## Finance-AW149 Online Services

**Question 1**

Ted just won the lottery, and he must choose among three award options. He can elect to receive a lump sum today of $61m, to receive 10 end-of-year payments of $9.5 million, or to receive 30 end-of-year payments of $5.5 million.

i. If he thinks he can earn 7% annually, which should he choose?

ii. If he thinks he can earn 9% annually, which is the best choice?

iii. Explain how interest rates influence the award options.

Today is your grandmother’s 55th birthday. She plans to retire on her 65th birthday and wants to put aside the same sum of money every birthday (starting today) up to and including her 65th birthday. She then wants to be able to withdraw $10,000 every birthday (starting from her 66th) up to including her 85th birthday. She believes that an interest rate of 10% per annum is a reasonable estimate. How much does she need to put aside on each birthday?

You borrow $50,000 repayable in monthly instalments over 10 years. The nominal interest rate is 12% per annum. After 3 years have passed, the lender increases the interest rate to 13.5% per annum and you are given the choice of either increasing the monthly repayment or extending the term of the loan. What would be the new monthly repayment? (3 marks)What would be the new loan term?(2 marks)(Note: students may use the following formula to solve for n)

Mickey is planning to save $50,000 per quarter for 10 years. Savings will earn interest at an (nominal) interest rate of 12% per annum. Calculate the present value for this annuity if interest is compounded semi-annually.

**Question 2 **

Consider two 12% (coupon rate) $100 government bonds that differ only in that one matures in 2 years’ time and the other in 5 years’ time. Both bonds pay coupon annually.

i. What will be the price of each bond, given the required yield is 10% per annum? What will be the price of each bond, given the required yield is 14% per annum?

ii. Explain the price movements in response to interest rate changes as evidenced by parts (i) and (ii).

The required rate of return on the shares in the firms identified in parts (i) to (iii) is 15% per annum. Calculate the current share price in each part.

i. The current dividend per share in Firm A is $1.50, which is expected to remain constant.

ii. The current dividend per share in Firm B is 80 cents. This dividend is expected to grow at 5% per annum.

iii. Current dividend per share in Firm C is 60 cents. The dividend has been growing at 12% per annum in recent years, a rate expected to be maintained for a further 3 years. It is envisaged that the growth rate will then decline to 5% per annum and remain at that level indefinitely.

A major pension fund is interested in purchasing Ted’s stock. The pension fund manager has estimated Ted’s free cash flows for the next 4 years as follows: $3million, $6million, $10 million, and $15 million. After the 4th year, free cash flow is projected to grow at a constant 7%.

Ted’s WACC is 12%, the market value of its debt and preferred stock totals $60 million, and it has 10 million shares of common stock outstanding.

i. What is the present value of the free cash flows projected during the next 4 years?

ii. What is Ted’s total value today?

iii. What is an estimate of Ted’s price per share?

**Question 3 **

A number of capital structure theories have been introduced to show that capital structure does matter in the presence of capital market frictions and imperfections: they are the trade-off theory, pecking order theory and market timing hypothesis. Provide a concise summary on trade-off theory, pecking order theory and market timing hypothesis and explain how a firm decides its debt/equity ratio based on each of the hypothesis/theory mentioned.

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**Question 4 **

AJI Limited current share price is $20 and it has just paid a $1 dividend. As AJI is a mature firm, this $1 dividend is expected to grow at a rate of 4% per year. What is an estimate of the return shareholders of AJI Ltd expected to earn?

AJI also has preference shares outstanding that pays $2 per share fixed dividend. If this stock is currently priced at $24, what is the return that preference shareholders expect to earn?

AJI has issued a 5 year bond with a coupon rate of 11% and par value of $1,000. The price received by AJI was $1,200. What is AJI’s pre-tax cost of debt?

AJI has 5m ordinary shares outstanding and 1 m preference shares outstanding. Its equity has a total book value of $50m and its liabilities have a book value of $20m. If AJI’s ordinary and preference shares are priced as in parts a) and b), what is the market value of the AJI’s assets?

AJI faces a 30% tax rate. Given the information in parts a) – d), and your answer to those problems, what is AJI’s WACC?

**Question 5 **

Your grandfather is planning to invest $25,000 into the following stocks

Collect the year-end (adjusted closing) stock prices for Rio Tinto Ltd and Cathay Pacific Airlines from the period 2010-2015. For each stock, show the annual stock returns. (Hint: students may collect stock prices from Yahoo Finance).

Based on the annual stock returns, calculate the average stock returns and standard deviation for each stock.

Calculate the covariance and correlation of annual stock returns between these stocks. Explain your answers.

Find the 30 days BAB (bank Accepted Bill) rate (risk-free rate) as at June 2015. (Hint: students may collect the risk-free rate from the Reserve Bank of Australia). Calculate the Sharpe ratio for Rio Tinto Ltd and Cathay Pacific Airlines. Which stock is performing better? Explain your answer.

Suppose grandfather invests 60% in Rio Tinto and 40% in Cathay Pacific Airlines, calculate the expected return and standard deviation for this portfolio. Is this portfolio perform better than the individual stock?

**Product code: Finance-AW149**

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