CFA L2 Cash flows, models, formulas, etc
CFA L2 Cash flows, models, formulas, etc
Terms in this set (108)
T-TEST for correlation
t = r √(n - 2) / √(1 - r^2)
What cash flow is used for Capital Budgeting?
Operating Cash Flow
CF = (S - C - D)(1 - T) + D
Or you can use = (S - C)(1 - T) + (TD)
S = sales
C = cash operating costs
D = depreciation expense
T = marginal tax rate
DO NOT USE Net Income!
What is the final cash flow?
The operating cash flow, plus the After Tax Non-Operating Cash Flow:
TNOCF = Salv + NWC Inv - T (Salv - BT)
Salv = pre-tax cash proceeds from sale of fixed capital
BT = book value of the fixed capital sold
Remember, book value is net of depreciation. Any gains on top of the book value are taxed. If the item was depreciated to zero value, then it is fully taxable.
How does inflation affect capital budgeting?
1. Nominal or Real cash flows must be discounted at Nominal or real rates respectively.
2. Unexpected increases in inflation reduce project value and vice versa
3. Inflation reduces tax savings from depreciation since depreciation is fixed based on the book value of assets
4. Inflation decreases the value of payments to bondholders (since payments are at a fixed value)
5. Inflation may affect revenues and costs differently. OCF can be higher or lower.
EP = NOPAT - $WACC
NOPAT = EBIT(1-TAX)
Market Value Added
Discount economic profit at the WACC
After Tax Cash Flow - Change in Market Value
Market Value in each period is simply the discounted future after tax cash flows
The change is from T1 to T0 (or over period)
Economic Rate of Return
Economic Income / Beginning Market value
= (After tax CF - Change in market value)
What is the firm value using residual income?
PV of RI
+ Equity Invested
+ Debt Invested
= Total Firm / Project value
Interest and principal payments discounted at Rd
Dividends and share repurchases discounted at Re
The sum of the two PVs is the value of the firm (can't use for projects)
How do we solve for cost of equity from for a firm with leverage?
Re = Ro + (Ro - Rd)(D/E)
Ro = Re for firm with no debt
This is Modigliani Miller Prop 2 : Cost of equity is a linear function of the debt to equity ratio with an intercept of Ro (Re/wacc of firm with no debt)
note: ALWAYS use market values of DE when available
Value of a levered firm
VL = VU + (t × d) - PV(cost of distress)
Target Payout model for dividends
Previous Div +
[ (expected increase in EPS) x (payout ratio) x (1/ #yrs for adjustment) ]
How does residual dividend model work?
Retained earnings are used to fulfill the equity portion of the capital budget.
The remaining retained earnings is paid out as dividents.
so if RE is 100 and D/E is 2 and Capital required is 50. note a 2/1 ratio of D/E would be 66.6% debt and 33.3% equity.
100 - 0.333x50 = 83.35
Double tax rate tax
Split tax rate
effective tax rate =
Corp Tax + (1 - Corp Tax) x (individual tax rate)
effective tax rate =
Corp Tax + (1 - Corp Tax) x (Div tax rate)
Taxes are paid at SHs tax rate. Difference comes from tax credit / debit.
What are the global dividend trends?
1. Lower portion of US companies pay divs compared to European coutnries
2. Globally there is a downward trend in divs
3. Stock repurchases has trended upwards in US, UK and EU
What's the best measure of dividend safety?
FCFE coverage ratio = FCFE / (dividends + share repurchases)
What are the 2 major objectives of governance?
1. Eliminate and reduce conflicts of interest
2. Use the company's assets in the best interest of investors and other stakeholders
What are the 4 core attributes of effective corporate governance?
1. Define rights of SHs and Stakeholders
2. Define and communicate responsibilities of mgrs and directors
3. Provide fair treatment in all dealings between Mgrs, Directors and SHs
4. Complete transparency and accuracy in financial/risk/ops disclosures
2. Rapid Growth
3. Mature Growth
1. C H
2. C H
3. H V
5. C H V
What is the FCF used to assess a target company?
