financial management paper 1

8/8/2019 Financial Management Paper 1

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FINANCIAL MANAGEMENT -- PAPER 1

CHAPTER:- INDIAN FINANCIAL SYSTEM

1. T-Bill Yield (k) = d

365

P

PF

Where, F = Face value of T-Bill (If not given assume 100)

P = Price / Issue Price of T-Bill

d = Maturity period in days.

CHAPTER:- TIME VALUE OF MONEY

COMPOUNDING

It is a process to find future value when present value is known.

SITUATION A:- SINGLE CASH FLOW

Compounded Annually Compounded many a times during the year

Method 1:-

FV = PV[(1+k) n ]

FVIF

Where, FV = Future Value

PV = Present Value

k = Interest Rate

n = No of Years

(1+k) n = Future Value Interest Factor

(FVIF)

Method 2:-

From the above method 1 we can draw one more

formulae, i.e,

FV = PV x FVIF n)k,(

Method:-

(a) Find Effective/Flat rate of Int. (r)

r = 1m

k1

m

+

Where, k = Interest Rate

m = No of times compounding is done

(b) Then apply FV = PV(1+r) n on annual basis

SITUATION B:- ANNUITY AT THE END OF THE YEAR


Method 1:-

FVA n = A( )

+

k

1k1n

FVIFA

Where, A = Annuity

Method 2:-

From the above method 1 we can draw one moreformulae, i.e,

FVA n = A x FVIFA n)k,(

Method:-


r = 1m

k1

m

+



(b) Then apply FVA n = A( )

+

r

1r1n

on

annual basis

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SITUATION C:- ANNUITY AT THE BEGINNING OF THE YEAR


Method 1:-

FVA n = A(1+k)( )

+

k

1k1n

FVIFA

Method 2:-


formulae, i.e,

FVA n = A(1+k) x FVIFA n)k,(

Method :-


r = 1mk1

m

+



(b) Then apply FVA n = A(1+r)( )

+

r

1r1n

on

annual basis

DISCOUNTING

It is a process to find present value when future value is known.

SITUATION A:- SINGLE CASH FLOW


Method 1:-

We know, FV = PV(1+k) n

or, PV = FV

k)+(1

1n

PVIF

Method 2:-


formulae, i.e,

PV = FV x PVIF n)k,(

Method 1:-


r = 1m

k1

m

+



(b) Then apply PV = FV

r)+(1

1n on annual

basis

SITUATION B:- ANNUITY AT THE END OF THE YEAR


Method 1:-

PVA n = A( )

( )

+

+n

n

k1k

1k1

PVIFA

Method 2:-


formulae, i.e,

PVA n = A x PVIFA n)k,(

Method:-(a) Find Effective/Flat rate of Int. (r)

r = 1m

k1

m

+



(b) Then apply PVA n = A( )

( )

+

+n

n

r1r

1r1on

annual basis

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SITUATION C:- ANNUITY AT THE BEGINNING OF THE YEAR


PVA n = Annuity + Annuity at the end of the

year compounded annually for (n-1)

yearsMethod 1:-

PVA n = A +

+

+

1-n

1-n

k)k(1

1k)(1A

PVIFA

Method 2:-


formulae, i.e,

PVA n = A + [A x PVIFA 1)-nk,( ]

RELATION BETWEEN NOMINAL INTEREST RATE, REAL INTEREST

RATE, AND INFLATION

(1+r) = (1+R)(1+a)

Where, r = nominal rate of Interest,

R = Real rate of Interest,

a = Inflation rate

EFFECTIVE/FLAT RATE OF INTEREST

Effective/Flat rate of Interest is found when compounding is done many a times during the

year, and the payment is done annually. Thus Effective/Flat rate of Interest is calculated as r =

1m

k1

m

+ .

Again, when payment is made rather than annually (may be monthly, quarterly, semi-

annually), then we will calculate Effective/Flat rate of Interest is calculated as per month, per

quarter, per semi-annual )r( as the case may be. Then we will find FV, FVA, PV, PVA )r(

taking into effect. For calculating it,

First, find Effective/Flat rate of Interest (r), calculated as r = 1m

k1

m

+ .

Then find Effective/Flat rate of Interest per month, per quarter, per semi-annual )r( ,

calculated as, )r( = 1r)1( m1

+

Then we will find FV, FVA, PV, PVA )r( taking into effect.

Example of discounting for Annuity at the beginning of the year compounded annually:-

Problem:- Annuity of Rs. 2000 is deposited at the beginning of the year for full 4 years with a

compound interest of 10% p.a. compounded annually. Find out the present value of the Annuity.

