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BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q6
Q7
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Year Return = d1+¿¿¿ = X (X-X ) (X-X )2
961.53+(20.75−31.25)
31.25 = - 28.7 -80.732 6517.65
971.53+(30.88−20.75)
20.75 = 56.19 4.158 17.288
982+(67−30.88)
30.88 = 123.44 71.408 5099.102
992+(100−67)
67 = 52.23 0.198 0.0392
003+(154−100)
100 = 57 4.968 24.681
260.16 11658.76
Expected return = 260.165
= 52.032
Market probability Dividend Expected Market Expected Condition Dividend price Mkt. priceGood 0.25 9 9 x 0.25 = 2.25 115 115 x 0.25 = 28.75Normal 0.50 5 5 x 0.5 = 2.5 107 107 x 0.5 = 53.5Bad 0.25 3 3 x 0.25 = 0.75 97 97 x 0.25 = 24.25
5.5 106.5Return of security¿d1+¿¿¿ = 5.5+¿¿ = 12%
**The current market price of the share is Rs 106 cum bonus 10% debenture of Rs 6 each, company had offered buyback of debentures at face value, so Rs 6 will be returned , thus net investment in share is Rs 100
Risk of securityProbability(P) Capital gain Dividend Return(X) P(X) P(X-X ¿¿2
Company has offered buyback of debenture at face value. Rate of interest of debenture is 10% whereas expected market rate of return is 12%, so investor should accept the offer of buyback.
PRAVINNMAHAJANCA CLASESS
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q8 Security X Security Y
In case of security X for 1% of return there is risk of 0.926%, and in security Y for 1% return risk is 0.644%. since for 1% of return , risk is lower in case of Y, so Y is better.
Q9 Security X Security Y
In case of security X for 1% of return there is risk of 0.774%, and in security Y for 1% return risk is 0.493%. since for 1% of return , risk is lower in case of Y, so Y is better.
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Risk premium is excess of return on risky securities over risk free securities. Risk premium on risky securities can be negative in short term due to negative movement or reduction in price but over a long term risk premium cannot be negative
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
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Return of portfolio is weighted average of return of each security in the portfolio. Risk of portfolio is not the weighted average of risk of each security in the portfolio.
Since the correlation between two securities is -1, so portfolio risk can be 0. But for portfolio risk to be 0 weight of securities in portfolio should be in the ratio of 2:1. Since weight of each security in portfolio is changed and weight of low risk security P is reduced and high risk
i. Investment in A to attain a minimum risk portfolio
WA =σB2−r σ Aσ B
σ A2 +σB
2−2 r σ Aσ B
= 302−0.10 .20 .30202+302−2 .0.10 .20 .30
= 8401180
= 0.711
WB = 1 – WA = 1 – 0.711 = 0.289For minimum risk portfolio investor will invest 71.1% i.e (5,00,000 X 0.711) 3,55,500 in A and 28.9% (5,00,000 X 0.289) 1,44,500 in B
PRAVINNMAHAJANCA CLASESS
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
WB = 1 – WA = 1 – 0.60 = 0.40For minimum risk portfolio investor will invest 60% i.e (5,00,000 X 0.60) 3,00,000 in A and 40 % (5,00,000 X 0.40) 2,00,000 in B
X YRisk (σ) 20% 25%Return 10% 15% r = + 0.5
Weight of each security for minimum risk portfolio
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
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RF = 7%, RM = 15%, σM = 20%
(i) Risk level of portfolio constructed by A. Expected rate of return of A is 18%
Return of portfolio = RF + (RM−RF
σM) σP
18 = 7 + ¿ ) σP
0.4 σP = 18 – 7σP = 27.5
Risk of portfolio = σP = WRfσRf + WMPσMP
27.5 = WRF.0 + WMP. (20)
WMP =27.520
= 1.375
WRf = 1 – 1.375 = -0.375A will shortsell 37.5% of risk free securities and invest 137.5% in Market portfolio
for return of 18% and risk at this level is 27.5%.
