Question 1 25 Marks
Use the following information about government bonds to answer the questions below
a) What are the future (i.e. after time 0) cashflows on each of the bonds? Set out the cashflows in a table
showing the amount and the timing of the cashflows for each of the bonds. The table should have a
column for the timing of the payment and for the amount of the payment.
b) Explain why the first bond can be thought of as a package of N zero coupon bonds where each of the
bonds matures for exactly $1.00 at the maturity date in 6 months time. What is the value of N here?
c) The second and third bonds can also be “replicated” by a combination of zero coupon bonds that mature
for $1.00 at times 6 months, 12 months and 18 months.Give details of how many units of these 3 zero
coupon bonds would be needed to create a portfolio of zero coupon bonds with the same cashflows as
bond 2, and then do the same for bond 3.
d) What are the implied zero coupon bond prices for bonds maturing in 6, 12 and 18 months? Write down
the equations you need to solve to obtain the prices of the zero coupon bonds from the prices of the
bonds in the table above. Set our your working to compute the prices of the zero coupon bonds from
e) Check whether it is true that the the yield to maturity on the 1-year bond is 4.0372% per half year or
8.0745% per annum convertible half yearly. Explain how you can use the excel PV function to check
this by pricing the bond via the PV function. Explain how you can use the excel RATE function to
compute this. Give details of the inputs to the PV function and the RATE function required here.
f) If a 1.5 year bond were issued for a price of $100 and a face value of $100, then what annual coupon rate
convertible semi-annually should it have? Use the prices of the zero coupon bonds to answer this
g) For corporate bonds, what factors affect the rating given a bond by ratings agencies?
h) Suppose that your firm experiences a credit ratings downgrade, from AAA to “junk bond” status. What
effect will this be likely to have on the market value of your firm’s existing debt securities?
i) Suppose your firm has issued a bond that has the same term and coupon rate as the above 1.5 year
government bond. If the ratings downgrade results in an increase in the yield spread from 1% to 3%,
what effect would this have on the market value of the corporate bond? (Note that the yield spread
means the difference between the yield to maturity on a corporate bond and the yield to maturity on a
government bond, or equivalently it is the extra yield required to induce an investor (and compensate
them for the extra risk) to invest in a corporate bond instead of a government bond
Question 2 25 MARKS
(i) What is a price earnings ratio? How can it be used as a basis for the valuation of shares? What are
some possible problems with using PE based valuation for shares?
(ii) What is a dividend discount model? How can it be used as a basis for the valuation of shares? What
are some possible problems with using dividend discount models for valuation for shares?
(iii) Consider the following 3 shares:
ï‚· Share A is expected to pay a dividend of $10.00 per annum for ever.
ï‚· Share B is expected to pay a dividend of $5.00 next year and to experience dividend growth at
4% p.a. for ever after.
ï‚· Share C is expected to pay a dividend of $5.00 next year, to experience a dividend growth rate of
20% p.a. for the next 5 years, and zero dividend growth thereafter.
Compute the market value of each of these shares at a capitalisation rate of 10% p.a.
Which firm has the highest share price?
What difference would it make if you value these firms at a capitalisation rate of 7% p.a. instead?
(iv) Suppose that Rapid Ripoff Real Estate Ltd is a “growth share”. The firm has the following financial
market capitalisation rate r = 17.5%
expected first year dividend 1 Div ï€½ $0.50 expected first year earnings 1 EPS ï€½ $0.75
dividend payout ratio = 1
0.50 0.6667 66.67%
return on equity = y = 24%
Compute the following :
(a) the expected growth rate in the firm's earnings
(b) the share price
(c) the present value of growth opportunities (PVGO)
(d) the PVGO as a proportion of the share price
Question 3 [25 marks ]
(a) JH runs a cleaning business. He is the sole proprietor of the business which is set up as a “sole
trader:”. He has a personal net worth of $500,000 and non-business liabilities of $50,000 being the
amount he owes the bank on a mortgage over his home. The business has 10 staff, annual sales of
$900,000, assets of $500,000 and liabilities of $100,000. JH is thinking of giving one of his
employees, SF, a 40% equity interest in this business, in return for $160,000. JH is unsure about
whether to do this via a partnership or via setting up a corporation in which he would own 60% of
the shares and SF would own 40% of the shares. SF has a personal net worth of $60,000 and would
need to borrow the difference of $100,000 to buy a share in the business.
Suppose the business is being sued for $2,000,000 by a former employee who suffered health
problems due to exposure to cleaning chemicals. It is uncertain whether the lawsuit will succeed.
(i) What is the main difference between a partnership and a private corporation in terms of the
risks involved for the owners of the business?
(ii) State 2 differences between a private corporation and a publicly listed corporation
(iii) What is the extent of JH’s exposure to risk of loss of his wealth if the business remains 100%
owned by him as a sole proprietorship? ( how much of his wealth is at risk in this scenario?)
(iv) Suppose SF takes 40% of the business under a partnership agreement and pays JH $160,000
for it. How does this change the level of JH’s exposure if the lawsuit by the former employee
(v) How does your answer to (ii) change if SF becomes a joint owner of the business set up as a
private corporation with shares instead of as a partnership? (Assume the shares are owned
60% by JH and 40% by SF.
2 marks each
(b) The tax system in country F is a progressive tax system similar to that in Australia. The 7 tax
brackets i=1:7, lower limit (L(i)) for the bracket, upper limit (U(i)) for the bracket, and marginal tax
rate (T(i)) for the bracket are as follows:
The last tax bracket with a 75% marginal tax rate was recently introduced into the tax system of
A famous and very wealthy actor, Mr GD, has decided to move from country F to country R where
they have a flat tax rate of 40%. Mr GD thinks that with his income of $1m per year his tax will be
lower in R than in F. The president of R is a big fan of Mr GD
The above data is set up in a spreadsheet in the cell range A1:D9 with text data / headings in rows 1
and 2 and numerical data in the other rows. Set up such a spreadsheet. Assume the taxpayer’s income
is in cell C11. Enter 1000000 in this cell
Set up a formula in cell E3 to compute that part of the tax payable for tax bracket 1.
