Prudent Man Rule and Prudent Investor Rule

Prudent Man Rule and Prudent Investor Rule

	old	new
	Prudent Man Rule	Prudent Investor Rule
To delegate any duties to others	NOT allowed (*2)	Yes
Impartiality standard (*1)	Yes	Yes
Preservation of the principal	Required	Permissible (*4)
Preservation of the purchasing power (*3)	Required	Required

(*1) The impartiality standard requires prudent handling of different interests, such as those of different beneficiaries (i.e. remaindermen and current-income beneficiaries).

(*2) The trustee was not allowed to delegate any duties to others.

(*3)  By earning a return sufficient to offset inflation.

(*4) Growth in the real value of the principal is permissible.

OAS (Option Adjusted Spread)

The OAS is a constant spread added to every interest rate in the tree so that the model price of the bond is equal to the market price of the bond.

Relative strength indicators

(Question)
The belief that there are

• patterns of persistence in returns
• reversals in returns

provides the most appropriate rationale for valuation using:

A. unexpected earnings.
B. relative-strength indicators.
C. standardized unexpected earnings.


Answer: B

PEG ratio

PEG ratio = P/E ratio / Annual EPS growth

Trailing PEG ratio = (P₀/E₀)/g
Leading PEG ratio = (P₀/E₁)/g

Underlying Earnings Per Share (EPS)

Underlying EPS = Adjusted EBT / Weighted average shares outstanding

Adjusted EBT = EBT + Unusual items-expense (*)

(*) Expense related to nonrecurring extraordinary items such as restructuring costs and asset write downs.

Standard IV(B) Duties to Employer: Additional Compensation Arrangements

Standard IV(B) Duties to Employer: Additional Compensation Arrangements

Offered reward by a client for	Disclosure to an employer?	Permission by an employer?
past investment performance	Yes	-
future investment performance (*)	Yes (in writing)	Yes

(*) The reward may or may not be given based on the performance in the future.

U.S. GAAP: Functional currency, Local currency, and Reporting currency

(Background)

Company	Description	Country	Currency
U	A U.S. parent company	US	USD
F	A Foreign subsidiary	F1	FC1
		F2	FC2

(1) operating, financing, and investing decisions related to the company F's operations are typically made by the company F's local management located in the foreign country F1.
(2) some of F1's accounts receivable are denominated in a different foreign currency called the FC2.

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(Question)
Which method is the best to use to translate the FC2 receivables into FC1, according to U.S. GAAP?

A. The current rate method.
B. The temporal method.
C. The method will depend on inflation.

Answer: B

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Temporal method

Company	Description	Country	Currency	Each currency is:
U	A U.S. parent company	US	USD	Reporting currency
F	A Foreign subsidiary	F1	FC1	Functional currency (*)
		F2	FC2	Local currency

(*) Because the company F is an independent subsidiary.

Under U.S. GAAP, first remeasure the FC2 receivables from FC2 to FC1 using the temporal method.

Reclassification of Investments in Financial Assets

Reclassification of Investments in Financial Assets (U.S. GAAP)

From ↓ \ To →	HTM	AFS	HFT	DFV
Held-to-maturity (HTM)	-	?	OK	OK
Available-for-sale (AFS)	?	-	OK	OK
Held-for-trading (HFT)	OK	OK	-	OK
Designated at fair value (DFV)	OK	OK	OK	-

• U.S. GAAP does permit securities to be reclassified into or out of held-for-trading or designated at fair value.
• Unrealized gains are recognized on the income statement at the time the security is reclassified.

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Reclassification of Investments in Financial Assets (IFRS)

From ↓ \ To →	HTM	AFS	HFT	DFV
Held-to-maturity (HTM)	-	OK(*2)	NG	NG
Available-for-sale (AFS)	OK(*1)	-	NG	NG
Held-for-trading (HFT)	NG	NG	-	NG
Designated at fair value (DFV)	NG	NG	NG	-

IFRS typically does not allow reclassification of investments into and out of fair value through profit or loss category and reclassification of investments out of held-for-trading category.

(*1) Debt securities classified as available-for-sale can be reclassified as held-to-maturity if the holder intends to (and is able to) hold the debt to its maturity date. The security's balance sheet value is remeasured to reflect its fair value at the time it is reclassified. Any difference between this amount and the maturity value, and any gain or loss that had been recorded in other comprehensive income, is amortized over the security's remaining life.
(*2) Held-to-maturity securities can be reclassified as available-for-sale if the holder no longer intends (or is no longer able) to hold the debt to maturity. The carrying value is remeasured to the security's fair value, with any difference recognized in other comprehensive income. Note that reclassifying a held-to-maturity security may prevent the holder from classifying other debt securities as held-to-maturity, or even require other held-to-maturity debt to be reclassified as available-for-sale.

Equity Method and Proportionate Consolidation: Effects on Income Statement

• Equity Method
• The investor recognizes its pro-rata share of the investee's earnings in one line of the income statement.
• Proportionate Consolidation
• The investor recognizes its pro-rata share of each income statement.

