Time Value of Money and Interest Rates I

Question 1 (30 marks)
Lecture 2: Time Value of
Money and Interest Rates I
Lecture 3: Time Value of
Money and Interest Rates II
Lecture 4: Valuing shares
and bonds

a)
8 marks
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 payments of $9.5 million per year at the end of each year
(the first payment occurs one year from now), or to receive 30 payments of $5.5
million per year at the end of each year (the first payment occurs one year
from now).

i.
If he thinks he can earn 7%
annually, which should he choose?(3
marks)

ii.
If he thinks he can earn 9%
annually, which is the best choice?(3
marks)

iii.
Explain how interest rates
influence the award options.(2 mark)

b) 7 marks
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.

i.
What would be the new monthly
repayment? (5 marks)

ii.
What would be the new loan
term?(2 marks) (Note:
students may use the following formula to solve for t)

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c) 4 marks
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. (Note: students may try
to convert the semi-annualrate to an effective annual rate, then to a quarterly
rate)

d)

Consider two
12% (coupon rate) $100 (face value) 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?

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

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

e) 4marks
The required rate of return on the shares of Firm C is
15% per annum (discount rate). 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. Calculate the current share price of Firm C.

Question 2 (20 marks)
Lecture 5: Net present value and other investment criteria
Lecture 6: Capital Budgeting

You are evaluating a proposal to buy a new
machine. The base price is $108,000, and
shipping and installation costs would add another $12,500. The machine is depreciated using prime cost
method (3 years useful life), and it wouldbe sold after 3 years for
$60,000. The machine would require a
$5,500 increase in net operating working capital(in year 0) and this will be
returned at the end of year 3. The
pre-tax labour costs would decline by $44,000 per year. The marginal tax rate is 35% and the WACC is
12%.

i.
What are the project’s annual
cash flows during years 0, 1, 2 and 3? (12 marks)

ii.
Calculate NPV (6 marks)and advise whether this
project should be accepted based on its NPV(2
marks).

Risk and Return

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

Rio Tinto
Ltd

Cathay
Pacific Airlines

The table below shows
the closing prices between 2008 and 2014.

Rio
Tinto Ltd (RIO.AX)

Cathay Pacific
Airlines (0293.HK)

December
2008

$29.97

$8.72

December
2009

$74.89

$14.48

December
2010

$85.47

$21.45

December
2011

$60.3

$13.32

December
2012

$66.01

$14.22

December
2013

$68.18

$16.4

December
2014

$58

$16.9

The monthly datais
collected from Yahoo Finance on 1st of November 2015.

a)
4 marks
For each stock,
show the annual stock returns.

b)
4 marks
Based on the
annual stock returns, calculate the average stock returns and standard
deviation for each stock.

c)
4 marks
Calculate the covariance
and correlation of annual stock returns between these stocks.

d)
4 marks
The risk-free
rate is 2.06% per annum. Calculate the
Sharpe ratio for Rio Tinto Ltd and Cathay Pacific Airlines. Which stock is performing better? Explain your answer.

e)
4 marks
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?