Valuation of bonds, shares and portfolio

1. Executive summary: Thisreportcoveredportfolio,bondandshare valuationof three different
companies providingan explanationaboutthe selectioncriteriaof anybondand share while investment
of the fundsinthe portfolio.The reportcoveredthe calculationof the expectedreturnandstandard
deviationof the portfolio.The reportalsocoveredthe valuationof three typesof bondwiththree
differentcouponratestoprovide aninsightwhile investinginthe bonds.The share valuationcalculated
the marketshare price of the shareswithno growth,normal growthand supernormal growth.
1. Portfoliovaluation
Shares
Type ExpectedReturn Standard Deviation CorrelationCoefficient
Share JAY 12% 18% -0.3
Share KAY 24% 32%
(a) To calculate covariance betweenshare Kayandshare Jay:
Covariance betweenShare JayandShare Kay = Correlationcoefficient of share Jay& Kay * Standard
Deviationof Share Kay* Standard Deviation of Share Kay
= -0.3* 0.18*0.32
= - 0.01728
(b) To calculate expectedreturnandstandarddeviationof aportfoliowith35% of share Jayand 65% of
share Kay
Expectedreturn:
Expectedreturnof the portfolio=0.12*0.35 + 0.24*0.65
= 0.042+ 0.156 = 0.198 = 19.8%

2. StandardDeviation: √𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒
Let’scalculate the Variance first
PortfolioVariance = w2
A*σ2
(RA) + w2
B*σ2
(RB) + 2*(wA)*(wB)*Cov(RA, RB)
= 0.352 * 0.182 + 0.652 * 0.322 * 2 * 0.35 * 0.65 * 0.01728
= 0.1225 * 0.0324 + 0.4225 * 0.1024 + 2 * 0.0039312
= .003969 + 0.043264 + 0.0078624
= 0.0550954
Variance=0.0550954
Nowstandarddeviation=√𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒 = √0.0550954 = 0.23472409= 23.47%
(c) To calculate weightsof eachshare sothat the returnof the portfoliobe equal to15.6%
Let be the weightsbe x and y
NowExpectedreturn= 0.12 * x + 0.24 * y
 0.156 = 0.12x + 0.24y ----------------------------(1)
Alsox+y= 1 ---------------------------------------------------- (2)
Solvingthese 2equations:
X= 0.7 = 70%
Y= 0.3 = 30%
(d) Variance of the portfoliowithweightscalculatedinpart(c) above
PortfolioVariance = w2
A*σ2
(RA) + w2
B*σ2
(RB) + 2*(wA)*(wB)*Cov(RA, RB)
= 0.702 * 0.182 + 0.302 * 0.322 * 2 * 0.70 * 0.30 * 0.01728
= 0.49 * 0.0324 + 0.09 * 0.1024 + 2 * 0.0036288
= 0.015876 + 0.009216 + 0.0072576

3. = 0.0323496
Nowstandarddeviation=√𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒 = √0.0323496 = 0.17985995 = 17.9%
2. Bond valuation
Jasmine Ltdisthinkingtoraise fundsfora new projectbysellingbonds.Followingare the three options
available tothem:
Bond CouponRate (%)
Coupon/Compounding
Frequency Yield
Term in
years Face Value
A 0% half-yearly 7.5% 5 $1,000
B 6.5% half-yearly 7.5% 10 $1,000
C 8.4% yearly 7.5% 8 $1,000
(a) To calculate the marketprice of eachbond:
BondA
Here C= 0%
n = 5 years
M = $1,000
I = 7.5%

4. Couponfrequency:half yearly
As thisiszerocoupon bond then
Thenmarketprice of the bond= 1000÷ (1 + 0.075)5
= $696.56
Market price of bond B:
Here C= 6.5
n = 10 years
M = $1,000
I = 7.5%
Couponfrequency:half yearly
Afterinsertingall the valuesinthe above formula,the marketprice of the bondB will be equal to
$958.94
Market price of bond C

5. Here C= 8.4%
n = 8 years
M = $1,000
I = 7.5%
Couponfrequency:yearly
Afterinsertingall the valuesinthe above formula,the marketprice of the bondB will be equal to
$1,052.72
(b) Whenthe marketprice of the bond ismore than the face value,we can say thatthe bondisissued
at premium
WhenMarket price of the bond islessthan the face value,the bondisissuedatdiscount
Whenmarketprice of the bondis equal tothe face value,the bondisissuedatpar
As perabove notes,we cansay that onlybondC is issuedatpremium, restbondA and B are issuedat
discount.
(c) If Jasmine Ltddecidestosell onlyBbondsandneedstoraise $465,260, thenletus calculate the be
numberof bondsB needstoissuedis
$465,260 / $958.94 = 485.181 = 485
Jasmine Ltdhas to issue 485 bondstoraise requiredfunds.