Solution:-

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Compounded Interest:- 10% p.a. compounded annually

Annuity is deposited at the beginning of the each year. Thus Annuity of Rs. 2000 deposited

at the beginning of the 1st year will be as same as Rs. 2000 and the Annuity of Rs. 2000 each

deposited at the beginning of the 2nd, 3rd, and 4th year will be calculated on Annuity at the end of the

year at 10% p.a. compounded annually for 3 years.

i.e, PVA n = Annuity + Annuity at the end of the year compounded annually for (n-1) years

Method 1:-

PVA n = A +

+

+

1-n

1-n

k)k(1

1k)(1A

or, PVA n = 2000 +

++1-4

1-4

.10)00.10(1

1.10)0(12000

or, PVA n = 2000 +

3

3

.10)10.10(

1.10)1(2000

or, PVA n = 2000 +

1331.0

331.02000

or, PVA n = 2000 + (2000 x 2.487)

PVA n = 4973

Method 2:-

PVA n = A + [A x PVIFA 1)-nk,( ]

or, PVA n = A + [A x PVIFA 10%,3)( ]

or, PVA n = 2000 + (2000 x 2.487)

PVA n = 4973

DOUBLING PERIOD

According to Rule 72, Doubling Period =

RateInterest

72

According to Rule 69, Doubling Period = 0.35 +RateInterest

69

SINKING FUND FACTOR (SFF)

We know, Annuity at the end of the year compounded annually,

FVA n = A( )

+

k

1k1n

or, A = FVA n

+

1k)(1

kn

Where,

+ 1k)(1

kn is known as Sinking Fund Factor i.e. SFF =

( )nk,FVIFA

1

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CAPITAL RECOVERY FACTOR (CRF)

We know, Annuity at the end of the year compounded annually,

PVA n = A

( )

( )

+

+n

n

k1k

1k1

or, A = PVA n ( )

( )

+

+

1k1

k1kn

n

CRF

Where,( )

( )

+

+

1k1

k1kn

n

is Capital Recovery Factor i.e. CRF =( )nk,PVIFA

1

PRESENT VALUE OF A PERPETUITY (P)

Present value of Perpetuity (P

) =k

I

Where, I = Instalment/Annuity

k = Rate of Interest

Net Present value of Perpetuity = Present value of cash inflow - Present value of cash outflow

Problem:- Mr. Farooq is considering to purchase a commercial complex that will generate a net

cash flow of Rs. 4,00,000 at the end of every year till perpetuity. Mr. Farooqs required rate ofreturn is 12%. How much should Mr. Farooq pay for the complex if it produces cash flow forever.

Solution:- We know, Present value of Perpetuity (P

) =k

I

Where, I = Instalment/Annuity = Rs. 4,00,000

k = Rate of Interest = 12% = 0.12

Present value = 333,33,330.12

4,00,000=

PRESENT VALUE OF CASH FLOWS GROWING AT CERTAIN % TILL

Present value =gk

yearoneofendat theflowCash

e

Where ek = Required rate of return, g = Annual growth rate in cash flows.

Problem:- Mr. Farooq is considering to purchase a commercial complex that will generate a net

cash flow of Rs. 4,00,000 at the end of one year. The future cash flows are expected to grow at the

rate of 4% per annum. Mr. Farooqs required rate of return is 12%. How much should Mr. Farooq

pay for the complex if it produces cash flow forever.

Solution:- We know, Present value =gk

yearoneofendat theflowCashe

Where ek = Required rate of return = 12% = 0.12

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g = Annual growth rate in cash flows. = 4% = 0.04

Present value = 50,00,000Rs.08.0

000,00,4

0.040.12

4,00,000==

RELATIONSHIP BETWEEN DIFFERENT FACTORS

(a). We know, FVIF = (1+k) n and PVIF = nk)+(1

1

Thus we can say, PVIF =FVIF

1

(b). We know, FVIFA =( )

k

1k1n +

and PVIFA =( )

( ) n

n

k1k

1k1

+

+

Thus we can say, PVIFA =FVIF

FVIFA

or, PVIFA = FVIFAPVIF

(c). We know, Sinking Fund Factor =1k)(1

kn+

Thus we can say, Sinking Fund Factor =FVIFA

1

or, Sinking Fund Factor =FVIFPVIFA

1

(d). We know, Capital Recovery Factor =( )

( ) 1k1

k1kn

n

+

+

Thus we can say, Capital Recovery Factor =PVIFA

1

or, Capital Recovery Factor =FVIFA

FVIF

[NOTE:- Relationships are not limited to these only. It can be drawn to any extent. There is no such

limitation of relationship]

CHAPTER:- LEVERAGERs.

