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BHM206 Financial Management

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BHM206 Financial Management

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Course Code: BHM206

University: Open Universities Australia

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Country: Australia

Questions:

Question 1

Natalie is planning to invest $5,000 in a bank term deposit for 5 years. The account will pay fixed interest of 2 per cent on the outstanding balance at the end of each quarter with the interest amounts being re-invested in the account and able to earn the same interest rate. What is the future value of her investment?

Question 2

An investor estimates the probabilities and related return of his portfolio under each of four scenarios (boom, good, poor and bust).

State of Economy Probability of State of Economy ReturnBoom 0.18 0.49Good 0.42 0.37Poor 0.23 0.22Bust 0.17 -0.12

(a)What is the expected return of the portfolio?(b)What is the variance of this portfolio? What is the standard deviation?

Question 3

Rio Tinto’s preference shares are selling at $43.50 on the market and pay a fixed annual dividend of $3.60 per share. The company has just released a new 5 year profit plan which predicts that earnings will grow at the rate of 5 per cent annually. a) What is the expected rate of return if investors are buying them at this price?b) If an individual investor had a required rate of return of 9.5 percent, what is the maximum price that investors would normally be willing to pay for the shares?

Question 4

A share has an expected return of 13.1%. Its beta is 0.87 and the risk-free rate is 5.7%. What must expected return on the market be?

Question 5

A share has an expected return of 12.2%, the risk-free rate is 3.5%, and the market risk premium is 7.1%. What must the beta of this share be?

Question 6

A bank is prepared to lend you funds at 8% p.a. compounded semi-annually or 7.8% p.a. compounded monthly. Which interest rate is preferable?

Answer:

Principal = $ 5,000

Interest rate = 2% per quarter

Time period = 5 years or (5*4) = 20 quarters

The compounding of interest is being done. Hence the relevant formula is shown below.

A = P (1+r)n

Here, P = $ 5,000, r=2%, n= 20

Hence, A = 5000*1.0220 = $ 7,429.74

(a) Expected return on portfolio = 0.18*0.49 + 0.42*0.37 + 0.23*0.22 + 0.17*(-0.12) = 0.2738 or 27.38%

(b) The variance on the portfolio can be computed using the computations shown below.

Variance = 0.0893 or 8.93%

Standard deviation = √Variance = √0.0893 = 0.2988 or 29.88%

a) Expected return on the preference shares = (Fixed dividend/Price)*100

Hence, expected return on Rio Tinto preference shares = (3.60/43.50)*100 = 8.28% p.a.

b) Now the return expected by the investor is 9.5%, hence let the price that investor would be willing to pay be P. Using the above formula, we get

9.5 = (3.6/P)*100

Solving the above, we get P = $ 37.89

The requisite formula as per CAPM approach is given below.

Expected return on share = Risk free rate + Beta*(Expected market return – Risk free rate)

In the given case, expected return on share = 13.1%, beta = 0.87 and risk free rate = 5.7%

Hence, 13.1 = 5.7 + 0.87*(Expected market returns – 5.7)

Solving the above, we get expected market returns = 14.21% p.a.

The requisite formula as per CAPM approach is given below.

Expected return on share = Risk free rate + Beta*Market Risk Premium

In the given case, expected return on share = 12.2%, market risk premium = 7.1% and risk free rate = 3.5%

Hence, 12.2 = 3.5 + Beta*7.1

Solving the above, beta of share = 1.23

The effective annual rate needs to be found for both the loans so that a comparison can be done.

Effective annual rate for the monthly compounded rate = [(1+(7.8/1200))12-1] *100 = 8.08%

Effective annual rate for the semi-annual compounded rate = [(1+(7.8/200))2-1] *100 = 8.16%

With regards to taking loan, a lower interest rate is preferable and hence the loan at 7.8% p.a. compounded monthly would be preferred over 8% p.a. compounded semi-annually.

a) The present value of the annuity of the cash flows would be the most amount that would be paid for the five year annuity. The relevant formula is stated below.

In the given case, P = $ 2,000, r = 7% p.a., n = 5 years

Hence, the most amount payable = 2000*(1-1.07-5)/0.07 = $ 8,200.4

b) This is perpetuity since the annuity payments would continue forever.

Hence, amount to be paid = (Annual cash inflows/Return rate) = (25000/0.06) = $ 416,666.7

a) At maturity the value of the bond must be equal to the face value of $ 700,000

Let the current price be P

Then, P (1+ (2.9/36500))110 = 700000

Solving the above, we get P = $ 693,909.09

b) Since the bill has been held for 80 days, hence the remaining maturity period is 30 days

30 days bill yields = 2.30% p.a.

Hence, P(1+ (2.3/1200))12 = $ 700000

Solving the above, we get P = $ 684,098.8

(a) In the given case EAR = 6.2%

The nominal rate needs to be found considering semi-annual compounding. Let the nominal rate be X% per half year

Then, (1+ (X/100))2 – 1= 0.062

Solving the above, we get X = 3.053%

The above would be used as a discount rate for the future cash flows expected from the bond in order to estimate the current value of bond.

Face value of bond = $ 1000

Coupon = 7% of 1000 = $ 70 payable semi-annually i.e. $ 35 after six months each

Maturity period = 20 years or 40 semi-annual periods

Here C = $ 35, i = 3.053% , n = 40, M = $ 1000

Therefore, bond price = [35*(1-(1/1.0305340))/0.03053] + 1000/1.035340 = $ 1,102.35

It is apparent that the bond is trading at a premium since the current price of bond exceeds the face value of bond.

(b) If the quoted interest rate is 6.2 % p.a., then this is nominal rate which would imply that for six months, the applicable interest rate would be 3.1%.

Here C = $ 35, i = 3.1% , n = 40, M = $ 1000

Therefore, bond price = [35*(1-(1/1.03140))/0.031] + 1000/1.03140 = $ 1,090.98

Clearly, the price of the bond has declined which is on expected lines considering that the discount rate was increased.

The relevant formula is shown below.

Average Real Return = Average Nominal Return – Average Inflation

Hence, average real return in ANZ = 3.1 – 1.1 = 2 %

THe relevant formula to be used is shown below.

Dn = D0 (1+r)n

Based on the given information, D0 =$ 3, r= 2.5% p.a, n = 8 years

Hence, D8 = 3 *(1.0258) = $ 3.66

The relevant formula for Gordon Dividend model is shown below.

Intrinsic share price = Next year dividend/(Required return – Dividend perpetual growth rate)

Next year dividend = $ 8, Required Return = 11% p.a., Dividend growth = 5% p.a.

Hence, current share price (P0) = 8/(0.11-0.05) = $133.33

Let the share price after 5 years be P5

Then, P0 = P5/(1+required return)5

Hence, 133.33 = P5/(1.115)

Solving the above, we get P5 = $ 224.67

Based on the given data, the following information is relevant.

D1 = $ 2

D2 = $ 5

D3 = $ 7

D4 = $ 8

D5 = $ 4.5

D6 = 4.5*1.035 = $ 4.66

Required return = 12% p.a.

Perpetual dividend growth from year 6 onwards = 3.5% p.a.

The stock price can be found by finding the present value of dividends from year 1 to year 5 along with the value of future dividends from 6th year onwards determined by the Gordon Dividend Approach.

Hence, stock price of ABC share = (2/1.12) + (5/1.122) + (7/1.123) + (8/1.124) + (4.5/1.125) + [(4.66/(0.12-0.035))/1.125] = $ 49.48

Thus, the current price of ABC share is $ 49.48.

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