(ii) Expected level of return or portfolio constructed by B having a risk of 15.81%Risk of portfolio = σP = WRfσRf + WMPσMP
15.81 = 0 + WMP. 20
WMP =15.8120
= 0.7905WRF = 1 - WMP
Rm = 16% , σM= 10% , RF = 8%
(i) If 100% is invested in market portfolioReturn = 16%Risk = 10%
(ii) If 100% is invested in risk free assetReturn = 8%Risk = 0
(iii) If investment in Risk free and market portfolio is in the ratio of 40% : 60%RP = WRfRRf + WMPRMP
= (0.40) (8) + (0.60) (16)= 12.8 %
Risk of portfolio is weighted average risk= WMPσMP
= (0.60) (10) = 6%Contd.
PRAVINNMAHAJANCA CLASESS
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
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(iv) Risk of portfolio is weighted average risk Contd.= WMPσMP
= (1.20) (10) = 12%
Return of portfolio = RF + (RM−RF
σM) σP
= 8 + (16−810
) 12 = 17.6%
Rf = 10%, RM = 18% , σM = 5%
Return of portfolio = RF + (RM−RF
σM) σP
16 = 10 + (18−105
)σP
6 = 1.6 σP
σP =61.6
= 3.75
Risk of portfolio is weighted average riskσP = WRfσRf + WMPσMP
3.75 = WRf. 0 + WMP.5
WMP =3.755
= 0.75
WRF = 1 – WMP = 1 – 0.75 = 0.25
If expected return is 20%
Return of portfolio = RF + (RM−RF
σM) σP
20 = 10 + ( 18−105
) σP
σP = 6.25σP = WRfσRf + WMPσMP
6.25 = WRf(0) + WMP. (5)
PRAVINNMAHAJANCA CLASESS
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
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Between A and B – A dominates B, B is cancelledBetween A and C – there is no dominationBetween And D – A dominates D, D is cancelledBetween A and E – There is no dominationBetween A and F – there is no dominationBetween C and E – there is no dominationBetween E and F – E dominated F, F is cancelledSo A, C and E are efficient securities
Securities in ascending order of risk Risk ReturnA 4 8E 5 9C 12 12
Investment in E gives return of 9% with risk of 5% whereas investment in portfolio of A and C gives return of 9 with risk of 6%. So investment in E is better.
Between U and V = U dominates V , V is cancelledBetween U and W = No dominationBetween U and X = U dominates and X is cancelledBetween U and Y = No DominanceBetween U and Z = U dominates and Z is cancelledBetween W and Y = No dominationU, Y and W are efficient securities
Securities in Increasing order of Risk Risk ReturnU 5 10Y 6 11W 13 15
ii) 80% in U and 20% in WRP = WURU + WWRW = 0.80 x 10 + 0.20 x 15 = 11%
100% investment in Y ER = 11% and Risk 6%Investment in Y gives return of 11% with risk of 6.6% whereas investment in portfolio of A and C gives return of 11% with risk of 6%. So investment in Y is better.