Sales Less:- Variable Cost Contribution

Less:- Fixed Cost/Operating Cost

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Where, EBIT = Earning before Interest & Tax/Operating profit = FV)Q(S ,

I = Interest/Fixed Financing Cost, pD = Preference Dividend

T = Tax rate

FINANCING BREAK EVEN POINT (Rs.)

Financing Break Even Point is that level of output at which DFL will be undefined (i.e.

Denominator is zero)

We know, DFL =

T)(1

DIEBIT

EBIT

p

DFL is (undefined) when denominator is zero (0).

i.e.T)(1

DIEBIT

p

= 0

or,T)(1

DIEBITp

+=

Thus, whenT)(1

DIEBIT

p

+= , Financial Break Even Point is achieved.

DEGREE OF TOTAL / COMBINED LEVERAGE (DTL / DCL)

Degree of Total / Combined Leverage (DTL / DCL) = DOL DFL

(a) Degree of Combined Leverage (DTL / DCL) =EBITinchange%

EPSinchange%

Quantityinchange%

EBITinchange%

or, Degree of Combined Leverage (DTL / DCL) =Quantityinchange%

EPSinchange%

(b) Degree of Combined Leverage (DTL / DCL) =

T)(1

DIEBIT

EBIT

EBIT

onContributi

p

or, Degree of Combined Leverage (DTL / DCL) =

T)(1

DIFV)Q(S

FV)Q(S

FV)Q(S

V)Q(S

p

or, Degree of Combined Leverage (DTL / DCL) =

T)(1

DIFV)Q(S

V)Q(S

p

Where, Q = Quantity sold, S = Selling Price per unit,

V = Varible Cost per unit, F = Fixed Cost/Fixed Operating Cost.

I = Interest/Fixed Financing Cost, pD = Preference Dividend

T = Tax rate, EBIT = Earning before Interest & Tax/Operating Profit

TOTAL / COMBINED / OVERALL BREAK EVEN POINT (Q)

Total / Combined / Overall Break Even Point is that level of output at which DCL / DTL will be

undefined (i.e. Denominator is zero)

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We know, DTL / DCL =

T)(1

DIFV)Q(S

V)Q(S

p

DTL / DCL is (undefined) when denominator is zero (0).

i.e.T)(1

DIFV)Q(S

p

= 0

or,T)(1

DIFV)Q(S

p

++=

or,

VS

T)(1

DIF

Q

p

++

=

Thus, whenVS

T)(1

DIF

Q

p

++

= , Total / Combined / Overall Break Even Point is achieved.

CHAPTER:- VALUATION OF SECURITIES

VALUATION OF BONDS

(a) Basic Bond Valuation Model:- Sometimes the holder of a bond receives a fixed annual interest

payment for a certain number of years and a fixed principal repayment (equal to par value) at

the time of maturity. Therefore, the intrinsic value or the present value of a bond can now be

written as:

)F(PVIF)I(PVIFA)P(V n,kn,k00 dd +=

Where, V 0 = Intrinsic value of the bond / Value of bond

0P = Present value of the bond, I = Annual interest payable on the bond

F = Principal amount (par value) repayable at the maturity time

n = Maturity period of the bond, kd = Required rate of return/ Capitalisation rate.

(b) Bond Value with Semi-Annual Interest:-Some of the bonds carry interest payment semi-

annually. As half-yearly interest amounts can be reinvested the value of such bonds would be more

than the value of the bonds with annual interest payments. Hence, the bond valuation equation can

be modified as:i. Annual interest payment i.e., I, must be divided by two to obtain interest payment semi-

anually.

ii. Number of years to maturity will have to be multiplied by two to get the number of half-

yearly periods.

iii. Discount rate has to be divided by two to get the discount rate for half-yearly period.

Thus with the above modifications, the bond valuation equation becomes:

+

=

n2,2

k

n2,2

k00 ddPVIFFPVIFA

2

I)P(V

Where, V 0 = Intrinsic value of the bond

0P = Present value of the bond

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2

I= Semi-annual interest payable on the bond

F = Principal amount (par value) repayable at the maturity time

2n = Maturity period of the bond (i.e total no of payments)

2

kd

= Required rate of return for half-year period.

ONE PERIOD RATE OF RETURN

If a bond is purchased and then sold one year later, its rate of return over this single holding

period can be defined as one period rate of return.

One period rate of return =

Real rate of return = One period rate of return Inflation rate

CURRENT YIELD

Current yield:-PriceMarketCurrent

InterestCoupon

YIELD TO MATURITY(YTM)

It is the rate of return earned by an investor who purchases a bond and holds it tillmaturity. The YTM is the discount rate which equals the present value of promised cash flows to

the current market price/purchase price.