NI + Net interest(1-TAX)
= Unlevered Net Income
± Change in Deferred Taxes Liability (assets)
+ NCC ± ΔNWC - Capex
NOTE exclude cash and ST debt from NWC calc
NOTE 2 Subtract interest income from Interest expense to get Net Interest
NOTE 3 Wacc is usually targets unless merger, then adjust for change in capital structure
Formula for post merger value
Gains to Target
Gains to Acquirer
Vat = Va + Vt + S - C
Gain Target = Tp = Pt - Vt
Gain Acq. = S - Tp = S - (Pt - Vt)
Vat = Value of combined company
Tp = Takeover Premium
Pt = Price of Target
V = post-merger value (acquirer + target)
S = synergies created by the merger
C = cash paid to target shareholders
Supply Side model for ERP
ERP = [(1+EINF )(1 + EΔRGDP)(1+EΔPE)] -1 + Expected yield on the index + RF
Fama French model for Return on Equity
RF + B xERP + BxSMB + BxHML
SBM small cap to large cap (avg return on 3 ports)
HML High P/B vs low P/B (avg return on 2 ports)
Pastor Stombau model for Return on Equity
Same as Fama Frech but add BxLIQ
B>0 for less liquid, 0 for normal, 1 for high liquid
BIRR model factors for Return on Equity?
Risk Free R +
Build up method
required return = R F + equity risk premium + size premium + specific-company premium
Intrinsic PE decomposition
Tang PE + Franchise PE
Tang PE + FFxGF
FF= (ROE - r) / (ROE x r)
GF = g / (r-g)
PE with inflation
[1 / (Rer + (1-λ)I )]
λ = Flow through rate
Rer is the real required return Re - Inflation
This is a leading PE
For EM inflation, what cash flow do we use?
NOPLAT but in this case it is simply EBIT - tax
There is nominal and real versions of each. They must be discounted with the nominal or real wacc.
Growth rates must be real or nominal too.
(1+ WACCn) = (1 + WACCr)(1 + Infl)
Plugs: to arrive at real net PPE, use real FCinv is a plug. To arrive at nominal FCinv we use nominal PPE as a plug.
[ Do(1+gl) + DoH(gs-gl) ] / (r-gl)
FCFF Adjustments - what needs to be added back or subtracted from Net Income?
1. Depreciation ADD
2. Amortization/impairment of intangibles ADD
3. restructuring expense ADD
4. restructuring gain (from reversal) SUBT
5. losses ADD
6. gains SUBT
7. Amort of bond discounts ADD
8. Amort of bond premiums SUBT
9. Increase in Deferred Tax Liabilities ADD but caution**
10. Increase in Deferred Tax Assets Subtract but caution**
**Deferred taxes liabilities should be added back or assets subtracted if they are expected to continue growing. IE company is growing
FCFF using ebit
EBIT(1-TAX) + Dep - FCinv - WCinv
Note, we don't remove NCC just Dep!
FCFF from EBITDA
EBITDA(1-TAX) + DEP(TAX) - FCinv - WCinv
FCFF from CFO
CFO + INT(1-TAX) - FCinv
Think, FCinv are from CFI so you must adjust, but WC is included in CFO so you can ignore WC
FCFE from FCFF
FCFE = FCFF - INT(1-TAX) + Net Borrowing
How do we deal with preferred shares in FCFF/E models?
Treat it like debt:
1. Any preferred dividends should be added back to the FCFF. This approach assumes that net income is calculated after preferred dividends have been subtracted.
2. WACC should also be revised.
3. FCFE should be increased by net issuances that year.
Justified leading PE
Justified Trailing PE
leading : (1-b)/(r-g)
trailing : (1-b)(1+g)/(r-g)
(ROE - g) / (r-g)
(Eo/So)(1-b)(1+g) / (r-g)
trailing justified PE x net margin
Justified Dividend Yield
(r-g) / (1+g)
it's as trailing PE were inverted but no 1-b
What is the alternate RI model for single stage constant growth?
