Unit Return computation with cash purchase vs. margin purchase

(1)

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)

(2)

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. • Notation:

)

(

)

(

)

(

E

g

P

D

E

r

E

=

+

g

P

D

r

=

+

AB B A B A B B A A P

W

S

W

S

W

S

r

SD

=

2 2

+

2 2

+

2

(3)

– 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

Unit 04:

1. Dividend Valuation Model – Assuming No Growth in Dividends Over Time

iM M i i

=

×

r

σ

β

ding

Outs

Shares

of

Number

Liability

Total

Assets

Total

NAV

tan

−

=

(4)

• 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 + (r

M

- r

f

)β

4. Price to Earnings Ratio

5. PEG Ratio

6. Stock Valuation Using P/E Ratio

• m = the “appropriate P/E ratio” • EPS = earnings per share

)

(

)

1 (

0

g

k

g

D

−

+

=

V

k

D

=

V

(5)

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

13. Equal Weighted Average

*Could add any number of stock prices to equation. Also assumes an equal dollar amount is invested in each stock

(6)

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) Unit 05: 1. Payout Ratio 0 0 1

P

D

P

HPR

=

+

−

n n n

r

P

r

D

r

D

P

)

1 (

)

1 (

...

)

1 (

1 1 0

+

=

(7)

2. Retention Ratio = 1- Payout Ratio or

3. Growth Rate

• ROE = return on equity • RR = retention ratio

Growth Rate g = ROE x RR

4. . Gross Domestic Product GDP • C = personal consumption

• I = gross private domestic investment • G = government spending

• E = net exports

GDP = C + I + G + E

Unit 06:

1. Current Ratio

2. The Quick Ratio

3. Inventory Turnover

(8)

5. Receivable Turnover

6. Fixed Asset Turnover

7. Gross Profit Margin

8. Operating Profit Margin

9. Net Profit Margin

10. Return on Assets

11. Return on Equity

(9)

13. DuPont System Return on Equity • Net Profit Margin

• Total Asset Turnover

• An equity multiplier that indicates the firm’s use of leverage.

14. Debt to Equity Ratio

15. Debt to Total Asset Ratio (Debt Ratio)

16. Times – Interest Earned Ratio

17. Expanded Coverage Ratio

(10)

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

3. Price of a Zero Coupon Bond

• 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

(11)

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

D =

1 + y

y

-

(1 + y) + n(c – y)

c[ (1 + y) - 1] + y

n

∑

m

t = 1

PVCF x t

_t

P

B

D =

(12)

Unit 08: Government Securities 1. Discount Yield 2. Yield to Maturity 3. Par Value • n = days to maturity/365 4. Compound Yield

5. Determining equivalent yields on tax exempt and non-exempt bonds • lc = yield on non-exempt bonds