Yield to Maturity(YTM) =

0.6P0.4F

n

PFI

+

+

or, YTM =

2

PFn

PFI

+

+

Where, I = Interest, F = Redemption Value, P = Issue Price (i.e Market Price), n = No. of years

EQUITY VALUATION

(A)Single Period Valuation Model:- This model is for an equity share wherein an investor holds

it for one year. The price of such equity share will be:-

D1

Year - 1

0P 1P

Now, 0P = PV of Dividend received received during Yr. 1 + PV of price of share after Yr. 1

1),(k11),(k10 ee PVIFPPVIFDP +=

or,)k(1

P

)k(1

DP

e

1

e

1

0+

++

=

=

k)+(1

FVPV

n

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Where, 0P = Current market price of the share, 1D = Expected dividend a year hence

1P = Expected price of a share a year hence, ek = Required rate of return/Capitalisation

rate

(B)Multi Period Valuation Model:- This model is for an equity share wherein an investor holds itfor more than one year (say 4 years). The price of such equity share will be:-

D1 2D 3D 4D

Yr. 1 Yr. 2 Yr. 3 Yr. 4

0P 4P

Now, 0P = PV of Yr. 1 Dividend + PV of Yr. 2 Dividend + PV of Yr. 3 Dividend + PV of Yr. 4

Dividend + PV of Redemption value of share at the end of Yr.4

4e

4

4

e

4

3

e

3

2

e

2

1

e

10

)k(1

P

)k(1

D

)k(1

D

)k(1

D

)k(1

DP

+

+

+

+

+

+

+

+

+

=

+=

n

k)(1

FVPVknow,We

EQUITY VALUATION WITH VARIATION IN DIVIDEND

(A) Valuation with Constant Dividends :- Assume that the dividend per share is constant year

after year (say till infinity), whose value is D, then Value of equity share ( 0P ) is calculated

as:-

D 1 2D 3D 4D D

Yr. 1 Yr. 2 Yr. 3 Yr. 4 Yr.

0P

The value of the stock ( 0P ) =ek

D [ ]===== DDDDDD 4321

Where, ek = Required rate of return / Capitalisation rate.

(C) Valuation with Constant growth in Dividends :- It is assumed that dividends tend to increase

over time because business firms usually grow over time. Therefore, if the growth of the dividends

is at a constant rate, the calculation of dividend for the coming years are calculated as :-

g)1(DD 1-nn += (Used to calculate when change in growth rate takes place)

or,n

0n g)1(DD += (Used to calculate when there is constant growth rate)

Where, nD = Dividend for year n, 0D = Dividend for year 0,

g = constant compound growth rate

D 1 2D 3D 4D D

Yr. 1 Yr. 2 Yr. 3 Yr. 4 Yr. 0P

Now, the Value of equity share ( 0P ) is calculated as:-

0P =gk

De

1

=

gkg)1(D

e

1

0

+[We know, n0n g)1(DD += ]

Where, ek = Required rate of return / Capitalisation rate, g = Growth rate,

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nD = Dividend for the year 1

Illustration:- Shetkani Solvents Ltd. Is expected to grow at the rate of 7% per annum and currentyear dividend is Rs. 5.00. If the rate of return is 12%, what is the price of the share today?

Solution:-

5D0 = 35.5D1 = 72.5D2 = 12.6D3 = 59.6D4 = D

Yr. 1 Yr. 2 Yr. 3 Yr. 4 Yr. 0P

The price of the share would be ( 0P ) = 10705.0

35.5

07.012.0

35.5

gk

D

e

1 ==

=

or,

The price of the share would be ( 0P ) = 10705.035.5

05.007.100.5

07.012.00.07)5(1

gkg)1(D 1

e

1

0 ===

+=+

(D) Valuation with Variable growth in Dividends:- Some firms have a super normal growth

rate followed by a normal growth rate. If the dividends move in line with the growth rate, the

price of the equity share will be calculated in 3 steps:-

Step 1

Expected dividend stream during the supernormal period of the super normal growth is to be

specified and the present value of this dividend stream is to be computed for which the

equation to be used in

= PV of Dividend of yr. 1 + PV of Dividend of yr. 2 + PV of Dividend of yr. 3 + PV of

Dividend of yr. 4 + . PV of Dividend of yr. n

= ne

n

4

e

4

3

e

3

2

e

2

1

e

1

)k(1D.........

)k(1D

)k(1D

)k(1D

)k(1D

+

+

+

+

+

+

+

+

+

+=

nk)(1

FVPVknow,We

= ne

a1-n

4

e

a3

3

e

a2

2

e

a1

1

e

a0

)k(1

)g1(D.......

