CFA-Level-I-Notes.pdf

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					Economics

Keynes: Sticky prices, so if Demand falls, Supply will fall, and employment falls
Expenditures GDP: Consumer Spending, Private Investment, Government expenditures

Real GDP = Planned C + I + G + NX

Planned consumption is determined 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, then inventory exists, employees will be
laid off, output will fall. Thus, investment is 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 is 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 and crowd out private 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 of loanable funds leaving interest
rates unchanged.
Automatic stabilizers ensure deficits in a recession and surpluses during booms and, thus,
mitigate policy lags. The three main are 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 Operations (Buy & Sell Treasury
Instruments), Discount Rate
M1 – currency in circulation, checkable deposits, traveler’s checks
M2 – M1 + saving deposits + 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 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 investments to be profitable, hence
raising investment spending. AD shifts to the right. In the short run, investment, output,
and prices increase. Lower real rates depreciate 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, prices must rise.
P = MV/Y

In the long run, nominal rates rise because expected inflation rises. N = I + R

If a policy change is fully anticipated, contracts 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 long-
run. 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 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 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
competitor does not produce at the quantity where ATC is 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 about demand
and must experiment with prices.

Oligopoly is a 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 so pronounced that Government imposes the
price ceiling of Average Cost to ensure normal (zero) economic 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. In the short run, 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
and a low elasticity of supply…in the 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       =       MPB           =        MPC                        cost-minimization
 PA                PB                    PC

For a given firm that holds all other 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 the fewest resources to produce
a product.
               P                   Domestic                     A – Domestic Producers Gain
                                    Supply       Quota         B, D – Deadweight Loss
WorldPrice +                                     Supply        A, B, C, D – Consumer Loss
Tariff                                                         C – Government Revenue
                A       B      C     D
 WorldPrice                                Domestic
                                            Demand
                                          Q

               Quotas are worse than tariffs because government gets nothing, foreign producers gain
               from higher prices.

               Less-developed countries artificially inflate the exchange rate on their currency,
               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 + Official Reserve Account = 0

               What will cause a nation’s currency to appreciate?
               • Slow growth of income relative to one’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 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 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 policy will result in
               budget surpluses. Reduced aggregate demand causes an economic slowdown and lower
               inflation. These discourage imports and encourage exports, resulting in a stronger $.
               Less demand for borrowing weakens the $. So results 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 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 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 Quotes – FC/DC

Banks make money on bid-ask spread, not on commissions on 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
rdomestic = rforeign =~ forward exchange rate – spot exchange rate
                                  spot exchange rate
forward (DC/FC) = spot(DC/FC) [1 + rdomestic]
                                     [1 + rforeign]

1 – rD – (1+rF)(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: 1 – 1/k2 = % 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 horizontal 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 in
response to the arrival of new information.

Updated Probability = Probability of new information given the event
Prior 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(RA)

Stock and put option on a stock have negative Covariance.
-1 <= Corr(Ri, Rj) = cov(Ri, Rj) <= +1
                       σRi * σRj
var(x1r1 + x2r2) = E{[x1r1 + x2r2 – E(x1r1 + x2r2)]2} = E{[x1(r1 – r1) + x2(r2 – r2)]2]
                = E[x12(r1 – r1)2 + x22(r2 – r2)2 + 2 x1x2(r1 – r1)(r2 – r2)]
var(x1r1 + x2r2) = x12E[(r1 – r1)2] + x22E[(r2 – r2)2] + 2x1x2E[(r1 – r1)(r2 – r2)]
                = x12var(r1) + x22var(r2) + 2x1x2cov(r1, r2) = x12σ21+ x22σ22+ 2x1x2σ12
                = x12σ21+ x22σ22+ 2x1x2ρiσiσj
                = w1w1cov(r1, r1) + w2w2cov(r2, r2) + 2 w1w2cov(r1, r2)
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 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?
nCr =     n! = 56
      (n-r)!*r!

Permutation Formula: rPr =        n!
                                (n-r)!
   1.   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.
   2.   Factorial is used with no groups. Only arrange n items n! ways.
   3.   Labeling applies to 3 or more sub-groups of pre-determined size. Each element of
        the group must be assigned a place, or label, in one of the three or more sub-
        groups.
   4.   Combination formula applies to only 2 groups of predetermined size. Look for
        the word “choose.”
   5.   Permutation formula applies to only 2 groups of 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 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<x<b) = 1/(b-a)
Cumulative Density Function: F(x) = 0 for x≤a, F(x) = (x-a)/(b-a), F(x) = 1 for x>=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 < RL)
   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: r0,1 = ln(1+R0,1) = ln(S1/S0)