[(ROE - r)xBo ] / (r-g)
How do we calculate residual income declining at a rate over time or remaining the same forever?
After calculating RI in each period, use this formula
RI / (1 + r - w)
This gives the RI at time T, it must be discounted to t=0
w is the persistence factor. If RI remains the same forever, w = 1 and the formula reduces to a perpetuity.
If w <1 RI declines slowly over time. (consistent with economic theory)
if w = 0, RI declines immediately to zero.
Note W must be between 0 and 1
What if we assume RI declines to industry average?
Use forecasted price to book to estimate the firm value at time T. The value of the stock is BVT x P/B
then PV of RI = [(Value - BVT) + RI ] / (1 + r)^T
Capitalized Cash flow method
FCFF1 / (WACC - g)
Excess Earnings method
Normalized earnings - WC charge - FC charge = Excess earnings
Excess earnings / (r - g) = value of intangibles
Firm Value = Value of intangibles + WC + FC (not charges but actual values)
Discount rate methods for private companies? 3
E.CAPM (include size and firm specific risk premia)
Build Up Method = CAPM with beta = 1, plus premiums for size, industry factors and company factors
DLOC Calc and when to use
DLOC = 1 - [ 1 / (1 + Control premium)].
DLOC is used to convert an a valuation done on a controlling basis, for an investment that you do not have controlling interest in. This can occur when using the Guideline Transaction Method
What is a Control Premium
A premium added to the value of an investment to account for a controlling interest. If a valuation was done on a public company that you plan to take control of, a premium should be added. So this is used in the Guideline public company method.
What is the total discount?
[1 - (1 - DLOC)(1 - DLOM)]
Again 3 ones!
DLOM is for lack of marketability. This would be applied for a noncontrolling equity interest in a private company.
How do I calculate price per share in venture capital method? IRR method?
POST = Present value of expected FV
PRE = POST - INV
F = INV / POST (F = fraction)
# Shares = x[F / (1 - F)] (x = founder's shares)
Price = INV / # of shrs
FW = INV(1+R)^t (future wealth)
F = FW/SP (Selling price)
# Shares = x[F / (1 - F)] (x = founder's shares)
POST = INV/F
PRE = POST - I
What about multiple financing?
POST2 = Present value at end
PRE2 = POST2 - INV2
POST1 = Present value of PRE2
PRE = POST1 - INV1
F2 = INV2 / POST2
F1 = INV1 / POST1
# Shares1 = x[F / (1 - F)] (x = founder's shares)
# Shares2 = (x + #shares1)[F2 / (1 - F2)]
Price1 = INV1/ # Shares1
Price2 = INV1/ # Shares2
List in order how you calculate the fund NAV each year
Paid in Capital (∑ Called)
=Nav before dists
=Nav after dists
How do you adjust Re for possibility of failure?
(Re + P) / (1 - P)
Where P = probability of failure
Acid test ratio
(Current assets - inventories ) / current liabilities
LT Debt to capitalization ratio
LT Debt / (LT Debt + Minority Interest + shareholders' common and preferred equity)
Total debt to capitalization ratio
(current liabilities + long-term debt) / ( Current liabilities + LT Debt + Minority Interest + shareholders' common and preferred equity)
What are the S&P Cash flows (5) and how do you arrive at them?
+/- Non cash charges
Funds from operations
+/- Change in NWC excl All debt and cash
Operating cash flow
- capital expenditures
Free operating cash flow
- cash dividends
Discretionary cash flow
+ asset disposals
+ other sources (uses)
Prefinancing cash flow
Debt service coverage
(Free op cash flow + interest) / (interest + annual principal payment)
S&P debt payback period
total debt / discretionary cash flow
Positive and negative butterfly shifts
1. Positive = yield curve is LESS curved (flatter)
2. Negative = yield curve is MORE curved (steeper)
A positive shift occurs when short and long term rates rise more than mid term rates. A negative occurs when mid term rates rise more than short and long rates.