)k(1

)g1(D

)k(1

)g1(D

)k(1

)g1(D

)k(1

)g1(D

+

++

+

++

+

++

+

++

+

+[We know,

g)1(DD 1-nn +=

Where, ek = Required rate of return / Capitalisation rate, nD = Dividend for the year n

ag = Growth rate during the period of super normal growth,

Step 2

The value of the share at the end of the initial growth period is to be calculated which as,

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ne

1n

ngk

DP

= + (as per the constant growth model)

which is then discounted to the present value. The discounted value is calculated as:-

Discounted value = ne

n

)k(1

P

+

Where, nP = Price of security at the end of n years, ek = Required rate of return,

ng = Normal growth rate after super normal growth period is over.

Step 3

Then add both the present value composites to find the value (Po) of the share which is

= Present value of dividend stream calculated in step 1 + Discounted Value (Price) of the share

at the end of the initial growth period ( nP -- i.e. super normal growth period)

VALUE OF SECURITIES WHOSE VALUE INCREASES WITH CONSTANT

GROWTH

When value of any security increases with constant growth, its value are shown as :-

Value of the security at the end of year n ( nP ) =n

0 g)1(P +

i.e.1

01 g)1(PP +=

i.e.2

02 g)1(PP +=

i.e.3

03 g)1(PP +=

Illustration :- Price of a car today is Rs. 250000. If the car prices expected to go up by 4% p.a. Find

the value of car in 3rd, 4th, and 5th year.

Solution :-

We know, nP =n

0g)1(P +

281216)04.01(250000P3

3 =+= 292465)04.01(250000P

4

4 =+=

304163)04.01(250000P

5

5 =+=

VALUE OF SECURITY BASED ON EARNING

Here Growth (g) = br

Where, g = Growth rate

r = Cost of Equity / Cost of capital / Capitalisation rate / Req. rate of return / Ret on investment

b = Retention ratio = 1 - Dividend Payout Ratio

Now, Current Value / MP of share ( 0P ) =brk

g)1(D

gk

D

e

1

0

e

1

+=

SOME IMPORTANT FORMULAE

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(a) Dividend Payout Ratio =(EPS)shareperEarning

(DPS)shareperDividend

or, Dividend Payout Ratio = 1 Retention Ratio

(b) Dividend per share (DPS) :- Earning per share (EPS) x Dividend Payout Ratio

(c) Dividend Yield =(MPS)shareperpriceMarket


=MPS

EPS

EPS

DPS

= ratetionCapitalisaRatioPayoutDividend

(d) Liquidation value per share =

s h aE q ugo u t s to fN o .

rs hp r ea n dc ta lt op ab eA m

f i r mt h eo fa s s e t st h ea l lgl i q u i df r o mr e a l i z eV a l u e

(e) Bond Trading (at premium or discount) = 100ValueFace

ValueFacepriceMarketCurrent

(f) Price-Earning ratio =(EPS)shareperEarning

(MPS)shareperpriceMarket

(g) Dividend Ratio =shareofValueFace


CHAPTER:- RISK AND RETURN

(1) Actual Stock rate of return ( jk ) =1-t

1-ttt

P

)PP(D +

Where, tD = Income or cash flows receivable from the security at time t.

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)PP( 1-tt = Capital Appreciation,

P t = Price of the security at time t at the end of the holding period = Prob x Price 1-tP = Price of the security at time t-1 at the beginning of the holding period or purchase

price.

(2) Expected Stock rate of return / Mean ( jk ) = gP

D

0

1 +

Where, 1D = Income / cash flows / Dividends receivable = g)1(D0 + [Here, D 0 = Current

Income]

P 0 = Current Purchase / Market Price of the security.

g = Growth rate during holding period.

(3) Expected Stock rate of return / Mean ( jk ) = jPk

Where, P = Probability associated with the possible outcome, jk = Actual Stock rate of return from the possible outcome.

(4) As per Single Index Model,

Expected Stock rate of return / Mean ( jk ) = mk+

Where, = mj kk , jk = Expected Stock rate of return / Mean = jPk

= Beta Coefficient of security, mk = Expected Market rate of return = mPk jk = Actual Stock rate of return, mk = Market rate of return.

(5) Required Stock rate of return :-It is calculated as per CAPM (Capital Asset Pricing Model), as below,

Required Stock rate of return ( jk ) = Risk-free + Risk-Premium

= )R(kR fmf +

Where, fR = Risk-free rate of return, = Beta Coefficient of security

mk = Market rate of return / Return on market portfolio.

(6) Equilibrium position is achieved when Required rate of return = Expected rate of return.

