalizing costs (especially those the firm had generally expensed in the past) a. Marketing and Solicitation Costs (AOL) b. Landfill and interest costs (capitalize management salaries, pr/travel/legal) c. Software development costs (before technological feasibility) d. Store preopening costs (capitalize training costs) e. Repair and maintenance costs Capitalizing costs increases (and stabilizes) reported profits and assets and equity and, thus, improves profit margins and debt-to-equity and interest coverage ratios. If costs are capitalized, the costs will be reported as an investing cash outflow. (2) amortizing costs over longer periods of time – be wary of companies that a. Write-off fixed assets too slowly, esp in industries that are experience technological advances b. Amortize intangible asset or leasehold improvements over long time pds c. Change the depreciation period existing fixed assets. d. Choose long amortization periods for inventory costs e. Use longer amortization pds for capitalized marketing or software costs 5.
Failing to record or improperly reducing liabilities a. Commitments: Take-or-Pay contracts structured as a joint venture with two purchasing companies contributing debt and equity capital to create a third company that produces the product. product. Both assets and liabilities liabilities are kept off the B/S of the two joint venturers, and their D/E and current ratios are more favorable. b. Contingencies: Potential liabilities liabilities are recognized when I. It is probable that assets have been impaired or a liability has been incurred II. The amount of the loss can be reasonably estimated c. Employee Stock Options – GAAP does doe s not require recognition so that the liability and compensation expense are kept off the B/S and I/S, resp.
d. Changes in Pension Assumptions: increases in the discount rate or rate of return on plan assets or decreases in the rate of compensation increase decreases the liability. e. Firms create reserves as liabilities to give themselves greater flexibility to smooth reported earnings and demonstrate an upward trend in income. They do this by deciding that their initial estimate of the liability is too high and thus reverse the expense. f. Revenue can be recognized when I. The earnings process is substantially complete II. The risk of ownership must have been transferred from the purchaser to the seller III. The firm must have received cash or some other asset which can be precisely measured IV. The transaction cannot be cancelled or revoked V. The transaction must have been performed at arm’s length Aggressive recognition causes a firm to overstate revenues, COGS, and net income and to understate its inventory and liabilities. When a company receives payment from a customer, it should ask: 1. Is this payment received in exchange for services rendered for which we have no future responsibilities? 2. Have the benefits and risks of ownership been bee n effectively transferred to the buyer? Conservative Accounting Choices: LIFO, Rapidly writing off goodwill, not reporting non-recurring gains, expensing initial start-up costs, not capitalizing software costs, not capitalizing other expenses, providing adequate provisions for contingent liabilities, using accelerated depreciation methods, using short useful life estimates for fixed assets, using completed contract method for long-term projects, using high bad debt reserves vis-à-vis the size of the accounts receivables, not using off-balance sheet financing, providing clear and adequate disclosures explaining accounting practices, reporting net income that closely matches cash flow from operations Aggressive Accounting Choices: Lengthening the estimated useful life of a fixed asset, Using straight-line method to depreciate fixed assets, Writing-off new investments, Accruing the loss associated with contingencies, undertaking major acquisitions without providing adequate disclosures making comparison with prior periods difficult, taking a “big bath” capitalizing normal operating costs, amortizing costs too slowly, shifting future expenses to the current reporting period as a special charge, Recording investment income as revenue, Recording revenue prematurely, manipulating advertising/R&D/maintenance and other discretionary expenses to smooth the earnings trend, selling assets or marketable securities to generate gains or losses adopting new accounting standards earlier or later to create a desired earnings trend, using reserves to create the desired earnings trend, frequently ch anging auditors,
