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Business Finance Practice Questions
Corporate Finance (Singapore Management University)
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QUESTION 1
What is the more formal name used for describing the corporate finance decision concerning how
the firm should raise finance from investors?
(a)
(b)
(c)
(d)
The capital structure decision
The capital budgeting decision
The dividend decision
The retained earnings decision
QUESTION 2
The assumed overall financial objective of a company is to:
(a)
(b)
(c)
(d)
Raise capital.
Reduce debt.
Maximise profits.
Maximise the market value of its ordinary shares.
QUESTION 3
A process by which, through the operation of interest, a present sum becomes a greater sum in the
future is:
(a)
(b)
(c)
(d)
The additive principle.
The accumulation principle.
The compounding principle.
The discounting principle.
QUESTION 4
An annuity in which the first cash flow is to occur immediately is known as a/an:
(a)
(b)
(c)
(d)
Ordinary annuity.
Ordinary perpetuity.
Annuity due.
Growth annuity.
QUESTION 5
What quarterly payment is necessary to accumulate $4.05 million over 22 years if the annual
interest rate is 4.5% compounded quarterly? Assume payments are made at the end of each
quarter.
(a)
(b)
(c)
(d)
$111,570
$72,737
$293,904
$27,179
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QUESTION 6
A bond selling at a premium should have:
(a)
(b)
(c)
(d)
A coupon rate higher than the YTM
A coupon rate lower than the YTM
A coupon rate equal to the YTM
A coupon rate equal to the current yield
QUESTION 7
Given the following information about Granite Ltd., what is the growth rate of its ordinary
shareholders? The required rate of return is 7.0 percent p.a., the current market price of its ordinary
shares is $36.50 and the last dividend paid to the firm’s ordinary shareholders was $2.15.
(a)
(b)
(c)
(d)
5.67%
1.04%
15.21%
2.70%
QUESTION 8
Given the following information:
EPS = $1.30
re = 8% p.a.
b = 0.30
g = 5% p.a.
what will be the share price?
(a)
(b)
(c)
(d)
$30.33
$18.56
$46.11
$2.35
QUESTION 9
What is the market price (to the nearest dollar) of a 5% p.a. quarterly coupon bond with a face value
of $1,000, five years to go until maturity when the current market yield is 6% p.a.?
(a)
(b)
(c)
(d)
$848
$1,500
$957
$1,201
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QUESTION 10
The director of capital budgeting for ABC Ltd has identified a project with the following expected net
cash flows:
Year
0
1
2
3
Expected Net Cash Flows
($60)
$70
$40
$35
This project has a 8% p.a. cost of capital. What is the project’ NPV?
(a)
(b)
(c)
(d)
$17.95
$63.54
$15.46
$66.89
QUESTION 11
Which of the following capital budgeting decision rules does not use the cost of capital, r, in its
calculation:
(a)
(b)
(c)
(d)
IRR
NPV
Payback Period
Both a) & b)
QUESTION 12
Sunk costs can be defined as:
(a)
(b)
(c)
(d)
Incremental costs.
Opportunity costs.
Cost that has already been incurred but is relevant to future decision making.
Cost that has already been incurred and is irrelevant to future decision making.
QUESTION 13
You are given the following information about the possible returns from an investment:
Return
12%
9%
6%
Probability
30%
40%
20%
The expected return on this investment is:
(a)
(b)
(c)
(d)
1.32%
8.40%
3.20%
6.55%
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QUESTION 14
The capital market line:
(a)
(b)
(c)
(d)
Describes the equilibrium risk-return relationship for efficient portfolios.
Describes the equilibrium risk-return relationship for all portfolios.
Describes the equilibrium risk-return relationship for riskless portfolios.
Describes the equilibrium risk-return relationship for risky portfolios.
QUESTION 15
The return on treasury notes is expected to be 7.5%. The market risk premium is 8%. What is the
expected return on a stock with a beta of 1.3?
(a)
(b)
(c)
(d)
17.90%
8.15%
12.95%
12.35%
QUESTION 16
What is the more formal name used for describing the corporate finance decision concerning how
the firm should raise finance from investors?
(a)
(b)
(c)
(d)
The capital structure decision
The capital budgeting decision
The dividend decision
The retained earnings decision
QUESTION 17
The assumed overall financial objective of a company is to:
(a)
(b)
(c)
(d)
Raise capital.
Reduce debt.
Maximise profits.
