(a) Consider an investment where you receive a cashflow of +$400,000 per year for the first 5 years (times 1,2,3,4,5) and then $300,000 per year for the next 5 years (times 6-10), then $200,000 per year for the next 5 years (times 11-15) and then $100,000 per year for the next 5 years (years 16-20) and at time 20 years you also receive an additional +$1,000,000. These cashflows happen at the end of each year.
- Create a cashflow table for this cashflow showing the amount of the cashflow at each time (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20)
- Check if it is true that this cashflow can be thought of and valued as a combination of
(i) an annuity of $100,000 per year for 5 years, and
(ii) an annuity of $100,000 per year for 10 years, and
(iii)an annuity of $100,000 per year for 15 years, and
(iv)an annuity of $100,000 for 20 years and
(v) a lump sum payment of -$4,000,000 paid at time 20 years
Hint: you could create a table with separate columns for each of these cashflows and another column for the combination cashflow
(b) Suppose that it will cost you $1,500,000 to invest in this project. Check if it is true that the rate of return on the investment is 25% per year effective, by computing the Present Value of the project's future cashflows at this rate as a combination of the 5 cashflows in part(a), then compare this to the amount it costs you to initiate the project. You need to value each of the 5 cashflows identified above separately and from that compute the value of the combination.
(c) Explain in words how you could use excel to compute the value of the project's future cashflows using the PV function to compute the value of each of the 5 separate cashflows. What inputs do you need for the PV function for each of these? What result did you obtain?
(d) Use the excel IRR function to compute the internal rate of return for this project
(e) Use the excel NPV function to compute the NPV of the project's cashflow without breaking up the cashflow into the 5 components
(f) Write an excel spreadsheet to implement the calculations for the above parts of the question. Explain
in words how you could use the goal seek function to compute the interest rate in part (d) instead of
using the IRR function.
(g) Compute the payback period for this project. Critique this method for making investment decisions.
Question 2: rights issue vs public issue of new shares 25 marks
Consider the following rights issue:
- Company XYZ has N = 20,000,000 shares on issue and is listed on the stock exchange.
- The current cum rights share price is $50.00 cum S S
- The firm announces a rights issue: For each n=2 shares held the existing shareholders have 1 rights to
buy 1 new shares for a price of X $40.00 . The right to buy the new shares must be exercised at the end of a 4 week "subscription" period.
(a) Suppose the ex rights date is in 2 weeks time and the exercise date of the rights is in 4 weeks time. Explain what is meant by the term "ex rights date"?
(b) How many new shares (M) will be issued if all the rights are exercised?
(c) How much money will the company raise via the rights issue if all the rights are exercised?
(d) The theoretical ex rights price of the shares is ' NSMX S
N M
. What values of M, N, S and X should you use for this calculation? Compute the ex rights price for this example.
(e) By how much will the share price drop on the ex rights date?
(f) Compute the amount of the payoff per right for this example using the formula max ,0 N payoff S X N M
(g) Suppose the firm was considering an alternative of raising the new share capital via a new public offering at $25.00 for new shares and plans to issue the number of new shares required to raise the same amount of new capital as for the rights issue.
- What are the differences between these methods of raising new equity capital in terms of who canbuy the shares, the costs involved, the time taken, control of the firm and the impact of "underpricing" on existing shareholders?
- Estimate the impact on the share price of the public offer going ahead. By how much will the shareprice change? (hint: similar effect to a rights issue but with a different exercise price)
- If you were an existing shareholder, would you prefer the firm to raise the new money via a rightsissue or via the public offer? Why? (hint: the price will change, who benefits ? the new shareholders or the old ones?)
- Would it make a difference to your answer if you currently own 50% of the shares in the firm?
- Would it make a difference to your answer if you currently own 10% of the shares in the firm but
you can't afford to buy new shares via the rights issue?
Question 3
(a) Your firm is a property developer / building construction firm and its main business is constructing residential real estate in remote mining towns in Australia. It can construct a new home in less than two months using pre-fabricated materials. The land in these remote mining towns is quite cheap and the local government is usually happy to have development in their area, so getting approval from council for building is relatively easy. The properties which are being constructed are cheap to build and can be sold to workers who work in the mining industry at a substantial profit. The beta of this residential real estate is 1.25. The risk free rate of interest is 4%. The expected return on the stock market index (the market portfolio) is 8%. The beta of the shares of your firm is 0.80.
