fcs 5510 formula sheet *note: the formulas i expect you to...
TRANSCRIPT
FCS 5510 Formula Sheet
*Note: The formulas I expect you to know are
colored in Red. They are either more conceptually
based, or are more commonly used than the
others. You need to have a passing familiarity with
the rest of the formulas, but I do not expect you to
memorize them. If you see these formulas you do
need to know in general what they are used for.
Note present value (PV) and future value (FV)
formulas are not here because I assume you
learned them somewhere else in one of the
prerequisite classes. You do need to understand
the setup of those formulas.
Unit 01
1. Return computation with cash purchase vs. margin purchase
• P0= the purchase price of the security
• P1= the selling price of the security
• M=margin
• n = number of shares
Return with cash purchase = ( P1 *n - P0 *n)/ (P0 * n)
Return with margin purchase = (P1 *n - P0 *n ) / (P0 * M *n)
If commission/transaction costs C are involved, then
Return with cash purchase = ( ( P1 *n - P0 *n) – C)/ (P0 * n)
Return with margin purchase =( (P1 *n - P0 *n ) –C) / (P0 * M *n)
Unit 02
1. Tax owed or saved
Tax owed or saved = Taxable amount * marginal tax rate
2. Expected Return
• E(r)= the expected return
• E(D)= the expected dividend or interest income
• P= the price of the asset
• E(g)=the expected growth in the value of the asset
3. Realized Return (Note this formula is pretty much the same as the expected
return except the numbers in expected returns are expected instead of real)
• r= the realized return
• D= the realized dividend or interest income
• P= the price of the asset
• g=the realized growth in the value of the asset
4. A Portfolio Standard Deviation (SDP) of Two Assets
• Notations:
– SA = Standard Deviation of asset A
– SB = Standard Deviation of asset B
– WA = Portfolio weight of asset A
– WB = Portfolio weight of asset B
– rAB=Correlation coefficient of assets A & B.
• Portfolio SDP of assets A and B is
5. Beta Coefficient
• Beta coefficient is an index of volatility of an asset relative to the volatility of
the market.
)()(
)( gEP
DErE +=
gP
Dr +=
ABBABABBAAP rSSWWSWSWSD 22222 ++=
• Notation:
– βi = Beta of asset i
– σi = Standard Deviation of return on asset i
– σM = Standard Deviation of return on the market
– riM=correlation coefficient between the return on asset i and the
return on the market
Unit 03
1. Net Asset Value
2. The Jensen Index (Also called Alpha)
3. The Treynor Index
4. The Sharpe Index
iM
M
i
i r×=σ
σβ
dingOutsSharesofNumber
LiabilityTotalAssetsTotalNAV
tan
−=
Unit 04
1. Payout Ratio
2. Retention Ratio = 1- Payout Ratio or
3. Current Ratio
4. The Quick Ratio
5. Inventory Turnover
6. Average Collection Period
7. Receivable Turnover
8. Fixed Asset Turnover
9. Gross Profit Margin
10. Operating Profit Margin
11. Net Profit Margin
12. Return on Assets
13. Return on Equity
14. Return on Common Equity
15. DuPont System Return on Equity
• Net Profit Margin
• Total Asset Turnover
• An equity multiplier that indicates the firm’s use of leverage.
16. Debt to Equity Ratio
17. Debt to Total Asset Ratio (Debt Ratio)
18. Times – Interest Earned Ratio
Unit 05:
1. Expected Return
• E(d) = expected dividend
• P = price of the stock
• E (g) = expected growth
E(r) = (E(d)/P) + E(g)
2. Dividend Valuation Model – Assuming No Growth in Dividends Over Time
• V=Valuation
• D=Dividends
• k=Discount rate=Required return
2. Dividend Valuation Model-Dividend grows at rate g
• V=Valuation
• D0=Initial dividend (first year)
• k=Required return
• g=Dividends annual growth rate
3. Required Return (k) – in some other occasions the notation is rs
• rf = the risk free rate (i.e.Treasure Bill rate)
• rM = the return on the market
• β = the stock's beta
K=rf + (rM - rf)β
4. Price to Earnings Ratio
5. PEG Ratio
)(
)1(0
gk
gD
−
+=V
k
D=V
6. Stock Valuation Using P/E Ratio
• m = the “appropriate P/E ratio”
• EPS = earnings per share
P = (m)(eps)
7. P/B Ratio
8. Adjusted PEG Ratio
9. Return on Equity
10. Profit Margin
11. Price Weighted Average
*Could add any number of stock prices to the equation.