FC ≠ LC ≠ RC

If FC ≠ LC ≠ RC,

LC: Local currency (e.g., some of the subsidiary's account receivable are denominated in a currency different from FC, a subsidiary's functional currency)
FC: Functional currency (e.g., a subsidiary is an independent company)
RC: Reporting currency

then under U.S. GAAP, remeasure the LC first from LC to FC using the temporal method.

Current Rate Method and Temporal Method: Translation Gain/Loss

A foreign subsidiary of a U.S. company

Operations	from January 1, 2007
Foreign Currency	FC

B/S of foreign subsidiary

(in FC)	12/31/2007	12/31/2008
Cash and accounts receivable	5,000	5,200
Inventory	3,800	4,900
Net fixed assets	6,200	7,400
Total assets	15,000	17,500
Current liabilities	2,000	2,000
Long-term debt	9,000	9,500
Shareholders' equity	4,000	6,000
Total liability and equity	15,000	17,500

Exchange Rate

Spot on 1/1/2008	$0.35/FC
Spot on 12/31/2008	$0.45/FC
Average spot (2008)	$0.42/FC

Translation Gain/Loss: Current Rate Method and Temporal Method

Method	Current method	Temporal method
Exposure	Equity (H) Assets (C) = Liabilities (C) + Equity (H) + Translation gain or loss	Cash and accounts receibable - Current liabilities - Long-term debt >0: Net monetary assets <0: Net monetary liabilities
Equity	Beginning: +4,000 (positive) Ending: +6,000 (positive) ΔEquity = +6,000 - (+4,000) = +2,000 (positive)
Net monetary assets or liabilities		12/31/2007 5,000 - (2,000 + 9,000) = -6,000 12/31/2008 5,200 - (2,000 + 9,500) = -6,300 ΔNet monetary assets = -300 < 0 → change in exposure is negative; increase in net monetary liabilities
Foreign Currency	Appreciated	Appreciated
Translation gain or loss	Translation gain Assets (C) > Liabilities (C) + Equity (H) Assets (C) = Liabilities (C) + Equity (H) + Translation gain (>0)	Translation loss FC appreciated while net monetary liabilites icreased.
Reported on	Balance sheet	Income statement

(H) Historical exchange rate
(C) Current exchange rate

Reclassification: SPE

(Background)
A company has reported its investment in the SPE (Special Purpose Entity) using the equity method, but an analyst believes that the consolidation method more accurately reflects the company's true financial position, so the analyst makes the appropriate adjustment to the financial statements.

(Question)
What are the likely effects on return on assets (ROA) and net profit margin (ignoring any tax effects) of correctly adjusting for the company's investment in the SPE using the acquisition method?

	ROA	Net profit margin
A.	No change	Decrease
B.	Decrease	No change
C.	Decrease	Decrease

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Reclassification: SPE

Accounting		IFRS
		Equity method → Consolidation (acquisition) method
Net income (NI)		→
Total Assets		↑
Revenue		↑
ROA = NI/Total Assets		→/↑= ↓
Net profit margin = NI/Revenue		→/↑ = ↓

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Answer: C

Reclassification: Available-for-sale Securities

(Background)
A company reported an unrealized gain in its most recent income statement related to debt securities that are designated at fair value (held-for-trading).

(Question)
A company reclassifies debt securities as available-for-sale. Ignoring any effect on income taxes, which of the following best describes the effects of the necessary adustments?

A. Net income is lower and asset turnover is higher.
B. Return on assets is lower and debt-to-equity is lower.
C. Return on equity is lower and debt-to-total capital is not affected.

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Available-for-sale Securities

Accounting		U.S.GAAP
		Held-for-trading → Available-for-sale
Reported in		Net income → Comprehensive income as part of shareholders' equity
Net income (NI)		↓
Total Equity		→
Total Assets		→
Total Liabilities		→
ROA = NI/Total Assets		↓/→ = ↓
ROE = NI/Total Equity		↓/→ = ↓
Asset turnover = Revenue/Total Assets		→/→ = →
Debt to Equity		→/→ = →
Debt to Total Capital		→/→ = →

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Answer: C

Goodwill

Goodwill

		Business combinations (*1)
Method		Acquisition
Identifiable assets Identifiable liabilities		Fair value (*2)
Goodwill (*3)		IFRS Full goodwill or Partial goodwill U.S. GAAP Full goodwill

(*1) e.g., merger, purchase, or consolidation
(*2) at the time of the acquisition
(*3) Full goodwill > Partial goodwill

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(Question)
If an acquirer decides to purchase only 80% of a target company, under IFRS they will have the option to:

A. report the acquisition as either a business combination or as acquisition.
B. value the identifiable assets and liabilities of the target at their current book values or at fair market value.
C. report more or less goodwill depending on the accounting method they choose.