If a firm’s reported earnings are predictable because revenues and expenses are not highly cyclical and the firm has little operating and financial leverage Warning Signs: 1. Increase in A/R > Increase in Sales firm is recognizing revenues prematurely or being too loose in extending credit to customers 2. Increase in inventory > increase in sales/COGS/AP may indicate that the company has not charge COGS on some sales or the inventory requires a write-off because it is outdated 3. Increase in Gross PPE relative to the increase in total assets may indicate that the enterprise is capitalizing maintenance and repair costs rather than expensing them 4. Decrease in Gross PPE may mean firm is not investing enough. 5. Decrease in operating expenses relative to sales may indicate that the enterprise is capitalizing costs that it should be expensing 6. Cash flow from operations that is significantly different from net earnings should indicate that the firm’s quality of earning is suspicious due to a high-level of non-cash expenses or non-cash income recorded on the income statement. Alternatively, the firm’s firm’s expenditures for working capital may be too high. 7. Change in accounting estimate or principle, auditor, CFO, or outside counsel 4 categories of nonrecurring items are: 1. Unusual or infrequent (gains or losses from disposal of a business segment, gains or losses from the sale of assets or investments in subsidiaries, provisions for environmental remediation, impairments & write-offs) are reported pre-tax before net income from continuing operations (i.e., above the line) 2. Extraordinary – Unusual and Infrenquent (losses from expropriation of assets, gains or losses from early retirement of debt, uninsured loss from fire). Below the line, but watch for companies that are “accident prone.” 3. Disposal of an operation by the measurement data and the time between the measurement period and the disposal date is referred to as the phaseout period. On the measurement date, the company will accrue any estimated loss during the phaseout period and any estimated loss on the sale of the disposal. Gain only after sale sale is complete. 4. Accounting Changes: Prior years’ financial statements need to be restated if: a. Change from one inventory accounting method to another b. Change to or from the full-cost method c. Change to or from the percentage-of-completion method d. Any change just prior to an initial public offering
Summary of Analyst Adjustments Balance Sheet 1.Consolidate assets and liabilities of VIE’s 2.Capitalize PV of operating leases, take-or-pay commitments, contingencies (which increases the leverage ratio) 3.Mark-to-market marketable securities, long-term investments, long-term debt 4.A/R: Check fluctuation in Bad Debt Expense as % of A/R 5.Inventories: Add LIFO reserve to the LIFO inventory balance to get FIFO 6.PPE- Mark-to-market real estate, run impairment test on fixed assets 7.PPE- Uncapitalize interest expense 8.Eliminate Goodwill 9.Reduce/Increase equity by increase/decrease in marking-to-market long-term debt 10. Eliminate reported pension plan asset. asset. Use funded status of the pension and postretirement benefit plans to to get the economic liability (asset). Reduce equity by elimination of asset + increase in liability (which increases ROE). 11. Stock option plans cause ca use reclassification of paid-in-capital and RE. 12. Change deferred tax liability (due to accelerated depreciation and employee benefits) to expected tax liability. If significant upward trending, trending, then low possibility possibility of reversal, so zero out the liability and increase the equity. 13. Change deferred tax assets (due to PPE leases, employee benefits, self-insurance accruals) to zero. 14. Use FMV of Comprehensive Loss Account Acco unt which contains accruals for minimum pension liabilities, unrealized securities gains and losses, and cumulative translation adjustments. Changes should be offset offset by changes in in other B/S accounts. Normalize Operating Earnings by expensing capitalized interest and options. Comprehensive income allows for all changes in equity (other than owner contributions and distributions) from valuation changes to assets and liabilities (minimum pension liabilities, unrealized gains/losses on available-for-sale securities, cumulative foreign currency translation adjustments. You can include the other B/S changes such such as change in deferred tax liability and asset, adjustment for long-term debt mark-to-market, adjustment for capitalized interest, change in pension plan funded status. CASH FLOW Capitalizing R&D results in higher current cash flow over expensing. If operating leases are capitalized, CFO should be split into interest paid (CFO) and repayment of debt (CFF) Equity method instead of consolidation distorts cash flows. Traditional Cash Flow = Net Income + Depreciation + Change in Deferred Taxes CFO = Traditional Cash Flow ± net changes in noncash current assets and liabilities FCF = CFO – CAPEX – dividends