(7) If Expected rate of return > Required rate of return, then stock is underpriced.

Decision BUY[Note:- Ex. Suppose Required ROR is 12%, and Expected ROR is 16%. Thus here we require

minimum to minimum return of 12%, but above that we are expecting to get 16%. Thus we will be

in benefit of 4% (16% - 12%). Thus our decision will be to buy the security as it is underpriced.]

If Expected rate of return < Required rate of return, then stock is underpriced.

Decision SELL

[Note:- Ex. Suppose Required ROR is 16%, and Expected ROR is 12%. Thus here we require

minimum to minimum return of 16%, but we are expecting to get return of 12% only leading to loss

of 4% . Thus whatever the security we are holding we will sell them off to minimise loss as it is

overpriced.]

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(8) Expected Stock Risk / Standard Deviation ( j) =2

jj )kP(k

Where, P = Probability associated with the possible outcome,

jk = Actual Stock rate of return, jk = Expected Stock rate of return / Mean =

jPk

(9) Standard Deviation ( ) = (VAR)Variance

i.e. j= jVAR [Where, j= Standard Deviation of stock]

i.e. m = mVAR [Where, m = Standard Deviation of market]

(10) Beta Coefficient of Security ( ) = 2m

mj

)(

)k,(kCov.

Here, )k,(kCov. mj = )kk)(kk(P mmjj 2m )( =

2mm )kk(P

Where, )k,(kCov. mj = Covariance of return between stock and market

m = Standard Deviation of market,

jk = Actual Stock rate of return, jk = Expected Stock rate of return / Mean =

jPk

mk = Actual Market rate of return, mk = Expected Market rate of return = mPkP = Probability associated with the possible outcome.

(11) Beta Coefficient of Security ( ) = returnofratemarketinchange%

returnofratestockinchange%

=m

j

kinchange%

kinchange%

(12) Coefficient Correlation (r) =mj

mj )k,(kCov.

Where, )k,(kCov. mj = Covariance of return between stock and market =

)kk)(kk(P mmjj

j= Standard Deviation of stock =2

jj )kP(k

m = Standard Deviation of market =2

mm )kP(k

(13) Expected Portfolio rate of return ( pE ) = ..................EWEWEW 332211 +++

Where, 1W = Weight / Proportion of stock 1 in portfolio,

1E = Expected return from stock 1,

2W = Weight / Proportion of stock 2 in portfolio,

2E = Expected return from stock 2.

(14) Expected Portfolio rate of return ( pE ) = )R(kR fmf +

Where, fR = Risk-free rate of return, = Beta Coefficient of Portfolio calculated as below,

mk = Market rate of return / Return on market portfolio.

(15) Portfolio Beta ( p) = ..................WWW 332211 +++

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1= Beta Coefficient of stock 1,


2 = Beta Coefficient of stock 2.

(16) Portfolio Standard Deviation ( p ) = 21212

2

2

2

2

1

2

1 rww2ww ++


1 = Standard Deviation of stock 1,


2 = Standard Deviation of stock 2,

r = Coefficient Correlation

(17) CAPITAL ASSET PRICING MODEL (CAPM) :-

As per CAPM Model Required Required Stock rate of return ( jk ) is calculated, as below,Required Stock rate of return ( jk ) = Risk-free + Risk-Premium

= )R(kR fmf +

Where, fR = Risk-free rate of return, = Beta Coefficient of security,

mk = Market rate of return / Return on market portfolio,

)R(k fm = Market Risk Premium / Slope of Security Market Line (SML)

The graphical representation of CAPM Model is known as Security Market Line (SML),

where Market Risk Premium )R(k fm is the slope of Security Market Line (SML).

(18) Current Market Price of security ( 0P ) =gk

D

j

1

Where, 1D = Income / cash flows / Dividends receivable from the security during holding period.

= g)1(D0 + [Here, D 0 = Current Income / cash flows / Dividends received]

jk = Required stock rate of return, g = Growth during the holding period.

(19) Coefficient of Variance =Mean

)(DeviationStandard j

Where, Stock Standard Deviation ( j) =2

jj )kP(k

Mean = Expected Stock rate of return ( jk ) = jPk

(20) Price Earning Ratio (P/E Ratio) =(EPS)shareperEarning

(MPS)shareperpriceMarket

(21) As per Du-Pont Analysis,

Return on Equity (ROE) = NP Margin Asset Turnover Ratio Debt-Equity Ratio / Asset-EquityRatio

[NOTE:- Here in this chapter, in every formulae apply full %, i.e. do not convert % into decimals

for calculations. For Ex. If there is 6%, then take 6 inspite of 0.06]

CHAPTER:- SOURCES OF LONG-TERM FINANCE

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(a) Ex-Right Value of a share / Value of the share, after the Right issue =1N

SNP0

+

+

Where, N = No. of existing shares required for 1 right share

P 0 = Actual Market Price / Existing price of share / Current Price / Cum-Rights price per share

S = Subscription price at which rights shares are issued.