Answer: C

Goodwill

Goodwill

	U.S. GAAP	IFRS
Reported as	Asset	Asset
Amortization?	No	No
frequency for impairment test	At least annually	At least annually
test for impairment	CV > FV of the company (*)	CV > Recovervable amount(*)
	different test with IFRS as above	different test with U.S.GAAP as above
impairment loss	same	same

(*) Impairment loss is recognized in this case.

Pooling of interests method & Purchase acquisition method

• An acquirer's accounting standard: IFRS
• An acquirer exchanged common stock for all of the outstanding shares of the acquired company.

Pooling of interests method & Purchase acquisition method

		Pooling of interests method	Purchase acquisition method
Acquired (purchased) company	Assets	Included on the acquirer's B/S At BV (*2)	Included on the acquirer's B/S At FV (*1)
Acquired (purchased) company	Liabilities	Included on the acquirer's B/S At BV (*2)	Included on the acquirer's B/S At FV (*1)
	Reported goodwill	No (*3)	Yes (*4)

(*1) FV: Fair Value (at the time of the purchase)
(*2) There is NO adjustment of balance sheet asset and liability values to their fair values.
(*3) The purchase price is NOT reflected on the balance sheet of the acquiring firm.
(*4) Reported goodwill could be depending on the fair value of the identifiable assets and liabilities compared to their book values.

Autocorrelation

Quarterly data = 36 quarters
Model: autoregressive model with a lag one independent variable (which is statistically different from zero)

Also include lag two and lag four terms, given the magnitude of the autocorrelations of the residuals shown below?

Significance level: 5%
df: 36-1=35
Critical t-value: 2.03 for a two tail test, 1.69 for a one-tail test

Autocorrelation

Lag	Autocorrelation	Standard error	t-statistic
1	0.0829	0.1690	0.49
2	0.1293	0.1690	0.76
3	0.0227	0.1690	0.13
4	0.1882	0.1690	1.11

n: number of observations = 36 - 1 = 35 → one quarter is lost because we have a lag one term, so there are 35 observations in the regression.
Standard error = 1/df^0.5 = 1/35^0.5 = 0.1690
t = autocorrelation/standard error

The critical t-value is 2.03 for a two-tail test, so none of the t-statistics indicate that the autocorrelations are significantly different from zero. Therefore, we do not need to include additional lag terms.

Adjusted R-squared

R-Square (R^2) is the proportion of variation in the dependent variable (Y) that can be explained by the predictors (X variables) in the regression model.

R²
= (regression sum of squares)/(total sum of squares)
= (regression sum of squares)/(regression sum of squares + error sum of squares)


As predictors (X variables) are added to the model, each predictor will explain some of the variance in the dependent variable (Y) simply due to chance. One could continue to add predictors to the model which would continue to improve the ability of the predictors to explain the dependent variable, although some of this increase in R-Square would be simply due to chance variation. The adjusted R-Square attempts to yield a more honest value to estimate R-Square.

Adjusted R-Square = 1-((1-R^2)*(N-1)/(N-k-1))
N: number of observations
k: number of predictors

When the number of observations (N) is small and the number of predictors (k) is large, there will be a much greater difference between R-Square and adjusted R-Square (because the ratio of (N-1)/(N-k-1) will be much less than 1).

By contrast, when the number of observations is very large compared to the number of predictors, the value of R-Square and adjusted R-Square will be much closer because the ratio of (N-1)/(N-k-1) will approach 1.

Cash Flow After Tax (CFAT) and Equity Reversion After Taxes (ERAT)

Cash Flow After Tax (CFAT) = NOI - Debt service - Income tax payable

• Borrowed money face value = $40,000,000 * 80% = $32,000,000
• Interest rate = 7%
• Interest payment per year for interest only loan = $32,000,000 * 7% = $2,240,000
• Depreciation per year = $1,250,000
• Annual growth rate of NOI = 5%

Cash Flow After Tax (CFAT)

Tax
Year	1	2	3	4	5
NOI	$4,200,000	(*6) $4,410,000	(*11) $4,630,500	(*16) $4,862,025	(*21) $5,105,126.25
Depreciation	$1,250,000	$1,250,000	$1,250,000	$1,250,000	$1,250,000
Interest expense	(*1) $2,240,000	$2,240,000	$2,240,000	$2,240,000	$2,240,000
Taxable income	(*2) $710,000	(*7) $920,000	(*12)  $1,140,500	(*17) $1,372,025	(*22) $1,615,126.25
Tax rate (*26)	0.40	0.40	0.40	0.40	0.40
Income tax payable	(*3) $284,000	(*8) $368,000	(*13) $456,200	(*18) $548,810	(*23) $646,050.5
CFAT
NOI	$4,200,000	(*6) $4,410,000	(*11) $4,630,500	(*16) $4,862,025	(*21) $5,105,126.25
Debt service	$2,240,000	$2,240,000	$2,240,000	$2,240,000	$2,240,000
Pretax cash flow	(*4) $1,960,000	(*9) $2,170,000	(*14) $2,390,500	(*19) $2,622,025	(*24)  $2,865,126.25
Income tax payable	(*3) $284,000	(*8) $368,000	(*13) $456,200	(*18) $548,810	(*23) $646,050.5
Cash flow after tax	(*5) $1,676,000	(*10) $1,802,000	(*15) $1,934,300	(*20) $2,073,215	(*25) $2,219,075.75