Maximise the market value of its ordinary shares.
QUESTION 18
A method of calculating interest in which, during the entire term of the loan, interest is computed on
the original sum borrowed is the:
(a)
(b)
(c)
(d)
Present value method.
Simple interest method.
Compound interest method.
Interest rate method.
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QUESTION 19
Which of these answers best describes an ordinary annuity?
(a) A series of equally sized regularly occurring cash flows extending indefinitely into the future,
with the cash flows occurring at the end of each period
(b) A series of equally sized regularly occurring cash flows extending n periods into the future,
with the cash flows occurring at the start of each period
(c) A series of equally sized regularly occurring cash flows extending n periods into the future,
with the cash flows occurring at the end of each period
(d) A series of equally sized regularly occurring cash flows extending indefinitely into the future,
with the cash flows occurring at the start of each period
QUESTION 20
Debt Ltd borrowed $100 000 from its local bank to finance the purchase of new equipment. Annual
payments are required over five years at a fixed interest rate of 10% p.a. How much is each annual
payment?
(a)
(b)
(c)
(d)
$27 398.18
$20 000.00
$26 379.75
$24 444.12
QUESTION 21
A bond selling at a discount should have:
(a)
(b)
(c)
(d)
A coupon rate higher than the YTM
A coupon rate lower than the YTM
A coupon rate equal to the YTM
A coupon rate equal to the current yield
QUESTION 22
Given the following information about Stone Ltd., what is the growth rate of its ordinary
shareholders? The required rate of return is 8.0 percent p.a., the current market price of its ordinary
shares is $36.00 and the last dividend paid to the firm’s ordinary shareholders was $2.10.
(a)
(b)
(c)
(d)
5.67%
2.04%
15.21%
8.20%
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QUESTION 23
The expectations theory of the term structure of interest implies that:
(a) Interest received on securities is in accordance with term to maturity.
(b) Bond investors can expect to achieve the same return over any future period, regardless of
the security in which they invest.
(c) There is a premium due to uncertainty about the future level of interest rates.
(d) There is a risk that borrowers may default on the payment of the principal.
QUESTION 24
According to the expectations theory of the term structure of interest, if the 1-year bond rate today is
6% p.a. and the 2-year bond rate today is 7% p.a., what is the 1-year bond rate next year?
(a)
(b)
(c)
(d)
6%
6.75 %
7.5 %
8%
QUESTION 25
The corporate finance manager of Baidi4us Ltd has identified a project with the following expected
net cash flows:
Year
0
1
2
3
Expected Net Cash Flows
($80)
$50
$30
$27
This project has a 6% p.a. cost of capital. What is the project’s NPV?
(a)
(b)
(c)
(d)
$19.31
$16.54
$21.56
$84.21
QUESTION 26
Which of the following capital budgeting decision rules does not use the cost of capital, r, in its
calculation:
(a)
(b)
(c)
(d)
IRR
NPV
Payback Period
Both a) & b)
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QUESTION 27
What are sunk costs?
(a) Costs associated with research and development.
(b) Costs associated with exploration.
(c) Costs that are past outlays that should not influence the decision to continue or terminate a
project.
(d) Costs associated with negative net present value projects.
QUESTION 28
An investment has the following possible returns:
Return
13%
8%
5%
Probability
40%
50%
10%
The expected return on this investment is:
(a)
(b)
(c)
(d)
2.80%
9.70%
4.30%
7.60%
QUESTION 29
A security market line:
(a)
(b)
(c)
(d)
Explains the covariance between the returns on the risky asset and the market portfolio.
Explains the covariance between the returns on the risky asset and a riskless asset.
Is a graphical representation of the CAPM.
Is a graphical representation of the CML.
QUESTION 30
The return on treasury notes is expected to be 6.5%. The market risk premium is 7%. What is the
expected return on a stock with a beta of 1.5?
(a)
(b)
(c)
(d)
12.26%
7.25%
18.25%
13.33%
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QUESTION 31
The concept of investors being risk averse means that:
A. investors will always prefer an investment that carries less risk.
B. investors require higher returns to compensate for carrying more risk.
C. the investment's risk is the predominant feature considered by the investor.
D. investors will make all possible attempts to avoid systematic risk.
QUESTION 32
The ultimate objective of investment and financing decisions is to maximise:
A. the number of projects the company is invested in.
B. the amount added to the value of the owner's wealth.
C. the salaries of all employees of the firm.
D. the repayments that are made of debt.
QUESTION 33
The principle that a dollar is worth more the sooner it is to be received is the:
A. value principle.
B. value of money principle.
C. time value of money principle.
D. Fisher effect.
QUESTION 34
A company has $25 million in cash and the interest rate is 12%. The company has decided to
invest $20 million in assets, and the investment has a net present value of $5 million. What is the
wealth of the company's shareholders immediately after the investment plan is announced?