Favourable income differential per share (convertibles)
coupon interest - (conversion ratio x dividends per share) / (conversion ratio)
premium payback period ratio (convertibles)
market conversion premium per share / favorable income differential per share
Single Monthly Mortality SMM calc
How do you calculate the prepayment amount given an SMM?
SMMm × (mortgage balance at beginning of month m−
scheduled principal payment for month m)
Remember to subtract the scheduled principal first!!
What is the prepayment measure for auto-backed loans and how do you convert it to SMM?
Absolute prepayment speed (ABS <- confusing)
SMM = ABS / (1 - (ABS x m-1))
m = months since origination
Cash flow yield on an MBS - 2 steps
Calculate the IRR based on mothly interest and prepayment
Convert IRR to bond equivalent yield
= 2[(1+ CFYm)^6 - 1]
essentially compound for six months and multiply by 2
How do we measure the total effect of duration and convexity?
≈(−ED × Δy × 100) + (EC × Δy^2 × 100)
Note the duration is a negative effect and convexity is a positive effect. With convexity you need to square the change in yield.
Forward price and value and value continuous
F = (So - PVD)x(1+rf)^T
V long = (St - PVDt) - (F / (1+rf)^(T-t))
V Long = [ St / e^d(T-t) ] - [ FP / e^rf(T-t) ]
Note with continuous we do not use ^(T-t) we actually multiply by T/365
FRA price and define h and m
[1 + L(h+m)(h+m/360) / 1 + L(h)(h/360) - 1] x 360/m
for a 3X9 FRA
h = 90
m = 180!! (it between 9-3 = 6 months!)
[ 1 / 1 + L(h-g)(h-g/360) ] - [ 1 + FRA(m/360) / (1 + L(h+m-g)(h+m-g/360) ]
Currency FWD price and value
FP = So (1+drf)^T / (1+frf)^T
V = [St /(1 + frf)^(T-t)] - [F/(1 + drf)^(T-t)]
What is cost of carry?
Cost of carry = Future value of storage costs - benefits.
A future price should be the future value of the asset plus the cost of carry
So(1+Rf)^T + FV(costs - benefits)
When you add the cost of cash flows
So(1+Rf)^T + FV(costs - benefits) - FV(cash flows)
What does a conversion factor do?
Converts the Tbond future to the cheapest to deliver to equalize prices on bonds with different coupons
FP = [(Bo - PVC)(1+rf)^T ] x (1/CF)
CF is conversion factor
Put call parity for stock options and forward options
C - P = S - X/rf
C + (X - F)/rf = P
Market model - what are 3 calcs? How do you get sys risk?
Ri = αi + βi x ERm
σ²i = B²σ²m + σ²ie (variance of error)
that is Systematic risk + Nonsystematic risk
CovRiRj = βiβjσ²m
assumes error is zero and errors are not correlated to assets or themselves
Decision rule for adding a share to a portfolio?
Sharpe new > Sharpe portfolio x CORR
Sharpe = (ER - Rf) / σ (stdev)
As number of shares in a portfolio increases, variance approaches?
σ²p = [2/n] avg(σ²) + (n-1/1) x avg(cov)
assumes equal weighting
Equation for CAL / CML ?
ERp = Rf + [(ERi - Rf)/σi] σp
Expected return on portfolio is Rf plus sharpe ratio of asset i times portfolio stdev
For CML it is the same except Ri is actually Rm (assumes all investors have same expectations so hold the same risky portfolio.