NOI: Net operating income

(*1) $32,000,000 * 7% = $2,240,000
(*2) $4,200,000 - $1,250,000 - $2,240,000 = $710,000
(*3) $710,000 * 0.40 = $284,000
(*4) $4,200,000 - $2,240,000 = $1,960,000
(*5) $1,960,000 - $284,000 = $1,676,000

(*6) $4,200,000 * (1+5%)^1 = $4,410,000
(*7) $4,410,000 - $1,250,000 - $2,240,000 = $920,000
(*8) $920,000 * 0.40 = $368,000
(*9) $4,410,000 - $2,240,000 = $2,170,000
(*10) $2,170,000 - $368,000 = $1,802,000

(*11) $4,200,000 * (1+5%)^2 = $4,630,500
(*12) $4,630,500 - $1,250,000 - $2,240,000 = $1,140,500
(*13) $1,140,500 * 0.40 = $456,200
(*14) $4,630,500 - $2,240,000 = $2,390,500
(*15) $2,390,500 - $456,200 = $1,934,300

(*16) $4,200,000 * (1+5%)^3 = $4,862,025
(*17) $4,862,025 - $1,250,000 - $2,240,000 = $1,372,025
(*18) $1,372,025 * 0.40 = $548,810
(*19) $4,862,025 - $2,240,000 = $2,622,025
(*20) $2,622,025 - $548,810 = $2,073,215

(*21) $4,200,000 * (1+5%)^4 = $5,105,126.25
(*22) $5,105,126.25 - $1,250,000 - $2,240,000 = $1,615,126.25
(*23) $1,615,126.25 * 0.40 = $646,050.5
(*24) $5,105,126.25 - $2,240,000 = $2,865,126.25
(*25) $2,865,126.25 - $646,050.5 = $2,219,075.75

(*26) Tax rate on ordinary income

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Equity reversion after taxes (ERAT) = net selling price - mortgage balance - taxes

Selling price (net of expense) = 45,000,000*(1-7%) = 41,850,000
Mortgage balance outstanding = 40,000,000*80% = 32,000,000
Capital gains tax = 15%
Tax on recaptured depreciation = 28%
Tax rate on ordinary income = 40%

Equity reversion after taxes (ERAT)
= net selling price - mortgage balance - taxes
= 41,850,000 - 32,000,000 - (1,250,000*5*28% + (41,850,000-40,000,000)*15%)
= 41,850,000 - 32,000,000 - (1,750,000 + 277,500)
= 7,822,500

Equity Reversion After Tax (AKA after-tax proceeds from resale)

Equity Reversion After Tax
The amount of money left for the investor after all obligations of the transaction, and income taxes on the transaction.

Equity Reversion After Tax

Resale price	$1,300,000
Transaction costs	$100,000	
Outstanding mortgage	$900,000
Tax on gain	$180,000
Equity reversion after tax	$120,000	= $1,300,000 - $100,000 - $900,000 - $180,000 = $120,000

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Equity Reversion After Tax

Gross selling price	$45,000,000
Selling expense	($3,150,000)	=($45,000,000*7%)
Net selling price	$41,850,000
Original purchase price	$40,000,000
Accumulated depreciation	$6,250,000	=($1,250,000 * 5)
Adjusted basis (book value)	$33,750,000	= $40,000,000 - $6,250,000
Realized gain on sale	$8,100,000	= $41,850,000 - $33,750,000
Recaptured depreciation	$6,250,000	Net selling price > Original cost (this case) Recaptured depreciation = Accumulated depreciation Net selling price < Original cost Recaptured depreciation = Net selling price - (Original cost - Accumulated depreciation)
Long-term capital gain	$1,850,000	= $8,100,000 - $6,250,000
Tax on recaptured depreciation	$1,750,000	= $6,250,000 * 28%
Tax on long-term capital gain	$277,500	= $1,850,000 * 15%
Total tax on property sale	$2,027,500	= $1,750,000 + $277,500

• Selling expense = Gross selling price * 7%
• The property will be fully depreciated at a rate of $1,250,000 per year over 32 years.
• Investment horizon = 5 years
• Taxes
• Capital gains tax = 15%
• Taxes on recaptured depreciation = 28%
• Tax rate on ordinary income = 40%

Equity Reversion After Tax

Net selling price	$41,850,000
Outstanding mortgage balance	$32,000,000	= Original purchase price - Paid cash = $40,000,000 - $40,000,000 * (1 - 80%)
Pre-tax sales proceeds	$9,850,000	= $41,850,000 - $32,000,000 = $9,850,000
Tax on property sale	$2,027,500
Equity reversion after tax	$7,822,500	= $9,850,000 -  $2,027,500