A. $30 million
B. $10 million
C. $28 million
D. $25 million
QUESTION 35
If a term deposit paid an interest rate of 24% p.a. over the past six months, and the current balance
is $1008, what was the amount initially invested?
A. $812.90
B. $681.08
C. $900.00
D. $975.00
QUESTION 36
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What is the present value of the following cash flow stream, discounted at 7% p.a.: Year 1, $100;
Year 2, $400; Years 3 through 20, $300?
A. $2859.20
B. $3563.40
C. $3078.63
D. $2782.40
QUESTION 37
A Ltd is currently paying a dividend of 90 cents per share. Assume that the investors expect this
dividend to be maintained indefinitely and that they require a return of 15% on the investment.
What is the value of A's shares?
A. $0.14
B. $16.66
C. $6.00
D. $1.05
QUESTION 38
According to the expectations theory of the term structure of interest, if the 1-year bond rate today
is 6% p.a. and the 2-year bond rate today is 7% p.a., what is the 1-year bond rate next year?
A. 6%
B. 6.75%
C. 7.5%
D. 8%
QUESTION 39
Sunk costs can be defined as:
A. incremental costs.
B. opportunity costs.
C. cost that has already been incurred but is relevant to future decision making.
D. cost that has already been incurred and is irrelevant to future decision making.
QUESTION 40
If a company has on issue debentures paying a coupon rate of 12% p.a. and the market yield on
similar securities is 18 per cent, what is the correct cost of debt the company should use when
estimating the WACC?
A. None of the given options.
B. 15%
C. 12%
D. 18%
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QUESTION 41
Given that shares have an expected dividend stream of 10 cents in perpetuity and that the current
market price of the shares is $2.40, calculate the cost of equity capital of these shares.
A. 8%
B. 12%
C. 10%
D. 4.2%
QUESTION 41
A weak-form efficient market can best be described as a market in which:
A. trading strategies based upon past share prices cannot earn abnormal profits.
B. all publicly available information is fully reflected in share prices.
C. share prices follow predictable trends.
D. trading strategies based on past information can earn abnormal profits.
QUESTION 43
Corporate decisions include:
A. investment decisions.
B. financing decisions.
C. dividend decisions.
D. all of the given options
QUESTION 44
The concept of market efficiency embodies the idea that:
A. investors want to be compensated with higher returns for all the unsystematic risk they bear, and expect
prices to adjust in an instantaneous and unbiased way.
B. all investors are fully informed about the potential returns for a given firm, and therefore the share price is a
fair representation.
C. share prices respond to new information in a way that is both unbiased and instantaneous.
D. because holders of debt do not share in the high returns in good economic periods, they require a higher
rate of return relative to the risk they bear.
QUESTION 45
The investments component of finance takes the viewpoint of the _______ rather than a company.
investor
QUESTION 46
The value that the financial markets place on a company’s debt and equity securities will depend on the _____ and expected return
on investments in those securities.
risk
QUESTION 47
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If a shareholder wishes to sell his or her shares in order to finance greater consumption, the greater the ______, the greater are his
or her consumption opportunities.
share price
QUESTION 48
An investor who is ______________ will choose a risky investment only if the expected return on the investment is high enough to
compensate the investor for bearing the risk.
risk averse
QUESTION 49
The purchasing power of money increases over time as a result of ____________.
inflation
QUESTION 50
A company has an indefinite life.
TRUE
QUESTION 51
The market value of a company is calculated as the sum of the net assets and owners equity on the company's balance sheet.
FALSE
QUESTION 52
Pursuing a goal of maximising the market value of a company's shares is easy when:
A. dividends are growing at a constant rate.
B. there is limited uncertainty.
C. there are limited market imperfections.
D. there are no market imperfections and no uncertainty.
QUESTION 53
Given a perfect capital market and perfect certainty, the firm will always undertake a project where:
A. the future rate of return on the project is greater than the interest rate available in the capital market.
B. the future rate of return on the project is less than the interest rate available in the capital market.
C. the current rate of return on the project is less than the return available on projects undertaken by
competitors.