PRAVINNMAHAJANCA CLASESS
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q36
20 fb-id PRAVINN MAHAJAN CA CLASSES
M NDividend 10 3Cl. Price 220 290
Op. Price2,00,0001,000
= 2001,50,000500
= 300
Return of security¿d1+¿¿¿
M = 10+(220−200❑)
200 = 15%
N = 3+(290−300❑)
300 = - 2.3%
Portfolio return(31.03.09) = RP = WMRM + WNRN
=2,00,0003,50,000
x 15 + 1,50,0003,50,000
x (-2.3) = 7.63%
ii. M NDividend 20 3.5Expected MP 220 x 0.2 + 290 x 0.2 + 310 x 0.5
√289.6 = 17.017Portfolio Risk Return coeff. of varitionPQ 16.8 15.5 1.083 Portfolio PQ is most efficientQR 21.03 17 1.237 as it has least co.eff. of variationPR 17.017 12.5 1.36
PRAVINNMAHAJANCA CLASESS
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q39
22 fb-id PRAVINN MAHAJAN CA CLASSES
Probability Stock A PA Stock B PB Stock C PC.25 14 3.5 15 3.75 33 8.25.75 12 9.0 3 2.25 -6 -4.5Expected return 12.5 6.0 3.75
Expected return of equally weighted portfolio = RP = WARA + WBRB + WCRC
= 0.33 x 12.5 +0.33 x 6 + 0.33 x 3.75 = 7.84%
ii. Standard deviation of A, B and Cprobability P(A-A ¿¿2 P(B-B ¿¿2 P(C-C ¿¿2 P(A-A ¿¿(B-B ¿¿ P(C-C ¿¿(B-B ¿¿
β = 0.6since β of stock 1 is higher and β is index of systematic risk so systematic risk of stock 1 is higherSince β of stock 2 is lower and β is index of systematic risk, so systematic risk of stock 2 is lower and unsystematic risk is higherSince σ of stock 2 is higher so stock 2 is more riskier
Return of security ¿d1+¿¿¿ Returns from market index% of index appreciation Div yield Total
200125+(279−242)
242 X 100 = 25.62%
1950−18121812
X 100 = 7.62% 5% 12.62%
200230+(305−279)
279 X 100 = 20.07%
2258−19501950
X 100 = 15.79% 6% 21.79%
200335+(322−305)
305 X 100 = 17.05%
2220−22582258
X 100= (1.68%) 7% 5.32%
Year S (S-S¿¿2 M (M-M ¿¿2 (S-S¿¿(M-M ¿¿2001 25.62 22.1841 12.62 0.3844 - 2.92022002 20.07 0.7056 21.79 73.1025 - 7.1822003 17.05 14.8996 5.32 62.7264 30.5712
62.74 37.7893 39.73 136.2133 20.469
σM = √ 136.21333 = 6.738% COVS.M =
20.4693
6.823
βS = COV S .M
σM2 =
6.82345.4006
= 0.15
This is a low β stock
PRAVINN MAHAJAN CA CLASESS
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q54
Q55
30 fb-id PRAVINN MAHAJAN CA CLASSES
Systematic Risk = βS2 x σM
2
X = (0.71)2 x 2.25 = 1.134225Y = (0.27)2 x 2.25 = 0.164025
Unsystematic Risk = σ S2 - Systematic risk of security
X = 6.30 - 1.134 = 5.166Y = 5.86 - 0.164 = 5.696
β of Portfolio is value weighted β of security constituting the portfolio
βP = WX. βX + WY. βY
= (0.50 X 0.71) + (0.50 X 0.27) = 0.49
Portfolio Variance = Systematic Risk of Portfolio + Unsystematic Risk of Portfolio
βP2 . σM
2 + Weighted average unsystematic Risk of each security in
the portfolio=(0.49)2. (2.25) + (0.50)2 X 5.166 + (0.50)2 X 5.696=0.5402 + 1.2915 + 1.424=3.2557
i. βS = rS.M x σSσM
A = 0.60 x 2015
= 0.80
B = 0.95 x 1815
= 1.14
C = 0.75 x 1215
= 0.60
ii. Covariance of 2 securities (NEW CONCEPT)(CHECK DERIVATION)
= βSECURITY 1 X β(SECURITY 2) X σM2
COVA.B = 0.80 X 1.14 x (15)2 = 205.20COVB.C = 1.14 X 0.60 X (15)2 = 153.90COVC.A = 0.60 X 0.80 X (15)2 = 108
iii. (σP)
¿√W A2 . σ A
2 +WB2 . σ B
2+WC2 . σC
2 +2.COV A .B .W A .W B.+2.COV B.C .WB .WC+2.COV A. C .W A .W C .