COV(i,m) / σ²m
Easy way to remember portfolio variance formula
All the ²s go on the left. This also helps you remember Corr and Cov
σ²p = w₁²σ₁²i + w₂²σ₂² + 2w₁w₂ρσ₁σ₂
with three assets just make sure you add a term for each combination on right
Foreign currency risk premium
[E(S₁) - F ] / S₀
Currency exposures. Explain the two types
ϒ = ϒ(LC) +1
ϒ = domestic currency exposure (from the ICAPM)
ϒ(LC) = local currency exposure
Local currency exposure is how much the asset changes to its own exchange rate. Since my own currency is perfectly negatively correlated to the company's domestic currency, we add + 1.
What if my shares in telefonica drop 5 % when the euro rises 10% (ie ϒLC = -0.5) well obviously I gain 100% from the rise in the euro ϒ = ϒLC + 1 = 0.5, my shares rise 5%.
Explain traditional model and money demand model for FX rate exposure for economies
Traditional = J-curve. Rates drop bringing inflation thus hurting trade balance but in long term more competitive thus increasing gdp, so neg correlation in long run, pos in short.
Money demand: Increase in GDP increases demand for currency, rates rise. thus pos correlation of FX to gbp. This doesn't apply to emerging market countries though
Explain theories of FX exposure for bonds. Free markets theory and Govt intervention theory
Free Markets Theory: Increase in
interest rates causes money to flow into country pushing up FX rate. Thus FX is negatively correlated to Bonds
Government intervention theory: If currency falls below target, government increases interest rates to push FX back up. So positive correlation with FX and bonds
Avg Ri - Avg Rb / Stdev (Ri-Rb)
Steps for treynor black (assuming you have gathered your alphas)
1. Determine market expectations
2. Find mispriced stocks and calc alphas
3. Determine weightings (wi) for active portfolio by taking αi / σ²εi for each security and then dividing the values by the sum of all of them. (ie information ratios)
4. Compute βa αa and σ²a for active portfolio (all weighted avg except σa² = ∑wi²σi²
5. Calculate weight for total portfolio (maximises sharpe)
Wa = Wo / 1+ [(1-βa)Wo]
Wo = α / σ² / (rm-rf)/σ²m
6 Determine weights of all items.
ifrs vs gaap for inventory write downs
IFRS: inventory is reported on the balance sheet at the lower of cost or net realizable value (est sales price - cost). Inventory can be written up after if its value rises
GAAP inventory is reported on the balance sheet at the lower of cost or market. Market is usually equal to replacement cost and cannot be greater than net realizable value. No write-ups allowed.
LIFO inventories are less likely to have write-downs (lower inv)
How does capitalized costs affect S.E. versus expensed costs?
SE is larger by the increased amount of retained earnings in that period only! Capitalized costs create an asset but reduces cash, so that has zero effect on shareholders equity.
So ROA and ROE are slightly higher initially, but as the asset is depreciated over time ROA and ROE will be lower for the capitalizing firm.
How do IFRS and gaap differ on impairing capitalized assets?
IFRS: If book value exceeds fair value (discounted cash flows less selling costs) it is impaired and written down.
GAAP: If book value >
cash flows, it's impaired. The is
- book value (just like ifrs)
Equity method goodwill
the excess of the purchase price over the proportionate share of the investee's book value is allocated to the investee's
net assets (net of liabilities) based on their fair values. Any remainder is considered goodwill
Cost - % Net assets = excess purchase price
excess purchase price - (FV assets - BV assets)x% ownership
Net income on equity method
Investors net income = Net income% - depreciation on excess allocated to fair value of assets.
Depreciation = %(FV Assets - BV Assets) / # years depreciation.
•This only occurs if the purchase price was in excess of the book value of assets, which in reality is almost always.
•Any upstream transactions (bought from investor) are eliminated if they are not confirmed. Eliminate % of ownership.
Investment on balance sheet in the equity method
Purchase price + equity income (calculated previously) - dividends
Describe acquisition method.
• Revenues, expenses, assets and liabilities are combined.
• Cash is deducted for expense, or capital stock credited in share purchase
• Intercompany transactions are eliminated
• Minority interest is recorded if owning less than 100%.