Tax on recaptured depreciation & Tax on long-term capital gain

Tax on recaptured depreciation & Tax on long-term capital gain

Gross selling price	$60,000,000
Selling expense	($4,200,000)	=($60,000,000*7%)
Net selling price	$55,800,000
Original purchase price	$40,000,000
Accumulated depreciation	$6,250,000	=($1,250,000 * 5)
Adjusted basis (book value)	$33,750,000	= $40,000,000 - $6,250,000
Realized gain on sale	$22,050,000	= $55,800,000 - $33,750,000
Recaptured depreciation	$6,250,000	Net selling price > Original cost (this case) Recaptured depreciation = Accumulated depreciation Net selling price < Original cost Recaptured depreciation = Net selling price - (Original cost - Accumulated depreciation)
Long-term capital gain	$15,800,000	= $22,050,000 - $6,250,000
Tax on recaptured depreciation	$1,750,000	= $6,250,000 * 28%
Tax on long-term capital gain	$2,370,000	= $15,800,000 * 15%
Total tax on property sale	$4,120,000	= $1,750,000 + $2,370,000

• Selling expense = Gross selling price * 7%
• The property will be fully depreciated at a rate of $1,250,000 per year over 32 years.
• Investment horizon = 5 years
• Taxes
• Capital gains tax = 15%
• Taxes on recaptured depreciation = 28%
• Tax rate on ordinary income = 40%

Depreciation Recapture

Purchase price = $10,000
Horizon for depreciation = 8 years
Total depreciation deduction = $6,000
Selling price in Year 8 = $6,000

[1] Selling price = $6,000 < Purchase price = $10,000
Recaptured gain = $6,000 - ($10,000 - $6,000) = $2,000
→reported as either ordinary income or capital gain, depending on the type of property that is sold.

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Purchase price = $10,000
Horizon for depreciation = 8 years
Total depreciation deduction = $6,000
Selling price in Year 8 = $15,000

[2] If Selling price > Original cost (purchase price), then
Recaptured depreciation = Accumulated depreciation = $6,000

If the equation in [1] is applied, then
Recaptured gain = $15,000 - ($10,000 - $6,000) = $5,000 + $6,000= $11,000 (incorrect)

Built-up Method

Capitalization Rate R₀(BU) = pure rate + liquidity premium + recapture premium + risk premium

• The interest rate on U.S. government bonds after adjustments for real estate based tax savings = 5.0%
• → pure rate
• The premium investors require for the illiquidity of real estate investments = 2.5%
• → liquidity premium
• The average real estate return net of appreciation = 1.25%
• → recapture premium
• The real estate investment risk premium = 3.0%
• → risk premium

Capitalization Rate R₀(BU) = 5.0% + 2.5% + 1.25% + 3.0% = 11.75%

Market Extraction Method

A real estate to be purchased

Units	60
Price	$40,000,000
Net Operating Income (for the first year after the sale)	$4,200,000
Historical annual growth rate of NOI	5%
Investment horizon	5 years
Selling price	$45,000,000 $60,000,000

A real estate similar to the real estimate above

Average selling price (per unit)	$1,250,000
Annual net operating income (per unit)	$135,000
Annual gross operating income (per unit)	(1/0.80)*$135,000

Market extraction method:
Capitalization Rate R₀ = NOI/MV = $135,000/$1,250,000 = 10.80%

Credit Enhancement

Credit Enhancement

Credit Enhancement
internal	Excess servicing spread funds (a type of reserve fund) Overcollateralization
external	Letters of credit Bond insurance

Credit Enhancement

	Credit Card Receivable ABS
Excess servicing spread	The ABS issuer pays a coupon to investors that is less than the coupon earned on the collateral. The excess of cash inflows over cash outflows is used to fund credit losses in the collateral.
Letter of credit	A letter of credit is a third party, usually a bank, guarantee against collateral losses up to a certain point. Defaults on the collateral are thus mitigated to a certain extent. The third-party guarantees are subject to the weak-link philosophy and any credit downgrades associated with the third party will negatively affect the rating of the ABS.
Overcollateralization	Total principal of collateral > Total principal of tranches (Total principal of collateral - Total principal of tranches) = extra collateral When (Total principal of collateral - Total principal of tranches) < 0, collateral defaut would first be absorbed by the extra collateral. Then losses from defaults (a credit event) are absorbed by subordinated tranche until the principal backing the tranche is exhausted. Home equity loan ABS.

Interest-Only(IO) and Principal-Only (PO) strips

Interest-Only(IO) and Principal-Only (PO) strips

interest rate	↑	↓	favorable prepayment	downside risk	convexity
prepayment	↓	↑
IO price (or return)	↑	↓	slow	Contraction risk
PO price (or return)	↓	↑	fast	Extention risk	negative at low current rate

(Question)
Which of the following statements about interest-only (IO) and principal-only (PO) strips is least accurate?