- Use the capital asset pricing model to estimate the return on these real estate assets. Check if it istrue that the return is 12%
- Use the capital asset pricing model to estimate the return on the shares. Check if it is true that thereturn is 6%
- What risks are involved for investors who invest in this type of residential real estate?
- How do these risks compare to buying residential real estate in one of Australia's capital citiesinstead of in a remote mining town?
- What risks are involved for investors who buy shares in this firm?
- How do these risks compare to the risks involved in buying a well diversified portfolio of shares?
(b) Compute the average return, variance of return and standard deviation of return from the following sample of returns on stock A over 11 different periods.
Year 1 2 3 4 5 6 7 8 9 10 11
Retur
n
7.00
%
4.00
%
5.00
%
3.00
%
8.00
%
1.00
%
10.00
%
9.00
%
2.00
%
6.00
%
11.00
%
Check whether it is true that
- the average return is 6% and
- the variance of return is 0.001100 expressed as a decimal
- the standard deviation of return is 3.3166%
- either verify these results or correct them
- which excel functions should you use for these purposes?
(c) Two stocks A and B have returns of 15% and 15% p.a. respectively.
The standard deviation of return for stock A is 40% and the standard deviation of return for B is
30%.
The correlation between the returns is ρ=0.00.
Using this information,
- compute the expected return and
- standard deviation of return
on a portfolio where you have $50 invested in stock A and $50 invested in stock B.
Check if it is true that the results are: Expected return = 25%, standard deviation = 20%. Show your working to compute these results. Would you prefer to invest $100 into stock A or $100 into this equally weighted portfolio of A and B? Why?
(d) Suppose that you have x% of your money invested in stock A and y%=100%-x% of your money invested in stock B. Using excel, compute the expected return and the standard deviation of return for portfolios of A and B where the proportion invested in stock A varies from 0% to 100% going up in steps of 5%. This gives you 21 different portfolios to consider. Create a graph showing the relationship between the risk (as measured by the standard deviation of the portfolio) and the expected return. Create a table setting out the expected return and the standard deviation of return for each of these 21 portfolios. Which combination of A and B produces the lowest risk (as measured by the standard deviation)?
(e) Repeat this for the situation where the correlation is -100% and where it is +100%. Graph the risk return combinations for all 3 values of the correlation on the same graph. Use excel to do this and create an "xy chart"
Question 4. When a corporation wants to make payments of its profits to shareholders, it can do so via a dividend, or via a share buyback.
Taxation of Dividends: For Australian shareholders, a dividend is taxed via the dividend imputation system. The amount of the cash dividend generates a tax liability of 1
0.70
D T where D is the cash dividend paid, and T is the investor's personal tax rate. The dividend carries with it a tax credit of
1 0.30
0.70
D which is the corporate tax already paid by the corporation on the profits that generated the dividend. The tax payable by the shareholder on the cash dividend is 1 0.30
0.70
D T
Taxation of capital gains: For Australian shareholders, a share buyback is taxed as a capital gain. The investor sells his or her shares back to the company. If you sell the shares for more than you bought them for and you held them for more than 12 months, then the gain on the sale is 50% taxable at the investor's personal tax rate. The tax payable on the sale proceeds of P per share would be PC T 0.50 where P
is the sale price of the shares and C is the cost of the shares. Suppose that you own 1000 shares of firm XYZ currently valued at $70 each. The firm plans to pay a dividend of $7 per share, which is a dividend yield of 10%. Alternatively the firm could buy back 10% of the shares at $70 each. Either way you would get a payment from the firm of $7000. You bought the shares 2 years ago for $50 each.
(a) Could it be more difficult and more administration work for a firm to do a share buyback instead of pay a dividend to shareholders? Why? Suggest reasons for why this may be so.
(b) What is the likely effect on the share price (i.e. up, down or no effect) of paying a dividend. Why? What is the likely effect on the share price (i.e. up, down or no effect) of doing a share buyback? Why?
(c) If your personal tax rate is 20%, which would you prefer, a dividend payment or a share buyback? Why? If your personal tax rate is 40%, would your answer be different? Why? Show your calculations to support your conclusions.
(d) Your firm has sold off one of its divisions to another firm and has received a large amount of cash, so that now 30% of the firm's assets is in the form of cash. The firm is trying to decide what to do with this cash and it is considering returning the cash to its shareholders. What are the advantages and disadvantages for the firm of returning the cash to shareholders?
(e) The Modigliani and Miller theory is that dividend policy is irrelevant to the share price of a firm. What is your view? Is this correct? Give reasons for your answer