(b) Theoretical Value of a Right share =1N

SP0

+

Where, N = No. of existing shares required for a right share

P 0 = Actual Market Price / Existing price of share / Current Price / Cum-Rights price per share

S = Subscription price at which rights shares are issued.

CHAPTER:- COST OF CAPITAL & CAPITAL STRUCTURE THEORY

(a) Cost of Debenture ( dk ) =

2

PFn

PFt)I(1

+

+

Where, dk = Post-tax cost of debenture capital,

I = Annual interest payment per debenture capital,

t = Corporate tax rate, F = Redemption price per debenture,

P = Net amount realized per debenture (MP can be taken if not given),

n = Maturity period.

When the difference between the redemption price and the net amount realized can be written

off evenly over the life of the debentures and the amount so written-off is allowed as tax-deductible

expenses, the above equation change as follows:-

Cost of Debenture ( dk ) =

2

PF

t)(1

n

PFt)I(1

+

+

(b) Cost of Term Loans ( tk ) = t)I(1

Where, I = Interest rate, t = Tax rate

(c) Cost of Preference Capital ( pk ) =

2PF

n

PFD

+

+

Where, pk = Cost of preference capital, D = Preference dividend per share payable annually

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F = Redemption price,

P = Net amount realized per share (MP can be taken if not given)

n = Maturity period.

Cost of Preference shares which is perpetual or irredeemable ( pk ) =P

D

Where, D = Preference dividend per share payable annually,

P = Net amount realized per share (MP can be taken if not given)

(d) Cost of Equity Capital ( ek ) :-

Dividend Forecast Approach :-

D 0 D 1

P 0 Growth (g)

gk

DP

e

1

0

=

or, gP

Dk

0

1

e +=

Where, ek = Cost of Equity, 1D = Expected dividend per share at the end of year

one, 0P

= Current price, g = Growth rate.

Capital Asset Pricing Model Approach (CAPM):-

According to this approach, the cost of Equity ( ek ) is reflected by the

following equation:

ek = Rf + (km Rf)

Where, kj = Required rate of return on security, Rf = Risk-free rate of return,

= Beta coefficient of security, km = Return on market portfolio.

Realized Yield Approach :-

Step 1:- Find the wealth ratio, which is calculated as,

Wealth ratio ( tW ) =1-t

tt

P

PD +

+=

+=

1

22

2

0

11

1P

PDW,

P

PDWi.e

Step 2:- Realized Yield = ( ) 1W..........WWW1/n

n321

Where, Dt = Dividend per share for year t payable at the end of year,

Pt = Price per share at the end of year t, n = Number of years.

(e) Cost of Retained Earnings / Reserves and Surplus ( rk ) :- Return foregone by Equityshareholders is known as Cost of Retained Earning ( rk ).

i.e. ek = rk (i.e. Cost of Equity = Cost of Retained Earning)

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(f) Cost of External Equity :- Cost of Equity when associated with floatation cost it becomes

Cost of External equity ( eK )

i.e. eK

=g

f)1(P

D

0

1 + = f-1

ke

Where, eK = Cost of External equity, 1D = Dividend expected at the end of year 1,

0P = Current market price per share, g = Constant growth rate applicable to dividends,

f = Floatation costs as a percentage of the current market price.

(g) Weighted Average Cost of Capital (WAC) = ttddrrppee kWkWkWkWkW ++++

Where, eW = Weight of Equity Capital, ek = Cost of Equity / Equity Capitalisation

rate,

pW = Weight of Preference Capital, pk = Cost of Preference Capital,

dW = Weight of Debenture, dk = Cost of Debenture,

tW = Weight of Term Loan, tk = Cost of Term Loan.

=

financeallofTotal

financeconcernedofportionfinanceofsourceanyofWeight

(h) As per Net Operating Income Approach,

Weighted Average Cost of Capital ( 0k

) = ddeekWkW +

When Debt is associated with tax payment, then,

Weighted Average Cost of Capital ( 0k ) = t)1(kWkW ddee +

Where, eW = Weight of Equity Capital, ek = Cost of Equity / Equity Capitalisation rate,,

dW = Weight of Debt, dk = Cost of Debt,

t = Corporate Tax.