= √¿¿
+2.( 13 ) .( 13 ). (108 )
= √ 1802.209 = √200.24=¿14.151
PRAVINNMAHAJANCA CLASESS
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
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iv. β of Portfolio is value weighted β of security constituting the portfolioβP = WAβA + WBβB + WCβC
= 13
x 0.80 + 13
x 1.14 + 13
x 0.60 = 0.847
v. Portfolio Systematic Risk = βP2 X σM
2
= (0.847)2 X (15)2 = 161.417Unsystematic Risk = Variance of portfolio – systematic Risk of Portfolio
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
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45 fb-id PRAVINN MAHAJAN CA CLASSES
Between A and B = B dominates , A is cancelledBetween B and C = No DominanceBetween B and d = No DominanceBetween B and E = No DominanceBetween B and F = No DominanceBetween B and G = No DominanceBetween B and H = no DominanceBetween C and D = No DominanceBetween C and E = no DominanceBetween C and F = No DominanceBetween C and G = C Dominates and G is cancelledBetween C and H = No DominanceBetween D and E = E Dominates and D is cancelled
Efficient Portfolios in increasing order of RiskRisk Return21 12.525 15.029 17.032 18.045 20.0
ii. out of efficient portfolios best portfolio is that in which risk premium per unit of risk is highest
Risk Return Risk Premium Risk Premium per unitIf RF is 12% of Risk
B 21 12.5 0.5 0.023C 25 15 3 0.120E 29 17 5 0.172F 32 18 6 0.187H 45 20 8 0.177Since Risk Premium per unit of Risk of F is highest. So it is the Best Portfolio if Lending and Borrowing is allowed at 12%.
Iii If Lending and Borrowing is not allowed then σ of 25% is at portfolio C which gives return of 15%. So maximum return at risk of 25% is 15%.
Required Return = RF + (RM−RF
σM) σ S
If borrowing and lending is allowed 12% then F is best portfolio, so market portfolio is F
12 + 18−1232
X 25
= 16.68%Risk of Portfolio σP = WMP σMP + WRFσRF
25 = WMP (32) + WRF(0)WMP = 0.78125 WRF = 0.21875
If borrowing and lending is allowed then optimal strategy is to invest 78.125% in F and 21.875% in Risk free and return at optimal strategy is 16.68%
PRAVINN MAHAJAN CA CLASESS
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q88
Q89
46 fb-id PRAVINN MAHAJAN CA CLASSES
Given the level of σ of security the Expected Rate of Return Prediction by CML is
Required Return = RF + (RM−RF
σM) σ S
10 + ¿) 40 = 33%
Actual return of security is 1000−875875
x 100 = 14%
Actual return of security of 14% is well below 33%. Thus this venture does not constitute an efficient portfolio. It bears some risk that does not contribute to the expected rate of return
Sharpe ratio is used as performance measure. Closer the sharpe ratio to CML, better is the performance of fund in terms of return against risk.
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
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i. SMl = RF + (RM – RF)βRM = 0.30 X 12 + 0.40 X 8 + 0.30 X(-4) = 5.6SML = 8 + (5.6 – 8)β
= 8 - 2.4 β