Simple Random Sample
Sampling error = sample mean – population mean = x(bar) - µ
       Where x(bar) ~ (µ,σ2/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 (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 sp2 = (n1 – 1)s12 + (n2 – 1)s22
        (sp2/n1 + sp2/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) - µd0       where d(bar) = sample mean difference = (1/n)Σdi
        sd(bar)               sd(bar) = standard error = sd/√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 χ2n-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 (only use 1 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
    √1-r2         df = n-2
Correlation captures the strength of linear relationships between 2 variables
Least-Squares Regression Line
Yi = b0 + b1Xi + εi explained by Yi = b0 + b1Xi
SSE = Σ(Yi – Y)2 = Σ(Yi – b0 - b1Xi)2 = Σεi2
b1 = cov(X, Y) ; b0 = Yi - 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.
R2 = r2 for one independent variable

Total variation = Σ(Yi – Y(bar))2 = SST
Unexplained variation = Σ(Yi – Yi)2 = SSE
Explained variation = Σ(Yi – Y(bar))2 = SSR
Variance = variation/(n-1)
SST = SSE + SSR
R2 = 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 ± tcsf = Y(hat) - tcsf < Y < Y(hat) + tcsf
  Where df = (n-2) and sf = standard error of the forecast (difficult to calculate)

F-statistic
H0: b1 = b2 = b3 = …. = 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 R2: Ra2 = 1 – [(n – 1)/(n – k – 1) * (1 – R2)]
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 rf)*(1 + inflation) – 1
Nominal risk-free rate ~> real rf + 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. Downward for
       decreasing.

Asset Allocation
Policy: Asset Classes
Policy: Weighting                   85-95% of return
Timing: How far can the manager deviate
Selection: of securities

σ12 = cov(r1, r2) = Σpi(Ri,1 – E[R1]) * (Ri,2 – E[R2])
                  = Σ(Rt,1 – R1(bar)) * (Rt,2 – R2(bar))
                                     N
var(x1r1 + x2r2) = x1 E[(r1 – r1) ] + x22E[(r2 – r2)2] + 2x1x2E[(r1 – r1)(r2 – r2)]
                    2          2

                = x12var(r1) + x22var(r2) + 2x1x2cov(r1, r2) = x12σ21+ x22σ22+ 2x1x2σ12
                = x12σ21+ x22σ22+ 2x1x2ρiσiσj
                = w1w1cov(r1, r1) + w2w2cov(r2, r2) + 2 w1w2cov(r1, r2)

Introduction of a risk-free asset changes the Markowitz efficient frontier from a curve
into a straight line called the Capital Market Line.
rc = wrp + (1 – w)rf;
E(rc) = wE(rp) + (1 – w)rf = rf + w[E(rp) - rf]
E(rp) - rf is the risk premium
σc = wσp since σf = 0
E(rc) = rf + σc[E(rp) - rf]
                       σp
(Jensen’s) α = (rI - rf) - βi(RM - rf)
Security Market Line: α = Rs – (Rf + β(RM) )
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
      σ2 m σ m
    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 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 Method
               d. Any change just prior to an IPO
               e. Distinct operation is discontinued, changes occur below 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 + Increase in Dividend
         Payable + Increase in Deferred Taxes

         FCF = Cash Flow from Operations – Capital Spending + Sale of 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 price, warrants are dilutive. Complex EPS
         denominator increases by (# of warrants) * (1 – Strike 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 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 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 options in prior years should be recorded as a
deferred tax asset offset by a reduction in retained earnings and an increase in paid-in-
capital.
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 included as a component in the operating Cash Flows.
Cash Flow is not immediately affected by the granting of options.

Analysis of Intercorporate Investments
Recognize dividends and interest in the year they are earned. Carrying values are
different under three different accounting treatments:
    a. Cost Method recognizes changes in the market values 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 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. These are measured at 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.

                                Security Classification
                       Trading              Available-for-Sale         Held-to-Maturity
B/S (carrying) value   Fair Market Value    Fair Market Value          Amortized Cost
                                            with unrealized G/L
                                            in equity
Recognized as          • Dividends          • Dividends                •   Interest
income                 • Interest           • Interest                 •   Realized G/L
                       • Realized G/L       • Realized G/L
                       • Unrealized 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.

                                  Activity Ratio Effects
                       Trading                Available-for-Sale       Held-to-Maturity
Unrealized Gains
Sales/Avg WC           Lower                   Lower                   Higher
Sales/Avg Tot Asset    Lower                   Lower                   Higher
Unrealized Losses
Sales/Avg WC           Higher                  Higher                  Lower
Sales/Avg TC           Higher                  Higher                  Lower


                               Liquidity Ratio Effects
                       Trading             Available-for-Sale          Held-to-Maturity
Unrealized Gains
CA/CL                  Higher                  Higher                  Lower
Unrealized Losses
CA/CL                Lower                 Lower                 Higher

                               Leverage Ratio Effects
                     Trading              Available-for-Sale     Held-to-Maturity
Unrealized Gains
Assets               Higher                Higher                Lower
Equity               Higher                Higher                Lower
Debt/Tot Capital     Lower                 Lower                 Higher
Debt/Equity          Lower                 Lower                 Higher
Unrealized Losses
Assets               Lower                 Lower                 Higher
Equity               Lower                 Lower                 Higher
Debt/Tot Capital     Higher                Higher                Lower
Debt/Equity          Higher                Higher                Lower