D. the current rate of return on the project is greater than the opportunity cost of forgone consumption.
QUESTION 54
Share prices change as a result of investors' reaction to _________ provided through investment, financing and dividend decisions
made by the managers of a company.
information
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QUESTION 55
The interest rate where interest is charged at the same frequency as the quoted interest rate is the:
A. nominal interest rate.
B. real interest rate.
C. compound interest rate.
D. effective interest rate.
QUESTION 56
An annuity in which the first cash flow is to occur immediately is known as a/an:
A. ordinary annuity.
B. ordinary perpetuity.
C. annuity due.
D. growth annuity.
QUESTION 57
An annuity in which the first cash flow is to occur after a time period that exceeds the time period between each subsequent cash
flow is known as a/an:
A. deferred annuity.
B. growth annuity.
C. ordinary annuity.
D. annuity due.
QUESTION 58
You have borrowed $1000 from a friend to pay for unforeseen car repairs, with an agreement to pay interest at an annual rate of
18%, compounding daily. If you repaid your friend after 90 days, how much would you need to repay?
A. $1044.38
B. $1045.00
C. $1045.37
D. $1043.56
QUESTION 59
Calculate the effective annual interest rate corresponding to 12% p.a., compounded quarterly.
A. 11.9%
B. 12.55%
C. 12.45%
D. 12.71%
QUESTION 60
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John has just been employed by a prestigious firm, drawing an annual salary of $300 000, paid at the end of each year. He plans to
work for five years before retiring. He buys a new luxury home with mortgage repayments of $5000 per month for the next 20 years
(payable at the end of each month), and donates $10 000 per annum forever to his favourite charity. What annual amount, in
present value terms, can John withdraw for the first five years of his retirement from the remainder of his savings? Assume an
annual interest rate of 6% p.a.
A. $93 926
B. $246 819
C. $94 754
D. $112 754
What is the present value of $500 payable in 10 years' time if the interest rate is 6% p.a.?
A. $290.50
B. $335.60
C. $895.40
D. $279.20
QUESTION 61
Kristy has to make rental payments of $1000 at the start of every month, throughout the four-year duration of her university course.
Her university fees are $4000 to be paid at the start of each year. She earns $1500 per month (paid at the end of each month) from
a part-time job. Assume an interest rate of 8% p.a. and that she keeps the part-time job for the next four years. How much money, in
present value terms, can she withdraw each month for the next four years?
A. $144
B. $126
C. $55
D. $177
QUESTION 62
The ______ interest rate is an interest rate calculated after taking out the effects of inflation.
real
QUESTION 63
A principle-and-interest loan is a common example of an __________ annuity.
ordinary
QUESTION 64
The annuity where the cash flows continue forever is called a ________.
perpetuity
QUESTION 65
The distinguishing feature of an annuity due is that the time period between the payment of each successive cash flow differs to the
frequency with which the interest compounds.
FALSE
QUESTION 66
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An individual borrowed $100 000 at a fixed interest rate of 12% p.a. for the entire loan term of 20 years. If the loan is to be repaid
through equal monthly instalments, then the regular repayment to the nearest dollar is $1101.
TRUE
QUESTION 67
The periodic cash flows from an investment in shares are called:
A. coupons.
B. interest.
C. capital gains.
D. dividends.
QUESTION 68
Given that dividends on a share are expected to remain indefinitely at $1 p.a. and that the required rate of return for the level of risk
on such a share is 15%, the correct price for this share:
A. cannot be ascertained from this information.
B. cannot be ascertained without regard to the management structure of the firm.
C. is $1.
D. is $6.67.
QUESTION 69
Assume the latest dividend per share, paid recently, for ACD Ltd is 90 cents and that the required rate of return on these shares is
15% p.a. If the current share price is $19.80, the expected growth rate on these shares is:
A. 0%.
B. 10%.
C. 5%.
D. 7.5%.
QUESTION 71
The ________________ of interest rates is the relationship between the interest rates and time to maturity.
term structure
QUESTION 72
Once a bond has been issued, its promised future cash flows are ___________.
fixed
QUESTION 73
The number of internal rates of return is limited to the:
A. number of investments being evaluated.
B. number of sign reversals in the cash flow stream.
C. direction of sign reversals in the cash flow stream.
D. none of the given options.
QUESTION 74
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The internal rate of return is the discount rate at which the net present value is equal to ________.
zero
QUESTION 75
A fundamental problem with using the accounting rate of return for project evaluation is that it ignores the ________________ of the
earnings stream.
timing
QUESTION 76
A major shortcoming in the use of accounting rate of return as a method of project evaluation is that it ignores the time value of
money.