ii. Market price at risk is co-efficient of SML. In this case, market price at risk is negative which provides that if risk decreases, return will increase which does not happen normally
III.Prob. S P. S P(S-S)2 M PM P(M -M )2 P(S - s)(M - M )0.30 18 5.4 38.988 12 3.6 12.288 21.8880.40 9 3.6 2.304 8 3.2 2.304 2.3040.30 -8 -2.4 63.948 -4 -1.2 27.648 42.048
6.6 5.6 42.24 66.24
ERs = 6.6 ERM = 5.6 σM = √P(M−M )2 COVSM = 6.4
√42.24 = 6.49%
βSEC = COV SM
σM2 =
66.2442.12
= 1.573
iv. Alpha of stock = Expected Return - Required Return6.6 - [8 – 2.4(1.573)] = 2.3752 underpriced
PRAVINNMAHAJANCA CLASESS
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q93
49 fb-id PRAVINN MAHAJAN CA CLASSES
S R β σ ei2 R−RF
βRank S (
R−RF
USR)β β2
USR Ʃ(
R−RF
USR)β Ʃ( β2
USR)
C=σM2 Ʃ(
R−RF
USR)β
1+σM2 Ʃ( β2
USR)
A 15 1.5 40 5.333 1 A 0.30 0.05625 0.30 0.05625 10 X 0.30
1+10 X 0.05625 =
1.92
B 12 2.0 20 2.5 3 F 0.35 0.075 0.65 0.13125 10 X 0.65
1+10 X 0.13125=
2.81
C 10 2.5 30 1.2 5 B 0.50 0.20 1.15 0.33125 10 X 1.15
1+10 X 0.33125 =
2.67
D 9 1 10 2 4 D 0.20 0.10 1.35 0.43125 10 X 1.35
1+10 X 0.43125=
2.54
E 8 1.2 20 0.833 6 C 0.25 0.208 0.45 0.63925 10 X 0.45
1+10 X 0.63925=0.61
F 14 1.5 30 4.67 2 E 0.06 0.072 0.51 0.71125 10 X 0.51
1+10 X 0.71125=0.63
Highest of all cut off rates is cut-off rate of portfolio i.e 2.81. so securities A & F are selected
PRAVINN MAHAJAN CA CLASESS
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q94
50 fb-id PRAVINN MAHAJAN CA CLASSES
S R β σ ei2 R−RF
βRank S (
R−RF
USR)β β2
USR Ʃ(
R−RF
USR)β Ʃ
( β2
USR) C=
σM2 Ʃ(
R−RF
USR)β
1+σM2 Ʃ( β2
USR)
1 19 1 20 14 1 1 1.7 0.05 0.7 0.05 10 X 0.71+10 X 0.05
=
4.67
2 23 1.5 30 12 2 2 0.9 0.075 1.6 0.125 10 X 1.6
1+10 X 0.125=
7.11
3 11 0.5 10 12 3 3 0.3 0.025 1.9 0.1510 X 1.9
1+10 X 0.15 =
7.6
4 25 2.0 40 10 4 4 1.0 0.10 2.9 0.25 10 X 2.9
1+10 X 0.25 =
8.28
5 13 1.0 20 8 5 5 0.4 0.05 3.3 0.3010 X 3.3
1+10 X 0.30 =
8.25
6 9 0.5 50 8 6 6 0.04 0.005 3.34 0.30510 X 3.34
1+10 X 0.305=
8.24
7 14 1.5 30 6 7 7 0.45 0.075 3.79 0.3810 X 3.791+10 X 0.38
=
7.90
Highest of all cut off rates is cut-off rate of portfolio i.e 8.82. so securities 1 to 4 are selected
Z =β
USR X [
R−RF
β - C ]
1 =120
X (14 – 8.28) = 0.286
2 =1.530
X (12 – 8.28) = 0.186
PRAVINN MAHAJAN CA CLASESS
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q95
Q96
51 fb-id PRAVINN MAHAJAN CA CLASSES
i. Risk Premium on each of 3 stocksΒ1 x Market Risk Premium + β2 x Market Risk
For β1 Premium for β2
Security A = 1.75 X 4 + 0.25 x 8 = 9%Security B = - 1 x 4 + 2 x 8 = 12%Security C = 2 x 4 + 1 x 8 = 16%
Risk Premium is 0Portfolio β1 and β2 is 0. This implies that by selecting the given Proportion of the portfolio of the Portfolio, investor has designed 0 risk portfolioSo, risk premium of Portfolio will be 0 & return of Portfolio will be equal to Risk free
If overall portfolio is insensitive to changes in factor 2 , β2 of Portfolio = 0
Portfolio β2 = WA X β2 of A + WB X β2 of B0 = WA X 0.80 + (1 - WA) x 1.400 = - 0.6 WA + 1.40WA = 2.33WB = ( 1 – WA)