A. The IO price is positively related to interest rates, and at low current rates, POs exhibit some negative convexity.
B. IO cash flows start out large and diminish over time. As a result, IO investors are most concerned with extention risk.
C. In general, the volatility of the combined IO and PO strips equals the price volatility of the source passthrough.


Answer: B

Convertible bond: valuation

Convertible bond = Straight bond + Call option on underlying common stock

Option Adjusted Spread (OAS) and Z-spread

Z-spread and Option Adjusted Spread (OAS)

	applied to a security with an option?	appropriate securities
Z-spread	No	Option-free corporate bonds Credit card ABS Auto loan ABS
OAS	Yes	Callable corporate bonds MBS

valuing the option on securities

Most appropriate models for valuing the option on securities

	model	embedded option (prepayment option) ?	typically exercised?	interest rate path dependent?
MBS	Monte Carlo	Yes	Yes	Yes
credit card ABS	simple discounted cash flow model	No	-	No

Economic Income and Total after-tax cash flow

A system purchased:
price = 700,000
shipping, site preparation, and installation cost = 100,000
Δinventory = 50,000
Δaccounts payable = 20,000

sale price = 75,000

Relevant Cash Flows for a Project

Year	1	2	3	4	Total
Sales	750,000	750,000	750,000	750,000
Variable costs	225,000	225,000	225,000	225,000
Fixed expense	75,000	75,000	75,000	75,000
Depreciation	264,000	360,000	120,000	56,000	(*11) 800,000
Earnings before tax (EBT)	186,000	90,000	330,000	394,000
after-tax cash flow	375,600	414,000	318,000	(*12) 292,400
Net income (*1)	(*2) 111,600	(*3) 54,000	(*4) 198,000
Tax rate (*5)	(*6) 40%	(*7) 40%	(*8) 40%	(*9) 40%
A system-related cash flow	(*10) -830,000			75,000
Total after-tax cash flow	375,600-830,000 =-454,400	414,000	318,000	292,400+75,000 = 367,400

WACC = 8%


(*1) Net income = Total after-tax cash flow - Depreciation
(*2) 375,600 - 264,000 = 111,600
(*3) 414,000 - 360,000 = 54,000
(*4) 318,000 - 120,000 = 198,000
(*5) EBT * (1-t) = Net income = Total after-tax cash flow - Depreciation
t = 1-Net income/EBT = 1-(Total after-tax cash flow - Depreciation)/EBT
(*6) t = 1-Net income/EBT = 1-111,600/186,000 = 40%
(*7) t = 1-Net income/EBT = 1-54,000/90,000 = 40%
(*8) t = 1-Net income/EBT = 1-198,000/330,000 = 40%
(*9) given based on the result of (*6), (*7), and (*8)
(*10) Initial investment outlay = (price + shipping, site preparation, and installation cost) + increase in net working capital  = (700,000 + 100,000) + (50,000 - 20,000) = 800,000 + 30,000 = 830,000
(*11) 264,000 + 360,000 + 120,000 + 56,000

(*12) EBT * (1-t) = Net income = Total after-tax cash flow - Depreciation
Total after-tax cash flow = EBT * (1-t) + Depreciation = 394,000 * (1-40%) + 56,000 = 292,400
or
(S-C)(1-t) + D*t = (750,000-225,000-75,000)(1-40%) + 56,000*40% = 270,000 + 22,400 = 292,400

Terminal year after-tax non-operating cash flow (TNOCF) = Sal_T + NWCInv - t * (Sal_T - B_T)
= 75,000 + (50,000-20,000) - 40% * (75,000 - 0) = 75,000
B_T=0 since original (price + shipping, site preparation, and installation cost) = 800,000 = cumulative depreciation at Year 4

Why does NWCInv have positive sign and need to be added back?
You spend some money at the start of the project on NWCInv to start up the capital budgeting project. When the project ends - you get that money back (it gets freed up) and you can sell the NWCInv including inventory, and whatever you procured in the beginning. Since you get it back, you have to add it back and account for it at the end of period cash flow.

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Economic Income = After-tax Operating Cash Flow - Economic Depreciation
Economic Depreciation = Market Value(beginning) - Market Value(ending)
Market Value(time=t) = Present Value of all remaining cash flows discounted at the WACC

Market Value(beginning, Year 3)
= CF₃/(1 + WACC)¹ + CF₄/(1 + WACC)²
= 318,000/(1 + 8%)¹ + 367,400/(1 + 8%)²
= 609,430

Market Value(ending)
= CF₄/(1 + WACC)¹
= 367,400/(1 + 8%)¹
= 340,185

Economic Income(Year 3)
= After-tax Operating Cash Flow (Year 3) - Economic Depreciation (Year 3 to 4)
= 318,000 - (609,430 - 340,185)
= 48,755

Equity Method: Removing the effects of the income reported under the equity method

• For a firm that reports equity income as non-operating income (not included in EBIT, but in Net Income)
• Removing the
• equity income from I/S (i.e. net income)
• equity asset on the B/S

Equity Method: Removing the effects of the income reported under the equity method

items	increase/ decrease/ unchanged
Equity	↓
Assets	↓
Asset Turnover Ratio (=Revenue/Assets)	→/↓ = ↑
Tax Burden (= Net Income / EBT)	↓/→ = ↓
Interest Expense	→
Operating Earnings; EBIT	→
Interest Coverage Ratio (=EBIT/Interest Expense)	→/→ = →

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(Question)
For a firm that reports equity income as non-operating icome (NOT included in EBIT), removing equity income from the financial statements would most likely result in:

A. an increase in the tax burden term in the extended Du Pont decomposition of ROE.
B. an increase in the asset turnover ratio.
C. a decrease in the interest coverage ratio.