(i ) As per Net Operating Income Approach,

Addition to firms Weighted Average Cost of Capital ( 0k ) = t)1(kW dd

Where, dW = Weight of Debt, dk = Cost of Debt, t = Corporate tax rate

(j ) As per Net Operating Income Approach,

Cost of Capital ( 0k ) =CompanytheofAssetsTotal/firmofValueMarket

EBIT/IncomeOperatingNet

Where, Net Operating Income = Interest on Debt + Equity Earnings,

Market Value of the firm = Market Value of Debt / Debt + Market Value of Equity / Equity,

Interest on Debt = Debt Cost of Debt ( dk ),Equity Earnings = Equity Cost of Equity ( ek ).

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(k) As per Net Operating Income Approach,

Cost of Equtiy Capital ( ek ) = ratioEquity-Debt)kk(k d00 +

Where, 0k = Cost of Capital / Overall Capitalisation rate, dk = Cost of Debt

Debt-Equity ratio = RatioEquity-Asset/Equtiy

Debt

(l) As per Miller and Modigliani Approach,

Present Value of tax shield = ct B

Where, ct = Corporate tax rate, B = Debt Capital.

(m) Tax advantage of Debt Capital / Tax Shield associated with Debt =

)t1(

)t1)(t1(1

pd

psc

Where, ct = Corporate tax rate, pst = Personal tax on Stock / Equity,

pdt = Personal tax on Debt income, B = Debt Capital.

(n) As per Du-Pont Analysis,

Return on Equity (ROE) = NP Margin Asset Turnover Ratio Debt-Equity Ratio / Asset-Equity Ratio

(o) Rate of return on Equity =EquityofueMarket val

PAT

(p) Unlevered firm is a firm who has no debt to pay.

CHAPTER:- DIVIDEND POLICY

(1) As per Traditional Model / Graham Dodd Model,

P =

+

3

EDM

Where, P = Market price per share, M = Multiplier,

D = Dividend per share (DPS), E = Earning per share (EPS)

(2) As per Walter Model,

P =

e

e

ek

k

D)(Er

k

D

+

Where, P = Market price per share, D = Dividend per share (DPS),

ek = Cost of Equity Capital / Equity Capitalisation Rate,

r = Internal rate of return, E = Earning per share (EPS).

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(3) As per Gordon Dividend Capitalisation Model,

P =brk

b)(1E

e

Where, P = Market price per share, E = Earning per share (EPS),

b = Retention Ratio, b)(1 = Dividend Pay-out ratio

ek = Cost of Equity Capital / Equity Capitalisation Rate,

br = Growth rate (g) = b r = Retention Ratio (b) Internal rate of return (r).

(4) Rule of Walter Dividend Capitalisation Model,

When, r > ek , then Dividend Pay-out Ratio = 0

When, r < ek , then Dividend Pay-out Ratio = 100%

Where, r = Return on Investment, ek = Cost of Equity Capital / Equity Capitalisation Rate.

(5) As per Miller & Modigliani Model (MM Model),

Calculation of Value of firm is done in 4 steps, such as,

STEP :- 1

Find Current Market Price of the share ( 0P ), such as,

0P =e

11

k1

PD

+

+

Where, 1D = Dividend to be paid at the end of the year,

1P = Market price of share at the end of the year,

ek = Cost of Equity Capital / Equity Capitalisation Rate.

STEP :- 2

Calculate amount to be raised by the issue of new shares ( 11Pn ), such as,

)nD(EIPn111

=

Where, 11Pn = Amount to be raised by the issue of new shares / Additional Equity Capital,

I = Total Investment required, E = Earning / Profit during the year,

n = No. of outstanding shares, 1D = Dividend to be paid at the end of the year,

1nD = Total Dividends paid, ( 1nDE ) = Retained Earnings.

STEP :- 3

Calculate the Number of additional shares ( 1n ) to be issued, such as,

1

11

1 P

Pnn =

Where, 1n = Number of additional shares to be issued,

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11Pn = Amount to be raised by the issue of new shares / Additional Equity Capital,

1P = Market price of share at the end of the year.

STEP :- 4

Finally, Calculate Value of the firm ( 0nP ), such as,

0nP =e

11

k1

EIP)nn(

+++

Where, 0nP = Value of the firm, n = Number of outstanding shares,

1n = Number of additional shares to be issued,

1P = Market price of share at the end of the year, I = Total Investment required,

E = Earning / Profit during the year, ek = Cost of Equity Capital / Equity Capitalisation

Rate.

(6) As per Net Operating Income Approach,

Market Value of the firm =0k

IncomeOperatingNet/EBIT[Where, 0k = Cost of Capital]

(7) Market Value of the firm = Market Value of Debt + Market Value of Equity.

financial management paper 1

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