= 1 – 2.33 = -1.33
ii. Portfolio β1 = 1Portfolio β2 = 0
Portfolio β1 = WA X β1 of A + WB X β1 of B + WRF X β1 of RF
1 = WA (0.50) + WB (1.50) + 0……………….(i)
Portfolio β2 = WA X β2 of A + WB X β2 of B + WRF X β2 of RF
0 = WA (0.80) + WB (1.40) + 0……………….(ii)
Solving (i) and (ii) WA = - 2.8 WB = 1.6WRF = ( 1 – (-2.8) – 1.6) = 2.2
PRAVINN MAHAJAN CA CLASESS
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q97
52 fb-id PRAVINN MAHAJAN CA CLASSES
i. WA =1,50,000
1,50,000−50,000 = 1.5
WB =−50,000
1,50,000−50,000= - 0.5
β1 β2
A 0.80 0.60B 1.50 1.20
W β1 Wβ1 β2 Wβ2
1.5 0.80 1.2 0.60 0.9- 0.5 1.50 -0.75 1.20 -0.6
0.45 0.3
β1 = 0.46 β2 = 0.3
ii. a. Fund other than funds from short selling of B = 1,00,000Funds from Short selling of B = 50,000
( 50% of funds other than from short selling of B)
b. Funds other than Bowned funds = 1,00,000Short selling RF = 1,00,000 2,00,000
Short selling of B = 50% of funds other than from B0.50 x 2,00,000 = 1,00,000
Investment in A 3,00,000Investment in B 1,00,000Short selling of RF 1,00,000
Solving (i) and (ii) RF + 0.4 RP1 = 7.60 ……..(iv)Solving (ii) ad (iii) 0.5 RF + 0.5 RP1 = 5 ……..(v)
Solving (iv) and (v) RP1 = 4 RF = 6Substituting values in (i) RP2 = 6
ER = RF + β1 (RP1) + β2 (RP2 ) = RF + 4β1 + 6β2
Required Return of Portfolio D = RF + 4β1 + 6β2
= 6 + 4(0.5) + 0.7 (6)= 12.2%
Expected return of D = 14%Since ER > RR, so Portfolio D is underpricedInvestor will short sell securities yielding 12.2% and buy portfolio DIf investor invests Rs 1,00,00 in portfolio D
Return from D 14% of 1,00,000 = 14,000Amount payable or return lost = 12,200Gain 1,800
PRAVINN MAHAJAN CA CLASESS
BG-3/3D PASCHIM VIHAR, NEAR PUNJABI BAGH PRAVINN MAHAJAN CA CLASSES 9871255244, 8800684854
Q99
54 fb-id PRAVINN MAHAJAN CA CLASSES
Required Return of Portfolio E = RF + 4β1 + 6β2
= 6 + 4(0.8) + 6(1) = 15.2%
Expected Return of Portfolio F = 15.2%Since ER = RR, so Portfolio E is correctly Priced. No Arbitrage.
Required Return of Portfolio F = RF + 4β1 + 6β2
= 6 + 4(0.6) + 6(0.5) = 11.40%
Expected Return of Portfolio F = 9%Since ER < RR, So Portfolio F is OverpricedInvestor will short sell Portfolio F and invest in securities yielding 11.40%If investor short sell Rs 1,00,00 of portfolio D
Return from securities = 11.4% of 1,00,000 = 11,400Loss of Return from Portfolio F = 9,000
Small Cap value = 4.5 + (0.90 x 6.85) + (0.75 x – 3.5) + (1.25 x 0.65) = 8.857Small Cap growth= 4.5 + (0.80 x 6.85) + (1.39 x -3.5) + (1.35 x 0.65) = 5.9925Large Cap value = 4.5 + (0.85 x 6.85) + (2.05 x -3.5) + 6.75 x 0.65) = 7.535Large Cap Growth = 4.5 + 91.165 x 6.85) + (2.75 x -3.5) + (8.65 x 0.65) = 8.48
Average Expected Return = 8.857 x 0.10 + 5.9925 x 0.25 + 7.535 x 0.15 + 8.48 x 0.50 = 7.754
Required Return = RF + β. (Risk Premium)Small Cap value = 4.5 + (0.90 x 6.85) = 10.665Small Cap growth = 4.5 + (0.80 x 6.85) = 9.98Large cap value = 4.5 + (1.165 x 6.85) = 12.48