RATIOS Internal Liquidity, Operating Performance, Risk Profile, Growth Potential, External Liquidity Gross Profits = Net Sales – COGS Operating Profits = Gross Profits – Operating Expenses = EBIT EBT = Operating Profits - Interest Net Income = Earnings After Taxes = EBT – Taxes Capital = Long-term debt + short-term debt + equity Capital = Total assets – deferred items Operating Profit Margin = EBIT/(net sales) or EBITDA/(net sales) Return on Total Capital = net income + interest expense = net income + interest expense Average total capital average total assets Return on Common equity = (net income – preferred dividends)/(average common equity Business Risk = (σ of operating income)/(mean operating income) for btw 5-10 yrs of dat Sales Variability = (σ of sales)/(mean sales) Operating Leverage = mean[absolute value(%∆Operating Earnings)] Earnings)] %∆Sales Total Debt Ratio = (Current Liabilities + Total Long-term Debt)/Total Capital Interest Coverage = EBIT/(Interest Expense) Sustainable Growth Rate, g = RR*ROE where RR = retention rate = (1 – dividends declared ) Operating income after taxes Where dividends declared = dividend payout ratio Operation income before taxes External Liquidity: number of shares traded during a given time period size of the bid-ask spread is negatively related to liquidity total market value of the outstanding securities number of shareholders is positively related to liquidity trading turnover is positively related to liquidity
DUPONT ANALYSIS
ROE = (Net Income/Equity) ROE * Sales = Net Income * Sales = (Net Profit Margin)*(Equity Turnover) Sales Sales Equity ROE *Sales * Assets = Net Income * Sales * Assets Sales Assets Sales Assets Equity ROE = Net Profit Margin * Total Asset Turnover * Financial Leverage Multiplier ROE = (Earnings Before Tax)(Sales Tax)(Sales)(Assets)(1-t) )(Assets)(1-t) Sales Assets Equity = [(EBIT)(Sales) – (Interest (Interest Expense)](Assets)(1-t) Expense)](Assets)(1-t) sales assets assets equity ROE = [(Operating)(Total Asset) – (Interest)](Financial)(Tax) Profit Turnover Expense Leverage Retention Margin Rate Multiplier Rate Cost of Preferred Stock K ps = D ps / Pnet, Pnet = P(1 – F), where F = flotation cost % Cost of Retained Earnings Required rate of return, k s = expected rate of return, k s* Required rate of return = r f f + risk premium Expected rate of return = (D1/P) + growth in dividends Where g = (retention rate)(ROE) = (1 – payout rate)(ROE) Cost of Newly Issued Equity > Cost of Retained Earnings k e = [D1 / [P0(1-F)]} + g If the firm does not earn k e on that portion of the investment project that is financed with the new equity capital, the firm’s growth rate of 7.2% will not be met, and the price of the firm’s stock will fall. fall. Thus, the sale of new equity is not by itself dilutive. The dilution of earnings comes about only if the new funds are not invested in such a manner as to cover the return of new equity capital. WACC = (wd)[k d(1-t)] + (w ps)(k ps) + (wce)(k s) The weights are based on the firm’s target capital structure and are thus based on the market value of the firm’s securities. If new equity comes from newly issued common stock, then use ke When the firm exhausts retained earnings and issues new stock, then the firm’s marginal cost of capital rises from WACC-ks to WACC-ke. WACC-ke. This point of exhaustion is given by: Retained earnings break point = BPRE = (retained earnings)/(equity fraction, wce) where RE = net income * retention rate, firm can change its payout ratio to shift the BP RE
Capital Budgeting – NPV Relevant Cash Flows are the Incremental Cash flows that occur iff the project is accepted. Sunk costs, such as a fee to a marketing research firm to forecast cash flows, are not included. Opportunity costs from using the asset (say, cash) in the project versus another should be included. Externalities (cannibalization) should be included. Shipping and installation costs are included in the depreciable basis of the asset.