TRUE
QUESTION 77
Which of the following statements is the correct treatment of finance charges in project evaluation?
A. Finance charges should be included in a project's net cash flows and in the discount
rate.
B. Finance charges should be included in a project's net cash flows and excluded from the
discount rate.
C. Finance charges should be excluded from a project's net cash flows and included in the
discount rate.
D. None of the given options is correct.
QUESTION 78
Residual value is:
A. past outlay of a project that has no bearing on future costs or benefits.
B. the portion of initial capital outlay that will be recovered.
C. past outlay, which should not influence the decision between continuing and terminating
a project.
D. cost associated with exploration.
QUESTION 79
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The term ________________ is used to describe a situation where the firm is prevented, through a shortage of funds, from
undertaking all acceptable projects.
capital rationing
QUESTION 80
Which investor has a positive attitude towards expected return and a negative attitude towards risk?
A. A risk-averse investor
B. A risk-neutral investor
C. A risk-seeking investor
D. A well-diversified investor
QUESTION 81
Risk aversion implies that:
A. an investor will prefer a higher expected return than a lower expected return.
B. an investor will refuse to bear any risk at all.
C. an investor will tolerate extra risk if it is expected that the return will compensate them for bearing it.
D. an investor will be indifferent to the level of risk providing that the expected return is identical.
QUESTION 82
Calculate the expected return from a portfolio consisting of three securities with the following expected returns and weights:
A. 0.114%
B. 12%
C. 11.4%
D. 36%
QUESTION 83
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An 'efficient' portfolio is one that:
A. combines assets whose returns are not perfectly correlated.
B. offers the highest expected return for a given level of risk.
C. holds a proportion of all possible assets.
D. combines many diverse assets.
QUESTION 84
Where two securities are perfectly positively correlated, there is no reduction in unsystematic risk through diversification.
TRUE
QUESTION 85
Portfolio theory, as initially developed by Markowitz (1952), assumes that the returns from investments are normally distributed.
TRUE
QUESTION 86
A well-diversified portfolio should have a beta significantly less than one.
FALSE
QUESTION 87
The capital asset pricing model (CAPM) assumes that all securities are priced according to their unsystematic risk.
FALSE
QUESTION 88
If a company is financed entirely by equity then variations in the return to shareholders are attributable only to:
A. financial risk.
B. business risk.
C. technology risk.
D. diversifiable risk.
QUESTION 89
Miller and Modigliani's Proposition 1 states that the dollar value of a company is independent of its capital structure.
TRUE
QUESTION 90
The use of equity financing creates a tax shield that results in a significant reduction in a company's tax liability.
FALSE
QUESTION 91
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Which of the following statements about market efficiency is true?
A. A market can be semi-strong-form and strong-form efficient but not weak-form efficient.
B. A market can be semi-strong-form efficient but not weak-form efficient.
C. A market can be semi-strong-form, weak-form or strong-form efficient but not all simultaneously.
D. A market must be weak-form efficient if it is semi-strong-form efficient.
QUESTION 92
Semi-strong-form efficiency can best be described as:
A. the ability of investors to earn abnormal profits from the over-reaction of share prices to news.
B. a market in which trading strategies based on past prices cannot earn abnormal profits.
C. a market in which trading strategies based on all publicly available information cannot earn abnormal
profits.
D. all information, public and private, is fully impounded in share prices
QUESTION 93
What is the present value of $500 payable in 10 years' time if the interest rate is 6% p.a.?
A. $290.50
B. $335.60
C. $895.40
D. $279.20
QUESTION 94
Matthew earns $10 000 per month for the next 25 years, after which he retires. During the first five years of retirement, he withdraws
$6000 at the start of each month, after which he dies. His son, Sean, inherits the remainder of Matthew's savings. It is further
stipulated in Matthew's will that Sean will be paid the money in equal payments at the start of every month, for the next 20 years.
Given a fixed interest rate of 9% p.a., calculate the amount of the monthly payments that Sean receives.
A. $98 250
B. $97 340
C. $98 270
D. $97 519
QUESTION 95
If a term deposit paid an interest rate of 24% p.a. over the past six months, and the current balance is $1008, what was the amount
initially invested?