How is goodwill calculated for acquisition? IFRS and GAAP
GAAP = full = (FV company - FV of net assets) x %
IFRS = partial = (Purchase price - %FV of net assets)
• Note, full method is allowed on IFRS
• Note: Always
e* net assets, exclude goodwill. This is also for equity method.
How is minority interest calculated?
With full goodwill, min interest = %(fair value of company)
With partial goodwill, min interest = %(Fair value of net assets)
Thus Full Goodwill results in a larger asset value (goodwill) and a larger equity value (minority interest).
What are the three measures of a pension plan liability?
• Projected benefit obligation (PBO) actuarial present value of all future pension benefits
• Accumulated benefit obligation (ABO) is the actuarial present value of all future pension benefits based on current salary levels
• Vested benefit obligation (VBO) is the amount of the ABO that is not contingent on future service
Reconcile beginning pension obligation to ending pension obligation
Obligation at beginning of period
+ Current service cost
+ Interest cost
+ Plan amendments
± Actuarial (gains) and losses
- Benefits paid
= Obligation at end of period
Calculate Pension Expense
Current service cost
+ Interest cost
- Expected return on assets
± Amortization of deferred (gains) and losses
+ Amortization of past service cost
= Net pension expense
Reconcile FV of plan assets from beginning to end of period
Fair value of plan assets at beginning of period
+ Actual return on assets
+ Employer contributions
- Benefits paid
= Fair value of plan assets at end of period
How do you calculate the net pension asset or liability on IFRS?
Funded status (fair value of plan assets - PBO)
± Unrecognized deferred (gains) and losses
+ Unrecognized past service cost
± Unrecognized transition (asset) or liability
= Net pension asset (liability) reported on the balance sheet
NOTE Add back losses and subtract gains. Just like everywhere. Unintuitive! This is because those amounts are reflected in the PBO but not on the I/S.
What are the two ways of calculated economic pension expense?
• Economic pension expense can be calculated by summing all of the changes in PBO for the period (except for benefits paid) and then subtracting the actual return on assets.
• Alternatively, economic pension expense is equal to the change in the funded status for the period excluding the firm's contributions.
Stock Options expense
Expense is at fair value and spread over the period from the grant date, to the date that they can be sold.
Temporal method conversions
• Monetary assets and liabilities are remeasured using the current exchange rate. (cash, receivables, payables, debt, assets&liab held at fair value)
• All other assets and liabilities are considered nonmonetary and are remeasured at the historical (actual) rate.
• Just like the current rate method, common stock and dividends paid are remeasured at the historical (actual) rate.
• Expenses related to nonmonetary assets such as COGS, depreciation expense, and amortization expense are remeasured based on the historical rates prevailing at the time of purchase.
• Revenues and all other expenses are translated at the average rate.
Where does the adjustments for FX changes go on Current Rate method and Temporal?
Current Rate: B/S = Cumulative Translation Adjustment = Plug that makes B/S balance
Temporal = I/S Gain/Loss.
How do you calculate the cumulative translation adjustment?
• Take last years ending retained earnings add the current years translated net income less any translated dividends
• Now statements are complete, simply add the CTA that makes the SE and Liabilities = assets
How do we calculate the translation gain or loss? (ie temporal)
We calculate the Retained earnings that makes the balance sheet balance.
Then we check if this relationship holds:
Ending RE = Beginng RE + NI - Divs.
We now add an I/S adjustment so that final NI makes the above formula balance.
CALC Agg Accruals
CALC CF Agg Accruals
Accruals ratio for both
NOAt = (TOTAL assets - cash) - (TOTAL liabilites - Total debt)
Agg Accruals = NOAt - NOAt-1
CF Agg Accruals = NI - (CFI + CFO)
Accruals ratio (NOAt - NOAt-1)/AVG(NOA)
Accruals ratio NI - (CFO+CFI)/AVG(NOA)