Type in =MAX(MIN(C3,$C$11)-B3,0)*D3
Copy this formula to the cell range E4:E9
This will calculate the tax for the other tax brackets
In cell C12 enter the formula =sum(E3:E9)
This will calculate the overall tax payable in country F
In cell C13 enter the formula =0.40*C11
This will calculate the overall tax payable if GD lives in country R
(i) Check if GD would pay lower tax in R than he would in F. Show details of your working to
answer this question.
(ii) At what income level would it make your tax lower in R than in F? Use excel’s goal seek tool
to answer this
(iii) Suppose SF is related (married) to JH and JH is paying himself an income of $200000 from
the business and he is thinking of “income splitting” by paying some part Y of his income to
SF so SF pays tax on that part of the income Y while JH pays tax on the income X where
X+Y = $200,000. Both JH and SF pay tax in country F. If X = $200,000 then check if the
total tax payable is as shown below.
How much lower would the total tax payable be if the income is split 60% to JH and 40% to
SF? Would a 50/50 split result in lower tax? Use a spreadsheet to do the calculations.
(v) Submit your spreadsheet file as part of your submission
Question 4: [25 marks]
You are considering applying for a home loan from the local bank. The bank will lend money at i ï€½ 4.00%
per year, convertible monthly and this is equivalent to 1
12 j i ï€½ ï‚´ ï€½ 0.3333% per month . The loan will be paid
by a series of constant repayments of amount R per month, at the end of each month, till the end of the term
of the loan. The loan term can be either 20, 25 or 30 years (or in months this is 240, 300 or 360 months. The
repayments are comprised of an interest component and a principle component so that by the end of the loan
term the loan is fully repaid. The maximum amount you can borrow from the bank depends on your after tax
income and your living expenses per month. The bank will only allow you to make a repayment per month
which is 50% of the amount of your after tax income left over after meeting these living expenses.
The maximum monthly payment is thus ï›monthly after tax income - living expenses 50% ï ï‚´
Suppose your after tax income is $10,000 per month and your living expenses is $4,000 per month, then
your maximum allowable monthly repayment is ï›$10,000 - $4,000 50% = $3,000 ï ï‚´
The bank won’t allow you to take on a loan commitment that exceeds this amount
(a) Explain in words why the equation that connects the interest rate per month (j), the repayment per month
(R ), the term of the loan (n) and the amount of the loan (L) is R anj L ï‚´ ï€¨ , ï€© ï€½
(b) What excel function can be used to compute the factor ï€¨ ï€© 1 1ï€¨ ï€© ,
j anj j
(c) What are the inputs to that excel function?
(d) Compute the annuity factor for the case where n = 300 and j = 0.3333%.
Check if it is true (it may not be!) that the result is 155.206864
(e) Hence estimate the maximum amount the bank will lend you. Check if it is true that the result is
The bank is conservative in its lending policy, and it wants to be sure that if interest rates were to increase by
1.80% per year (0.15% per month) then you would still be able to afford to make the loan repayments and
that these repayments would not exceed the monthly limit above. So it bases the amount it will lend you on
the quoted annual rate of interest (4% p.a.) plus this safety margin of 1.80% per year. However it charges
interest at the 4% p.a. rate. The safety margin is called an “interest rate buffer”.
If the interest rate increases then the value of the annuity factor changes
new a old a increase in a
anj anj anj ,, ,
The sensitivity of the factor
j anj j
to an increase in the interest rate from j to '
j j j
is measured by the ratio
, , anj , anj anj
This is the ratio of the change in the value of the annuity factor to the change in the interest rate.
It can be shown that 1
1 ,1 anj n
anj n j j j
(f) Compute this ratio for j ï€½ 0.3333% and n = 300. Check if it is true (it might not be!) that the result is -
It can be shown that
,1 , 1 n
anj anj n j j j
A mathematically equivalent formula is 1 1 , ,1 1 1
anj anj j n j j j j
The term 1 , ,1 1 n
Ia n j a n j j n j j
is the increasing annuity with payment sequence 1,2,3,…,n
(g) Compute the change in the value of the annuity factor for a 15 basis point increase in the interest rate per
month (let ï„ ï€½j 0.15% , compute ï„anj ï€¨ ï€© , ). Compute the new annuity factor
new a old a increase in a
anj anj anj ,, ,
Hence compute the maximum loan amount the bank will lend you allowing for the interest rate buffer
(h) Your grandmother has $450,000 in cash in a bank account that pays interest at 4% p.a. convertible
monthly. Her health has declined and she is considering moving into an aged care facility. She receives
$24,000 per year in a pension and the pension income is payable monthly. The aged care facility will
charge her an entry fee of $500,000 and an ongoing fee of 75% of her monthly pension to pay for food
and medical treatment. The rest of the pension would be absorbed through spending on entertainment,
food, local travel etc. As an alternative to the $500,000 entry fee she could pay $250,000 as an entry fee
and pay a rent of 6% of $250,000 per year as a monthly in advance rent for the rest of her lifetime. The
plan is for this rent to be paid from the money left in the bank account after paying the entry fee
($450K-$250K=$200K). She is aged 81. How long can she pay the monthly in advance rent for ? How
long will the money last? How old will she be when the money runs out? To answer this question you
need to write down and solve an equation of value for the term of the financing arrangement. How to do
this was covered in lectures. You could use the NPER excel function to numerically solve this problem.
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