12. Value Weighted Average
*Could add any number of stock prices to the equation
14. Geometric Average
*Can add any number of stock prices to the equation.
N = the total number of stocks included
Geometric average = (Price of Stock A * Price of Stock B)^(1/n)
15. Holding Period Return (HPR)
• P0 = purchase price
• P1 = sell price
• D = dividend
16. Dollar Weighted Rate of Return (True Annualized Rate of Return or Internal Rate
of Return)
0 01P
PDPHPR −+=
nn
n
r
P
r
D
r
DP
)1()1(...
)1(
11
0+
++
+++
=
Unit 06:
1. Gross Domestic Product GDP
• C = personal consumption
• I = gross private domestic investment
• G = government spending
• E = net exports
GDP = C + I + G + E
Unit 07: Fixed Income Securities: Bond Market and Valuation of Fixed-Income
Securities
1. Price of a Perpetual Security:
• PMT = annual interest payment
• i = discount rate
2. Price of a Bond
• PMT = Interest Payments Each Year
• FV = Final Principal Payment
• i = annual discount rate
• n = number of years to maturity
P PMT
i =
(1 + i)
P PMT x =
1 - 1
n
(1 + i)
1 n i
+ FV x
3. Price of a Zero Coupon Bond
• FV = Final Principal Payment
• i = annual discount rate
• n = number of years to maturity
4. Current Yield
5. Duration
• D = Duration
• PV = Present Value
• t = time (from 1 to m where m is maturity time)
• CFt = cash flow for year t
6. Simplified Formula for Duration Computation
• c = annual coupon (as a percentage)
• n = number of years to maturity
• y = the yield to maturity (reinvestment rate)
FV
(1 + i) P
=
n
Current Yield = Annual Interest Payment
Price of the Bond
∑ m
t = 1
PVCF x t t
P B
D =
Unit 08: Government Securities
1. Discount Yield
2. Yield to Maturity (annualized maturity)
3. Par Value
• n = days to maturity/365
4. Compound Yield
D = 1 + y
y -
(1 + y) + n(c – y)
c[ (1 + y) - 1] + y n
Discount Yield = Par Value - Price
Par Value
360
Days to Maturity x
Discount Yield = Par Value - Price
Par Value
365
Days to Maturity x
Par Value = Price x (1+ r) n
Compound Yield r = Par Value
Price ( )
1/n
- 1
5. Determining equivalent yields on tax exempt and non-exempt bonds
• lc = yield on non-exempt bonds
• lm = yield on municipal bonds (exempt)
• tf = federal marginal tax rate
• ts = state marginal tax rate
Mortgage Backed Securities
6. Determining expected annual payment from the MBS
loan amount/PVFS
PVFS is listed on p.77 (Chapter 3) of the textbook as PVAIF
7. Determining the current value of the MBS
Annual payment*PVFS
8. Determing the current value of the MBS with interest rate decline and refinancing.
Annual payment*PVFS + lump sum balance*PVF
PVF is listed on p.76 (Chapter 3) of the textbook as PVIF
*Please see slides 27-29 of Unit 8 Powerpoint for more information on MBS
im = ic(1 – tf – ts)
Unit 09: Options
1. Market Price of a call
2. Time Value of a Put
Unit 10: Commodities and Financial Futures
No formulas
Unit 11: Portfolio Management
1. Net Worth
Market price of a call = intrinsic value + time premium
Time Value of a put = price of the put – intrinsic value of the put
Net Worth = Total Assets – Total Liabilities