Average return = (10.665 x 0.10) + (9.98 x 0.25) + (10.3225 x 0.15) + (12.48 x 0.50)= 11.35%
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RF = 7% RM = 11% βEQUITY = 1.3
Since its an all equity firm so β of equity is β of Asset.ΒASSET = 1.3
II. Return OF Company = 0.5 x 13.2 + 0.3 x 12 + 11.2 x 0.2 = 12.44%
ii. Cost of capital i.e KE = 12.44%
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Market value of East , West and Central Division is in the ratio of 1:2:1,I.e there weights are @25% , 50% and 25% Let Risk of Division West is X, Risk of East is 1.5X and risk of central is 0.75X
i. Since it is an all equity company, So βASSET = βEQUITY = 1.24ΒASSET is Weighted average of β of Individual assets in the portfolioΒASSET = WEAST βEAST + WWEST βWEST + WCENTRAL βCeNtRAL
1.24 = 0.25 x (1.5X) + 0.50 x (X) + 0.25 x (0.75X)X = 1.167Thus βEAST = 1.167 x 1.5 = 1.7505
ΒWEST = 1.167 x 1 = 1.167ΒCENTRAL = 1.167 x 0.75 = 0.87525
ii. βASSET of PQR Ltd. = Asset βWEST x REVeNUe SENSTIVITY of PQR
REVENUE SENTIVITY OFWEST DIVISiON x
GEArING PQRGEARINGWEST
= 1.167 x 1.51
x 1.82
= 1.575545
iii. βASSET of XYZ before acquisition = WEIGHTED β(0.25 x 1.7505) + (0.50 x 1.167) + (0.25 x 0.87525)
= 1.24
βASSET of XYZ after acquisition=(0.25 x 1.750) + (0.50 x 1.575545) + (0.25 x 0.87525)
= 1.44
iv. Required rate of return of new project is discount rate of new projectRR = RF + (RM – RF)β
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Debt EquityWeight 0.30 0.70β 0.2
Project β = 1.2
ΒASSET = βEQUITY x E
E+D + βDEBT x
DE+D
1.2 = 0.30 x 0.20 + 0.70 x βE
βEQUITY = 1.62
ii. Debt – Equity = 40 : 60After re financing βASSET will remain same
ΒASSET = βEQUITY x E
E+D + βDEBT x
DE+D
1.2 = βEQUITY x 0.60 + 0.30 x 0.40βEQUITY = 1.8
i. Required return on EquityRRE = RF + β (RM – RF)
= 6 + 1.40 (6)= 14.4%
ii. ΒASSET = βEQUITY x E
E+D + βDEBT x
DE+D
= 1.40 x 47
+ 0 x 37
= 0.8
iii. Cost of capital = RF + β (RM – RF)= 6 + 0.8 (6) = 10.8%
iv. Discount rate = Cost of capital = 10.8%
v. RR = RF + β (RM – RF)= 6 +1.5 (6)= 15%
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i. Required return on EquityRRE = RF + β (RM – RF)
= 8 + 1.5 (10)= 23%
ii. ΒASSET = βEQUITY x E
E+D + βDEBT x D
E+D
= 610
x 1.5 + 410
x 0
= 0.9
iii. Company’s cost of capital8 + 0.9 (10)= 17%
iv. Any new business should yield more than cost of capital of company. So, discount rate shall be Cost of capital i.e 17%
v. D: E = 1: 9Asset β will remain same
ΒASSET = βEQUITY x E
E+D + βDEBT x
DE+D
0.9 = 0 x 110
+ βEQUITY x910
βEQUITY = 1
vi. Since βASSET is same so cost of capital will remain same i.e 17%
vii. β = 1.2RR = RF + β (RM – RF)
= 8 + 10 (1.2)
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ΒASSET = βEQUITY x E
E+D(1−tax rate) + βDEBT x
D(1−tax rate)E+D(1−tax rate)
= 1.40 x 0.70
0.7+.3(1−0.30)+ 0 x
0.3 (1−0.30)0.7+.3(1−0.30)
= 1.08After change in Debt equity ratio, Asset β will remain same
ΒASSET = βEQUITY x E
E+D(1−tax rate) + βDEBT x
D(1−tax rate)E+D(1−tax rate)
1.08 = βEQUITY x 0.6