Answer: B

Off-Balance-Sheet Item: Securitization of receivables

Elimination of the securitization of receivables as an off-balance-sheet item:

• Report securitized borrowing transaction
• Replace the receivables on the B/S
• Report a liability equal to the proceeds of the securitization transaction

Elimination of the securitization of receivables

Equity	→ (or small change)
Liabilities	↑
Assets	↑
Financial leverage = Total Assets / Total Equity	↑
Interest Expense (from the liability)	↑
Interest Coverage Ratio (=EBIT/Interest Expense)	↓

--
(Question)
A company formed a QSPE(Qualified Special Purpose Entity) and sold a portion of its receivables account to the QSPE.

If the FASB were to retroactively eliminate the allowance of QSPEs created for the securitization of receivables, the most likely impact on the companys financial statement would be:

A. an increase in equity and an increase in interest expense.
B. no change in assets but an increase in financial leverage ratios.
C. an increase in financial leverage ratios and a decrease in the interest coverage ratio.


Answer: C

Net Operating Asset

Net Operating Asset

		NOA
Payable (liability)	↑	↓
Inventory	↑	↑
Cash	↑	↓ (*)

(*) Cash is not an operating asset, but is deducted from Total assets to calculate net operating assets.

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(Question)
Regarding the balance sheet accrual ratio, which of the following, other things equal, would most likely lead to an increase in the ratio for a growing company?

A. Extending the time the firm takes to pay its suppliers.
B. A significant build-up of cash.
C. A build-up of inventory.

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Answer: C

Net Operating Asset
= Operating Asset - Operating Liabilities
= (Total Asset - Cash&Investment) - (Total Liabilities - Long term debt including current portion)

Net Operating Asset

	Net Operating Asset=	+Total Asset	-Cash&Investment	-Total Liabilities	+LTD incl. current portion
A.	↓		↑	↑
B.	↓		↑
C.	↑	↑

Economic Growth Theories

Economic Growth Theories

Economic growth theory	Classical	Neoclassical	New Growth(*3)
population growth	Positive effect	No effect
increasing the productivity of labor	No effect (*4)
increasing the rate of savings and investment	No effect (*4)
return to capital		↓(after a period of growth)
real interest rate		↓(after a period of growth)
per capita GDP will settle at a subsistence level?	Yes(*1)	Yes	No
continued growth (NOT level) in dividends			Yes(*2)
convergence with richer countries due to acess to the same world class technology and capital markets as its more advanced neighbors?		Unlikely (*5)
Equilibrium		Target rate of return (*6) = Real interest rates (*7)
Technological change (advances)		Increase Real GDP Savings Capital and lead to: Increased investment Higher dividend levels (NOT long-run growth rate) Higher savings do NOT affect a country's long-run economic growth rate.	Sustainable economic growth Higher dividend levels & Long-term dividend growth rates (through increased savings)

(*1) (1) higher population → (2) decreased return to labor (labor productivity); no permanent increase in labor productivity will result.
Anything that increases real GDP per hour of labor above subsistence level causes population growth that overwhelms the gains from increased productivity due to a greater level of capital.

(*2) because technological advances will be shared by many sectors of economy
(*3) AKA Endogenous Theory.

(*4) Neither condition would allow the country to increase the long-term level of real wages. Under the classical theory of economic growth, an economy would have a temporary improvement in the labor living standards as the real wage rate climbed above the subsistence wage rate, but over time population growth would lower capital per hour of labor and drive real GDP per hour of labor back towards the subsistence wage level.

(*5) Due to difference in savings rates and target rates of return.
The neoclassical growth theory model does imply that given access to the same technology and capital markets, then growth rates and income levels per person should begin to converge on a global basis. While some convergence has occured over time, many countries are just as far away from the rich countries as they have ever been. This lack of convergence in the real world is probably due to the fact that the neoclassical growth model leaves out many of the variables that must grow at the same rate in difference countries for convergence to occur. Obstacles to convergence include differences in population growth rates, in rates of technological change, and most importantly, in savings rates and target rates of return. In essence, if the countries do not have similar economic and demographic characteristics, then it would be difficult for them to grow at the same rate.