                             Profitability Ratio Effects
                     Trading                Available-for-Sale   Held-to-Maturity
Unrealized Gains
Pretax margin        Higher                Higher                No change
Profit margin        Higher                Higher                No change
Return on Assets     Higher                Higher                No change
Return on Equity     Higher                Higher                No change
Unrealized Losses
Pretax margin        Lower                 Lower                 No change
Profit margin        Lower                 Lower                 No change
Return on Assets     Lower                 Lower                 No change
Return on Equity     Lower                 Lower                 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         Criterion (degree of influence)              Method
Less than 20%        No significant Influence             Cost or market
20-50%               Significant Influence                Equity
Greater than 50%     Control                              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 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 upon sale of the investment. The parent also reports a
proportionate share of the 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 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 of the corresponding accounts from each of the
individual firms, less any intercompany transactions (revenues and COGS are both
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 Sub
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.

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 identifiable assets of the
enterprise as a whole. Include operating profit, identifiable assets, intersegment 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 segments (after eliminating intersegment
transactions) can be added up to get the earnings of the consolidated firm. Limitations of
segment cash flow data include lack of detailed information on liabilities and on cash
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 assets of one company are
assumed another company.
• The purchase price paid must be equated to the fair market value 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 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 date

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 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 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.
Net gains and losses and related amortization: Liability gains and losses result from
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 increases the PBO). Asset gains and losses result from 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 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 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 and service cost
(though it does increase the interest cost) which lowers pension 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 amendments

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 that if
the ABO exceeds the FMV of 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
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:
    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 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 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 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 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 at 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.

                                Rate used to translate           account using the…
Account                         Temporal Method                  All-Current Method
Nonmonetary assets              Historical Rate                  Current Rate
Nonmonetary liabilities         Historical Rate                  Current Rate
Common Stock                    Historical Rate                  Historical Rate
Equity (taken as a whole)       Mixed*                           Current Rate
Revenues and SG&A               Average Rate                     Average Rate
Cost of Goods Sold              Historical Rate                  Average Rate
Depreciation                    Historical Rate                  Average Rate
Net income                      Mixed*                           Average Rate

            Temporal Method                                 All-Current Method
Remeasure the B/S (Retained Earnings is a        Derive the I/S using the current rate
Plug)
Derive the COGS using avg rate on                Derive Retained Earnings = Beginning
purchases in (BI + P – EI)                       Retained Earnings + NI – Dividends
Derive Net Income                                Compute the B/S, translation adj (PLUG)
Derive the I/S and translation G/L               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 long-
term 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 will be negative.
If you hold a net liability position, a depreciating foreign currency increases the USD
value of the position. Hence, a positive 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 are not. Since COGS and
    depreciation are translated at the average 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 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 expenses. Deflating reported 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 to declines in earnings), very weak,
private (not audited), and newly public companies 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. Both assets and 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 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 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 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 changing 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
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 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. Use funded status of the pension and post-
retirement benefit plans to get the economic liability (asset). Reduce equity by
elimination of asset + increase in liability (which increases ROE).
11. Stock option plans cause 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, then low 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 which contains accruals for minimum
pension liabilities, unrealized securities gains and losses, and cumulative translation
adjustments. Changes should be offset by changes 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 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)]
                                              %∆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)(Assets)(1-t)
              Sales        Assets Equity

     = [(EBIT)(Sales) – (Interest 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
Kps = Dps / Pnet, Pnet = P(1 – F), where F = flotation cost %

Cost of Retained Earnings
Required rate of return, ks = expected rate of return, ks*
Required rate of return = rf + 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
ke = [D1 / [P0(1-F)]} + g

If the firm does not earn ke 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. 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)[kd(1-t)] + (wps)(kps) + (wce)(ks)
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. 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 BPRE
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 so it should be used for capital budgeting. It
assumes that the asset is placed in service in the middle of the 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 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. 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 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), σNPV = {ΣPi[(NPVi – E(NPV)]2}1/2, CVNPV = σNPV/ 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 single product lines 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) = (Variable cost per unit * Quantity) + 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/ks
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. 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. This is called symmetric information.
6) Debt has no effect on EBIT

In the MM no-tax world, the value 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 debt 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 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” earnings that are available after the needs of
         the optimal capital budget are supported. In other words, the residual policy
         implies that dividends are paid out of leftover earnings.

Variable dividends result in a higher required return on a firm’s stock and thus a lower
stock price, so 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 occurs. They are 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) provides the dilution effect
         1+q              q = # of warrants outstanding / total shares outstanding

Most convertibles are unsecured and junior to other debt issues. Therefore, smaller firms
or firms with hard-to-value products or business lines are more likely to issue such
securities. For these situations, it is hard to assess the risk of the debt. Issuing 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 (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 EPS goes even higher.

Gain (to bidder) = VBT – (VB + VT) = ∆VBT
In Cash: cost = bidder premium = cash price - VT
         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 return – required return = E(capital gain) + E(ROE) - E(ROE)
                                                     P = current stock price
Ex Post Alpha = HPR – Return on Similar Assets

				
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