Executive summary: This report covered portfolio, bond and share valuation of three different companies providing an explanation about the selection criteria of any bond and share while investment of the funds in the portfolio. The report covered the calculation of the expected return and standard deviation of the portfolio. The report also covered the valuation of three types of bond with three different coupon rates to provide an insight while investing in the bonds. The share valuation calculated the market share price of the shares with no growth, normal growth and super normal growth.

1. Portfolio valuation

Shares Type Expected Return Standard Deviation Correlation CoefficientShare JAY 12% 18% -0.3Share KAY 24% 32%

(a) To calculate covariance between share Kay and share Jay:

Covariance between Share Jay and Share Kay = Correlation coefficient of share Jay & Kay * Standard Deviation of Share Kay * Standard Deviation of Share Kay

= -0.3* 0.18*0.32

= - 0.01728

(b) To calculate expected return and standard deviation of a portfolio with 35% of share Jay and 65% of share Kay

Expected return:

Expected return of the portfolio = 0.12*0.35 + 0.24*0.65

= 0.042+ 0.156 = 0.198 = 19.8%

Standard Deviation: √ Variance

Let’s calculate the Variance first

Portfolio Variance = w2A*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

Now standard deviation= √ Variance = √0.0550954 = 0.23472409= 23.47%

(c) To calculate weights of each share so that the return of the portfolio be equal to 15.6%

Let be the weights be x and y

Now Expected return = 0.12 * x + 0.24 * y

0.156 = 0.12x + 0.24y ----------------------------(1)

Also x+y = 1 ---------------------------------------------------- (2)

Solving these 2 equations:

X= 0.7 = 70%

Y= 0.3 = 30%

(d) Variance of the portfolio with weights calculated in part (c) above

Portfolio Variance = w2A*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

= 0.0323496

Now standard deviation= √ Variance = √0.0323496 = 0.17985995 = 17.9%

2. Bond valuation

Jasmine Ltd is thinking to raise funds for a new project by selling bonds. Following are the three options available to them:

Bond Coupon Rate (%)Coupon/Compounding Frequency Yield

Term in years Face Value

A 0% half-yearly 7.5% 5 $1,000B 6.5% half-yearly 7.5% 10 $1,000C 8.4% yearly 7.5% 8 $1,000

(a) To calculate the market price of each bond:

Bond A

Here C= 0%

n = 5 years

M = $1,000

I = 7.5%

Coupon frequency: half yearly

As this is zero coupon bond then

Then market price 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%

Coupon frequency: half yearly

After inserting all the values in the above formula, the market price of the bond B will be equal to $958.94

Market price of bond C

Here C= 8.4%

n = 8 years

M = $1,000

I = 7.5%

Coupon frequency: yearly

After inserting all the values in the above formula, the market price of the bond B will be equal to $1,052.72

(b) When the market price of the bond is more than the face value, we can say that the bond is issued at premium

When Market price of the bond is less than the face value, the bond is issued at discount

When market price of the bond is equal to the face value, the bond is issued at par

As per above notes, we can say that only bond C is issued at premium, rest bond A and B are issued at discount.

(c) If Jasmine Ltd decides to sell only B bonds and needs to raise $465,260, then let us calculate the be number of bonds B needs to issued is

$465,260 / $958.94 = 485.181 = 485

Jasmine Ltd has to issue 485 bonds to raise required funds.

3. Share valuation

(a) NoChange Ltd has paid $4.25 as the last dividend with no expectations to increase in future dividends and no growth potential as well.

Market Price of the share:

P= Price of the share

r = Discount rate

Here, P needs to be claculated

Dividend = $4.25

r = 10%

∴P = $4.25/ 0.10 = $42.5

(b) ConstantGrowth Ltd has paid a dividend of $4.25 and expects to grow at 4% every year

Market price of the share

P= Market price of the share

D1 = Dividend to be paid next year

r = Discount rate

g = growth rate

Here P needs to be calculated

Do = $4.25

D1= $4.25 + $4.25 * 0.04 = $4.42

r = 10%

g = 4%

∴P = 4.42/ 0.10- 0.04 = $4.42/ 0.06 = $73.66

(c) SteadyGrowth Ltd has to pay a dividend of $4.25 next year and expects to grow at 4% every year

Market price of the share

P= Market price of the share

D1 = Dividend to be paid next year

r = Discount rate

g = growth rate

Here P needs to be calculated

D1= $4.25

r = 10%

g = 4%

∴P = 4.25/ 0.10- 0.04 = $4.25/ 0.06 = $70.83

(d) SuperGrowth Ltd has paid a dividend of $4.25 and expects a dividend to grow at 12% per year for next 3 years After 3 years, the dividends to grow constantly at 4% per year

To calculate the market price of the share we have to follow the below steps:

1. We have to find the three high growth dividends.

2. We have to then calculate the value of the constant growth dividends from the fourth dividend onward.

3. We have to then discount each value calculated in first and second step.

4. Then we have to add the discounted values to calculate the market price of the share

Period Dividend Calculation AmountPV 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 $4.484 D4 $5.97 x 1.04 $6.20

$6.20 / (0.10-0.04) 103.33$103.33/ 1.104

$103.33/1.4641  $70.57NPV $83.77

Thus the market price of the share is $83.77

(e) QuickGrowth Ltd has to pay $4.25 next year and then dividend to grow at 12% per year for the next three years. Dividends will grow at constant rate of 4% per year after the three years of quick growth.

Period Dividend Calculation AmountPV 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 $4.484 D4 $5.97 x 1.04 $6.20

$6.20 / (0.10-0.04) 103.33$103.33/ 1.104

$103.33/1.4641 $70.57NPV $83.31

Market price of the share is $83.31

Recommendations:

Investments should always be done in those bonds where the compounding of the interest is more frequently.

Only those shares to be purchased where there is a supernormal growth of dividends. Proportion of that share should be more in the portfolio which has high rate of return to have

more expected rate of return on the portfolio. Shares with less standard deviation are worth of investment.

Bonds issued at premium is a smart investment

Conclusion:

The bonds which have frequent compounding have more market value. The shares with supernormal growth have more market value. Expected rate of return of that portfolio will be more which has more proportion of the higher

rate of return investment. The shares and bonds with more standard deviation are not worth of investment.