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?
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
- What is the expected return of the portfolio?
- What is the variance of this portfolio? What is the standard deviation
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?
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?
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?
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?
Suppose that ABC Ltd pays $2000 at the end of each year for 5 years and the appropriate discount rate is 7%. What is the most we should pay for this offer?
ABC Ltd is trying to sell you an investment policy that will offer you $25000 per year forever. If the required return on this investment is 6%, how much will you pay for this policy?
(a) Money-Solutions Investments is buying a 180 day original term to maturity bank bill today. The bill matures in 110 days’ time. The bill has a face value of $700,000 and the current yield on this bill is 2.9%. Note that this is a quoted annual interest rate. How much will Money-Solutions Investments have to pay to buy the bill?
(b) After 80 days of holding the bill, Money-Solutions Investments wants to sell the bill on the secondary market. At that time, yields for 80 day bills are 2.85% and 30 day bill yields are 2.30%. How much will Money-Solutions Investments receive when it sells the bill?
Three years ago, an industrial company called Success Inc., issued 20-year bonds with a face value of $1000 and semi-annual coupon payments. The effective annual rate (EAR) or yield on other commercial and industrial bonds of similar risk and time to maturity is 6.2%, so the company decides to offer 7% annual coupon to attract investors.
(a) What would be a fair price for these bonds? Refer to your book and see if you should use EAR or MIR.Show all workings. Is the bond selling at premium, discount or par? Explain.
(b) If instead of having the EAR, you had the quoted interest rate equal to 6.2%, how would your answer change?
Suppose the average inflation rate over a three year period was 1.1% and ANZ offered the average nominal rate of 3.1% over this period.
What was the average real return for investors who invested in ANZ over this three year period?
The Ned Kelly Corporation has just paid a dividend of $3 per share. The dividend of this company grows at a constant rate of 2.5% per year. Based on this information, what will the dividend be in 8 years?
The next dividend for Gordon Growth Company will be $8 per share. Investors require a 11% return in companies such as Gordon. Gordon’s dividend increases by 5% every year. Based on the dividend growth model, what is the value of a Gordon’s share today? what is the value in 5 years?
ABC investments Ltd is expected to pay the following dividends over the next five years: $2, $5, $7, $8 and $4.5. Afterwards, the company will maintain a constant 3.5% growth rate in dividends forever. If the required return on ABC ordinary shares is 12%, what is the current share price?
- Calculation of expected return for portfolio
Hence, expected return for portfolio would be 27.38%.
- Calculation of standard deviation for portfolio
- Expected return for preference shares
The expected return for preference share of Rio Tinto
- Expected return for the investment = 9.5%
Price of investment that would be paid = x
Let the expected market return is x.
Thus, beta of the share would be 1.23.
Comparison would be made based on the effective annual rate.
- Effective annual rate (compounded monthly)
- Effective annual rate (compounded semi-annually)
Loan which shows minimum effective annual rate would be preferable option and thus, loan should be taken for the rate which is compounded monthly.
- Present value of annuity would be the amount that would be paid for the total period of annuity which is computed as shown below.
P = $ 2,000
r = 7% p.a.
n = 5 years
- It is apparent that annuity payments will be continued and hence, it is perpetuity
- Bond value would be same as face value at the maturity and hence, it would be $700,000.
Current price of bond is x.
- Lent maturity period would be 30 days as the bill would be held only for 80 days.
30 days of billing would yield at a rate = 2.30% p.a.
- Effective annual rate (given) = 6.2%
Let the nominal rate is x% semi-annually.
In regards to find the current price of the bond, the above shown nominal rate would be used as a discount rate for future cash flow.
Face value of the bond = $1000
Coupon = 7% of Face value of the bond = $70 payable (Semi-annually)
It represent that coupon would be $35 after each six month.
Maturity period = 20 years = 40 semi-annually
- Current price of the bond
Current price of the bond is more than the face value and hence, it can be said that bond is trading at premium price.
- Rate of interest (Quoted) = 6.2% p.a.
The above rate would be termed as nominal rate which indicates that for a period od six months the interest rate would be 3.1%.
The revision in the price of bond is computed below.
The new price of bond is reduced which is expected because the discount rate has been increased.
Average real return (ANX) = (Avg. nominal return) – (Avg. Inflation) = 3.1 – 1.1 =2%
Gordon Dividend Model
Dividend (Next year) = $ 8,
Required Return = 11% p.a.
Dividend growth = 5% p.a.
Current share price (P0)
Now, share of price after 5 years period is P5
P5 = $ 224.67
Relevant data and information
Perpetual dividend growth =3.5% p.a. (from 6 years onward)
Required return = 12% p.a.
Gordon Dividend Approach
Therefore, the stock price of ABC share would be $49.48.