Change in NWC = ∆current assets – ∆current liabilities Positive Change in NWC requires a cash outflow at the beginning of the project but gives a cash inflow at the end of the project when the need for additional working capital ends. MACRS is based on actual cash flows flows so it should should be used for capital budgeting. It assumes that the asset asset is placed in service in the middle of the first first year. Salvage value is not considered when determining depreciation. Cash Flow = [(revenue – cost – depreciation)(1-t)] + depreciation = (revenue – cost)(1-t) + (depreciation)(t) Net Terminal Year Cash Flow = Return of NWC + Salvage Value + (Book Value of Asset – Salvage Value)*(t) Add operating cash flow to get ge t total final year cash flow When evaluating mutually exclusive projects with different lives, use a.the Replacement Chain method so that the two projects have the same lifespan. lifespan. Eg, when comparing a printer that has a 3 year life with a copier that has a 6 year life, assume that we will buy a second printer in year 3 with the same cash flow assumptions. b.simpler Equivalent Annual Annuity (EAA) Approach 1. Step 1 – find each project’s NPV 2. Step 2 – Find F ind an annuity that equates to the project’s NPV over its individual life at the WACC 3. Step 3 – Select the project with the highest EAA Increase the WACC and FCF’s to account for inflation. Stand-Alone Risk is pure project Risk. Corporate Risk is the project’s contribution to the firm’s total risk and is relevant to undiversified stockholders such as small business owners and the firm’s employees, suppliers, and creditors. Market Risk is the risk associated with a project for a well-diversified stockholder.
Scenario Analysis – Worst Case, Base Case, Best Case E(NPV) = ΣProbi(NPVi), σ NPV = {ΣPi[(NPVi – E(NPV)]2}1/2, CV NPV = σ NPV/ E(NPV) Monte Carlo Simulation – Scenario Analysis repeated 1000 times to generate mean, variance
Project Risk – Beta 1.Pure Play Method: Look for other companies with with single product lines similar similar to that of the project being evaluated and then take an average to estimate the project’s beta. 2.Accounting Beta Method runs a regression of the company’s accounting ROA against the S&P return on assets.
Optimal capital structure maximizes the firm’s stock price by taking on as much debt (cheaper capital) as possible without adding too much default risk. The higher the firm’s inherent business risk (demand variability, sales price variability, input price variability, ability to adjust output prices as input prices change , operating leverage—the extent to which costs are fixed), the lower its optimal debt ratio. The higher the firm’s effective tax rate, the higher its optimal debt ratio. The higher the firm’s financial leverage, the more sensitive EPS becomes to changes in sales. High operating leverage indicates that a small change in sales will cause a large change in operating income. The level of sales that a firm must generate to cover all of its fixed and variable costs is called the breakeven point. The breakeven sales quantity, QBE, can be derived as: Sales Revenues = Operating Costs (Price per Unit)(Quantity) Unit)(Quantity) = (Variable cost per unit * Quantity) + Fixed Fixed Costs QBE = F / (P – V)
Degree of Operating Leverage DOL = percentage change in EBIT = ∆EBIT / EBIT Percentage change in sales ∆Q/Q DOLQ = Q(P-V) or, based on dollar sales rather than units, DOLS = S – VC Q(P-V) – F S – VC – F Degree of Financial Leverage DFL = (percentage change in EPS) / (percentage change in EBIT) DFL = EBIT / [EBIT – I] = EBIT / EBT Degree of Total Leverage combines the degree of operating and financial leverage DTL = (DOL)(DFL) = (%∆EBIT / %∆Sales)(% ∆EPSS / %∆EBIT) = %∆EPS/%∆Sales DTL = [Q(P-V)] / [Q(P-V) – F – I] DTL = [S – VC] / [S – VC – F – I] EPS = (Sales – FC – Variable Costs – Interest)(1 – tax rate)] / (shares outstanding) EPS = [(EBIT – I)(1 – t)] / (Shares Outstanding) If Debt/Assets (D/A) = 10%, then equity = 90% of shares at zero debt Since P = (P/E)(EPS), by increasing financial leverage you increase the volatility of EPS and thus increase the volatility of the stock’s price. P0 = DPS/k s WACC minimized where P0 maximized Modigliani and Miller proved that under a very restrictive set of assumptions, the value of a firm is unaffected by its capital structure. structure. These assumptions are: 1) There are no transaction costs 2) Taxes are nonexistent 3) There is no cost of bankruptcy 4) Investors and corporations borrow at the same rate 5) Investors and managers have the same information about the future investment opportunities of the firm. firm. This is called symmetric symmetric information. 