A. $812.90
B. $681.08
C. $900.00
D. $975.00
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Short Answer Questions
QUESTION 1
Describe briefly the 3 levels of market efficiency; weak form, semi-strong, and strong form.
Weak form:
- prices fully reflect the information contained in the historical sequence of prices
- Investors cannot devise an investment strategy to yield abnormal profits on the basis of an
analysis of past price patterns, i.e. using technical analysis
- Abnormal profits can still be earned via publicly available information
Semi-strong:
-
Asserts that current market share prices reflect not only historical price data but also all
publicly available information
Abnormal profits can still be earned via private information
Strong form:
-
Asserts that all information that is known to any market participant about a company is fully
reflected in market information
All analysis is useless in trying to achieve abnormal profits
QUESTION 2
Explain SML and CML. What do they stand for? What are they used for? Draw a diagram.
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The Capital Market Line (CML) gives the risk return relationship for portfolios consisting of some
combination of the market portfolio and the risk free asset, where risk is total risk (as measured
by standard deviation σp).
The Security Market Line (SML) is used for working out the risk and return relationship for
individual assets and portfolios other than those comprised of a combination of the market
portfolio and the risk free asset, and where risk is measured only by systematic risk (βeta βi).
Draw a diagram show the above and the straight line relationship with appropriate labels.
QUESTION 3
Explain the differences between hard capital rationing and soft capital rationing.
Hard capital rationing:
-
Imposed by Capital Markets - markets will not provide sufficient finance for a project at an
acceptable cost, i.e. markets will not provide financing for the project at a rate of interest that
will give the project a positive NPV.
Soft capital rationing:
-
Imposed by upper management to ensure subsidiaries prioritise investments.
Ensures discipline by lower level management – subsidiaries to only invest in highest NPV
projects.
QUESTION 4
A car loan of $40,000 is to be repaid by fixed instalments of principal and interest over seven years
at an interest rate of 8% p.a. compounded annually.
Required:
1. The annual instalment
2. The interest and principal portions of the fourth (4th) payment
3. If you win the lottery and repay the loan after the fifth (5th) payment how much will you need
to pay?
1. $7,683.00, i.e.
$ 40,000=PMT
[
]
1−( 1.08 )−7
$ 40,000
= $ 40,000=PMT [ 5.2064 ] =PMT
=$ 7,683
0.08
5.2064
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2. Interest = $2,036, Principle = $5,647, i.e.
Step 1 - PV 3=$ 7,683
[
]
1−(1.08)−4
=$ 7,683 [ 3.3121 ] =$ 25,447
(0.08)
Step 2 - $25,447 x 0.08 = $2,036
Step 3 - $7,683 - $2,036 = $5,647.
QUESTION 5
Suppose you have a riskless security at 4% and a market portfolio with a return of 9% and a
standard deviation of 7%. How should you go about investing your money so that your investment
will have a risk level of 13%?
Quickest way is to use the measure of relative risk to solve:
σ p 0.13
=
=1.86
σ m 0.07
Therefore invest 100% into the market portfolio and borrow 86% at the risk-free rate to invest further
into the market portfolio. Total holdings in the market portfolio = 186%
QUESTION 6
Explain the implications of an inverted yield curve. Draw a diagram.
-
We can use yield curves to predict interest rates
When yield curves are inverted long term interest rates are now below short term interest rates
This can be used to signal an environment of lower interest rates.
Lower interest rate environments are generally signals of a recessionary environment
Thus inverted yield curves can act as signals to an impeding correction in the market.
QUESTION 7
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Describe the three critical factors of cash, timing and risk in relation to financial decision making.
Cash:
-
Focus is always on cash-flows, not accounting earnings or accrued earnings
Timing:
-
Money has a time value; Decision-making in finance must take account of the timing of the
cash-flows.
Risk:
-
Risk refers to variability of a cash-flow stream. Assessing the risk associated with expected
future cash-flows is critical to investment decisions
QUESTION 8
Both Portfolio X and Portfolio Y are well diversified. The risk-free rate is 5%, and the return on the
market is 13%. The following information is available:
Portfolio
Analysts Forecast
Return
Beta
X
13%
1.00
Y
5%
0.25
In this situation, are Portfolio X and Portfolio Y over-valued or under-valued or properly valued? As
an investor, what will you do with these two portfolios in this situation?