6. 3. Share valuation
(a) NoChange Ltdhas paid$4.25 as the last dividendwithnoexpectationstoincrease infuture dividends
and no growthpotential aswell.
Market Price of the share:
P= Price of the share
r = Discountrate
Here,P needsto be claculated
Dividend=$4.25
r = 10%
∴ P = $4.25/ 0.10 = $42.5
(b) ConstantGrowthLtdhas paida dividendof $4.25 and expectstogrow at 4% everyyear
Market price of the share
P= Market price of the share
D1 = Dividendtobe paidnextyear
r = Discountrate
g = growthrate
Here P needstobe calculated
Do = $4.25
D1= $4.25 + $4.25 * 0.04 = $4.42
r = 10%
g = 4%

7. ∴ P = 4.42/ 0.10- 0.04 = $4.42/ 0.06 = $73.66
(c) SteadyGrowthLtd has to pay a dividendof $4.25 nextyearand expectstogrow at 4% everyyear
Market price of the share
P= Market price of the share
D1 = Dividendtobe paidnextyear
r = Discountrate
g = growthrate
Here P needstobe calculated
D1= $4.25
r = 10%
g = 4%
∴ P = 4.25/ 0.10- 0.04 = $4.25/ 0.06 = $70.83
(d) SuperGrowthLtdhas paida dividendof $4.25 andexpectsa dividendtogrow at 12% peryear for
next3 yearsAfter3 years,the dividendstogrow constantlyat 4% peryear
To calculate the marketprice of the share we have to follow the below steps:
1. We have to find the three highgrowthdividends.
2. We have to thencalculate the value of the constantgrowthdividendsfromthe fourthdividend
onward.
3. We have to thendiscounteachvalue calculatedinfirstandsecondstep.
4. Then we have to addthe discountedvaluestocalculate the marketprice of the share

8. Period Dividend Calculation Amount
PV values @ 10
%
Present
Value
1 D1 $4.25x 1.121
$4.76 0.909 $4.32
2 D2 $4.25x 1.122
$5.33 0.826 $4.40
3 D3 $4.25 x 1.123
$5.97 0.751 $4.48
4 D4 $5.97 x 1.04 $6.20
$6.20 / (0.10-0.04) 103.33
$103.33/ 1.104
$103.33/1.4641 $70.57
NPV $83.77
Thus the marketprice of the share is$83.77
(e) QuickGrowthLtdhas to pay$4.25 nextyearand thendividendtogrow at 12% per yearfor the next
three years. Dividendswillgrowatconstantrate of 4% peryear afterthe three yearsof quickgrowth.
Period Dividend Calculation Amount
PV values
@ 10 %
Present
Value
1 D1 $4.25 $4.25 0.909 $3.86
2 D2 $4.25x 1.122
$5.33 0.826 $4.40
3 D3 $4.25 x 1.123
$5.97 0.751 $4.48
4 D4 $5.97 x 1.04 $6.20
$6.20 / (0.10-
0.04) 103.33
$103.33/ 1.104
$103.33/1.4641 $70.57
NPV $83.31
Market price of the share is$83.31
Recommendations:
 Investmentsshouldalwaysbe done inthose bonds where the compoundingof the interestis
more frequently.
 Onlythose sharestobe purchasedwhere there isasupernormal growthof dividends.
 Proportionof thatshare shouldbe more inthe portfoliowhichhashighrate of return to have
more expectedrate of returnonthe portfolio.

9.  Shareswithlessstandarddeviationare worthof investment.
 Bondsissuedatpremiumisa smart investment
Conclusion:
 The bondswhichhave frequentcompounding have more marketvalue.
 The shareswithsupernormal growthhave more marketvalue.
 Expectedrate of returnof that portfoliowillbe more whichhasmore proportionof the higher
rate of returninvestment.
 The sharesand bondswithmore standarddeviationare notworthof investment.