(*6) achieved in the market
(*7) rates of return the investor wishes to earn

One-third rule

Labor Productivity

Real GDP per labor hour	2001	$20.00
Real GDP per labor hour	2007	$21.50
Capital per labor hour	2001	$35.00
Capital per labor hour	2007	$36.80

Growth in labor productivity = $21.50/$20.00 - 1 = 7.50%

Growth in capital per labor hour = $36.80/$35.00 - 1 = 5.14%
One-third rule: 5.14%*(1/3) = 1.71% → A part of increase in labor productivity

Growth in labor productivity due to improvements in technology: 7.50% - 1.71% = 5.79%

Standard IV(B) Duties to employer: Additional Compensation Arrangements

• It relates to additional compensation related to an employee's services to the employer.
• (e.g.) A part-time bartender job of a stock analyst
• The moonlighting is NOT related to his or her stock analysis job and, as such, does not violated the standard.
• There is nothing inherently unethical about working as a bartender, and moonlighting as a barkeeper dose not compromise his or her professional reputation, integrity, or competence.

CFA Institute Soft Dollar Standards

• Soft Dollar
• Commissions generated by
• external brokerage operations
• internal brokerage operations
• CFA Institute Soft Dollar Standards
• Voluntary, though firms that wish to claim compliance with the Standards must follow them completely.
• Client Brokerage
• Can be used to pay for a mixed-use research with the coveat that the research must be reasonable, justifiable, and documentable, and that the client brokerage is only used to pay for the portion of the research that will be used in the investment decision-making process.
• While research paid for by client brokerage should directly benefit the client, it does not have to do so immediately.

Interest Rate Cap, Floor, and Call

Interest Rate Cap, Floor, and Call

Interest rate		↑	↓	Payment(payoff) to a holder(i.e. long):
Interest rate Cap	long	+ (*1)	-	(interest rate - cap rate)*(Actual date/360)
Interest rate Floor	long	-	+	(floor rate - interest rate)*(Actual date/360)
Interest rate Call (*3)	long	+ (*2)	-

+: positive return
-: negative return

(*1) rise above the cap rate
(*2) rise above the strike rate
(*3) receive variable, pay fixed interest rate

Business Risk

unexpected change in the level of real business activity

Confidence Risk

unexpected change in the difference between the return of risky corporate bonds and government bonds

Build-up Method, Risk-Premium Approach, and Bond-Yield Plus Risk Premium Method

Build-up Method, Risk-Premium Approach, and Bond-Yield Plus Risk Premium Method

	Build-up Method	Risk-Premium Approach	Bond-Yield Plus Risk Premium Method (*4)
Applicable for a closely held companies?	Yes(*3)
Beta required?	No	Yes
A company's publicly traded debt required?			Yes
values as estimates	typically historical (*2)

Bond-Yield Plus Risk Premium Method:
required return = r_i= YTM(*1) of the company's long-term debt + Risk Premium

(*1) YTM: Yield To Maturity
(*2) that may not be relevant to current market conditions (weakness of the model)
(*3) where betas are not readily obtainable
(*4) The method simply adds a risk premium to the yield to maturity of the company's long-term debt.

Fama-French model (FFM) and Pastor-Stambaugh (PS) model

Fama-French model (FFM) and Pastor-Stambaugh (PS) model

	market	size	relative value	liquidity
Fama-French model (FFM)	Yes	Yes	Yes
Pastor-Stambaugh (PS) model	Yes	Yes	Yes	Yes

PS model:
r_i - R_f = e_M * (r_M - R_f) + e_S * (r_S - R_f) + e_V * (r_V - R_f) + e_L * (r_L - R_f)
r_i - R_f = e_M * RP_M + e_S * RP_S + e_V * RP_V + e_L * RP_L

Industry Life Cycle

1. pioneer: It is not clear that a product will be accepted in the industry.
2. growth: Proper execution of strategy is critical.
3. mature: Participationts compete for market share in a stable industry.
4. decline: Changing tastes have an impact on the industry.

pricing considerations: factors that directly affect pricing considerations

• product segmentation
• degree of industry concentration
• ease of industry entry
• price changes in key supply inputs

Industry Analysis

External factors

• technology
• government
• social
• demographic
• foreign

Others

• industry classification
• demand
• supply
• profitability

Persistence Factor: The strength of the persistence factor with respect to residual income

Persistence Factor: The strength of the persistence factor with respect to residual income

persistence factor	high	low
dividend payments	low
nonrecurring items on the I/S		significant

EBITDA as a poor proxy for both FCFF and FCFE

EBITDA as a poor proxy for both FCFF and FCFE

	FCFF	FCFE	EBITDA
NI	+	+
NCC	+	+
Int*(1-t)	+		N/A
WCInv	-	-	N/A
FCInv	-	-	N/A
Net borrowing		+	N/A
Tax paid	(*)	(*)	N/A

(*) included in NI


EBITDA is a poor proxy for both FCFF and FCFE.

FCFE: The most appropriate valuation model under relatively constant proportions of equity and debt financing

• Company's capital structure is reasonably stable
• FCFE > 0

Then FCFE is a simpler approach to valuation than ECFF, EVA, or residual income.