Calculate the required return for each portfolio using CAPM:
 Portfolio X:13%
 Portfolio Y:7%
Compare the required returns with the forecast/actual returns
Portfolio X
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Required return
Forecast/actual return
=13%
=13%
Therefore, the market for Portfolio X is in equilibrium.
Portfolio Y
Required return
Forecast/actual return
= 7%
= 5%
Therefore, the market for Portfolio Y is in disequilibrium.
Portfolio Y is overvalued and thus we recommend a SELL.
Long Answer Questions
Question 1
SingVest Corp. has developed the following forecasts for expected returns, standard deviations and
correlation coefficients for 2 securities, the market index and 90-day Treasury Notes. SingVest Corp
intends to use these forecasts as the basis for investment decisions for the next year.
Matrix
Security
A
B
Market Index (M)
90-day Treasury Notes (F)
Expected Return
(% per annum)
15
13
12.0
5.0
Standard Deviation
(% per annum)
6
5
4
0
Correlation Matrix
A
B
M
F
1
0.4
1
0.9 0.7
1
0.3 0.2 0.1
1
Required:
(a) Calculate the expected return and standard deviation of returns for a portfolio (P)
comprised of a 70% investment in Security A and 30% in Security B.
(b) What is the beta for Security A, Security B and the portfolio?
(c) Are the expected return forecasts provided by SingVest Corp consistent with a CAPM
equilibrium for securities A, B and the portfolio (P) from part (a).
(a) R=( W 1 ) ( R1 ) + ( W 2 ) ( R2 ) =( 0.70 ) ( 0.15 ) + ( 0.30 ) ( 0.13 )=0.1050+0.039=0.1440=14.40 %
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√
2
2
2
σ P= ( W 1 ) (σ ¿¿ 1)2+ ( W 2 ) ( σ 2 ) +2(W 1 )(W 2 )(ρ1,2)( σ 1 )¿ ¿
¿ √ ( 0.70 ) (0.06)2 + ( 0.30 ) (0.05)2 +2(0.70)(0.30)(0.40)(0.06)(0.05)
2
2
=√ ( 0.49 ) ( 0.0036 ) + ( 0.09 ) ( 0.0025 ) +0.000504
¿ √ 0.001764+0.000225+ 0.000504= √ 0.002493=0.04993=4.99 %
(b) Security A:
(0.90)(0.06)(0.04 ) 0.00216
=
=1.35
0.0016
(0.04)2
Security B:
(0.70)(0.05)(0.04) 0.0014
=
=0.875
0.0016
(0.04)2
Portfolio: (0.70)(1.35) + (0.875)(0.30) = 0.945 + 0.2625 = 1.2075
(c) Security A: 0.05 + (0.12 – 0.05)1.35 = 0.1445 = 14.45%. Therefore, Security A is
undervalued.
Security B: 0.05 + (0.12 – 0.05)0.875 = 0.1112 = 11.12%. Therefore, Security B is
undervalued.
Portfolio: 0.05 + (0.12 – 0.05)1.2075 = 0.1345. Therefore, Portfolio is undervalued.
QUESTION 2
You have bought a property and have six (6) different options on how to pay for the property
purchase. The six options are:
(i) $1,000,000 paid now
(ii) $ 250,000 p.a. paid every year for five years with the first payment now (five payments in
total)
(iii) $225,000 p.a. for six years with the first payment paid at the end of the first year (six
payments in total)
(iv) $100,000 now and $100,000 every six months for seven years (15 payments in total)
(v) $1,000,000 at the end of the fifth year and $1,250,000 at the end of the 10 th year (two
payments in total)
(vi) A $20,000 deposit paid now plus $100,000 paid forever from the rental of the property. The
first $100,000 is paid at the end of the first year.
Required
Using a required rate of return of 12% p.a., rank the order in which you would pay for the property
from cheapest to most expensive (costliest), and provide the PV of each option.
a. 1000000
b. 250,000+250,000
(
)
1− (1+0.12 )−4
=1009337
0.12
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c. 225,000
(
)
1−( 1+0.12 )−6
=925066
0.12
(
(
0.12
1− 1+
2
d. 100,000+100,000
0.12
2
−14
)
)
=1029498
e. 250,000 ( 1+ 0.12 )−5 +1250000 ( 1+ 0.12 )−10 =969893
f.
20000+
100,000
=853333
0.12
Order: f,c,e,a,b,d
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