6) Debt has no effect on EBIT In the MM no-tax world, the value v alue of a company is based on the value of the firm’s assets. The firm’s WACC is constant. When these assumptions are relaxed, we realize that there is a difference between the firm’s assets and what investors may be willing to pay for the shares that represent the assets. Since debt interest is tax deductible and dividends are not, optimal tax structure in a tax world (all other assumptions holding) will be 100% debt. With taxes and bankruptcy costs, WACC will fall at first as small amounts of de bt are added to the capital structure. As the firm continues to add debt to the capital structure,
the lender’s threshold level of risk is hit, and they start start to raise interest rate. The WACC finally starts to rise. High-tax bracket investors (like individuals) prefer low dividend payouts and low-tax bracket investors (like corporations and pension funds) prefer high dividend payouts. Residual Dividend Model – Target Dividend Payout Ratio Considers firm’s investment opportunity schedule, target capital structure, access to and cost of external capital Step 1: Identify the optimal capital budget Step 2: Determine the amount of equity needed to finance that capital budget for a given capital structure Step 3: Meet equity requirements to the maximum extent possible with retained earnings Step 4: Pay dividends with the “residual” “residual” earnings that are available after the needs of the optimal capital budget are supported. In other words, the residual residual policy implies that dividends are paid out of leftover earnings. Variable dividends result in a higher required return on o n a firm’s stock and thus a lower stock price, so firms firms maintain stable dividends. Thus, firms should 1.Project average values for their marginal cost of capital and IOS over the near term planning period (5 years) 2.Find the residual model payout ratio and dollars of dividends required during the planning period using the forecasted marginal cost of capital 3.Set a target payout ratio on the basis of the projected data Declaration date is the date the board of directors approves payment. Ex-dividend date is the cut-off date for receiving the dividend (two days before). Holder-of-record date is the date on which the shareholders of record are designated. Warrants are like options but they are issued by the firm so that capital is supplied to the firm upon their exercise. Upon exercise, dilution dilution occurs. They are most most often issued with private bond placements, but also with public debt, preferred and common stock. Warrant = 1 * BSM call value; the 1/(1+q) 1/(1+q) provides the dilution dilution effect effect 1+q q = # of warrants outstanding / total shares outstanding Most convertibles are unsecured and junior to other debt issues. issues. Therefore, smaller firms firms or firms with hard-to-value products or business lines are more likely to issue such securities. For these situations, situations, it is hard to assess the risk of the debt. Issuing straight straight debt with a higher interest rate causes the borrower to engage in asset substitution – playing in overly risky ventures.
Mergers: Horizontal (same LOB), Vertical (Up toward the ultimate consumer, down toward suppliers, to eliminate “hold up” problems), Conglomerate Benefits: Economies of Scale, Complementary Resources (sum is greater than the parts) Bootstrap Effect Assume no net gains in value from a merger. When a high growth prospects firm firm (high P/E) acquires with a low growth prospects firm (low P/E) by exchanging higher-priced shares for lower-priced shares, the number of shares outstanding of the acquiring firm increases, but by less than 1-for-1. Thus, the high-growth firm’s firm’s EPS goes even higher. Gain (to bidder) = VBT – (VB + VT) = ∆VBT In Cash: cost = bidder premium = cash price - V T NPV = gain – cost = VBT – (cash price - VT) In Stock: cost = (N*PBT) - VT, where N = number of shares the target receives PBT = price after merger announcement = VBT Total New Shares With stock, overvaluation of the target will be shared by target’s shareholders.
Ex Ante Alpha = expected expec ted return – required return = E(capital gain) + E(ROE) - E(ROE) P = current stock price Ex Post Alpha = HPR – Return on Similar Assets