0.6+0.4 (1−0.30)
AE is an all equity company therefore Asset β shall be equal to βEQUITY
So βASSET = 1
ΒASSET = βEQUITY x E
E+D(1−tax rate) + βDEBT x
D(1−tax rate)E+D(1−tax rate)
1 = βEQUITY x 3744
3744+3556 (1−0.35)
βEQUITY = 1
0.6183 = 1.62
i. Food division
ΒASSET = βEQUITY x E
E+D + βDEBT x D
E+D
= 0.9 x 11.4
+ 0 x 0.41.4
= 0.642Chemical division
ΒASSET = βEQUITY x E
E+D + βDEBT x D
E+D
= 1.2 x 11.25
+ 0
= 0.96Machine Tools
ΒASSET = βEQUITY x E
E+D + βDEBT x D
E+D
= 1.4 x 11.5
+ 0
= 0.933
ii. βASSET for midland as a whole shall be average of βASSET of all its division(0.643 x 0.5) + (0.960 x 0.3) + (0.933 x 0.20) = 0.7961
ΒASSET = βEQUITY x E
E+D + βDEBT x D
E+D
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iii. The cost of capital of each division may be calculated as required return on assets of division
iv. It is assumed that Amalgamated foods fairly represent Food Industry and studge chemicals and Chunky tools fairly represent chemical and tool industry. Further it is also assumed that Food, chemical and machine tools division of Midland Industry fairly Represent Amalgamated foods, Studge chemicals and chunky tools respectivelySo, each division of Midland Industry fairly represents their respective Industry. So above calculations are reliable
Since each company in the Industry represents overall industry so, β of one firm of that industry is equal to β of other firm of the same industry.
So βAsset of Gamma is equal to βASSET of Alpha Ltd.
Asset β of Alpha
βASSET = βEQUITY x E
E+D(1−tax rate) + βDEBT x
D(1−tax rate)E+D(1−tax rate)
= 1.30 x 4
4+1(1−0.40) + 0
= 1.13
asset β of Gamma shall also be 1.13
βASSET = βEQUITY x E
E+D(1−tax rate) + βDEBT x
D(1−tax rate)E+D(1−tax rate)
1.13 = βEQUITY x 3
3+2(1−0.4) + 0
βEQUITY = 1.582 PRAVINN
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βASSET = βEQUITY x E
E+D + βDEBT x D
E+D
= 1.32 x 11.2
+ 0 = 1.1
βASSET of Birla Motors will be equal to βASSET of Industry because it is assumed that Birla Motors is representing industry
βASSET = βEQUITY x E
E+D + βDEBT x D
E+D
1.1 = βEQUITY x 11.3
+ 0
βEQUITY = 1.43
i. RR = RF + βASSET (RM – RF)= 12 + 1.1(9)= 21.9%
ii. RREQUITY = RF + βEQUITY (RM – RF)
βASSET of B Ltd. will be equal to βASSET of A Ltd.
A Ltd. βASSET = βEQUITY x E
E+D + βDEBT x
DE+D
= 1.50 x 11.50
+ 0.30 x 0.501.50
= 1.1βASSET of B Ltd. Will be same as βASSET of A Ltd.
βASSET = βEQUITY x E
E+D + βDEBT x
DE+D
1.1 = βEQUITY x 11.80
+ 0.45 x 0.801.80
βASSET ofXY Ltd. will be equal to βASSET of AB Ltd.
AB Ltd. βASSET = βEQUITY x E
E+D(1−tax rate) + βDEBT x
D(1−tax rate)E+D(1−tax rate)
= 1.1 x 4
4+1(1−0.30) + 0
= 0.94βASSET of XY Ltd. Will be same as βASSET of AB Ltd.
βASSET = βEQUITY x E
E+D(1−tax rate) + βDEBT x
D(1−tax rate)E+D(1−tax rate)
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βASSET = βEQUITY x E
E+D(1−tax rate) + βDEBT x
D(1−tax rate)E+D(1−tax rate)
= 1.35 x 1
1+0.12(1−0.35)= 0.92
βASSET of A Ltd. Will be same as βASSET of shoe co.