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Queen's University

Commerce

COMM 121

Kory Salli

Fall

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Finance Midterm Exam Review
Shannon Bailey
Oct 2013
Chapter 1 / Lecture 1 & 2
Finance – the study of how and under what terms savings (money) is allocated
between lenders and borrower
Capital budgeting (capital expenditure) – the process of making and managing
expenditures on long lived assets
Capital structure – represents the proportions of the firm’s financing from current
and long term debt and equity (think of the firm like a pie, composed of debt and
equity)
Creditors – the persons or institutions that buy debt from the firm
Shareholders – the holders of equity shares
Value of the firm = debt + equity
-the shareholders’ claim on firm value at the end of the period is the amount that
remains after the debtholders are paid – they get nothing if the firm’s value is equal
to or less than the amount promised to debtholders, or they get the residual of the
firm’s value over the amount promised to debtholders if the firm’s value is greater
than the amount promised to debtholders
-debt and equity are contingent claims on the total firm value
Arbitrage – exploiting price differences to earn riskless profit. There must be an
absence of arbitrage – as soon as different interest rates are offered for essentially
the same risk free loans, arbitrageurs will take advantage of the situation by
borrowing at the low rate and lending at the high rate. The gap between both rates
will be closed quickly. i.e. Seinfeld video in class – travelling across state border to
get more money for beer cans
Sole proprietorship – a business owned by one person
-cheapest to own, no corporate income taxes, unlimited liability, the life extends
over the length of the sole proprietor, equity money limited to proprietor’s personal
wealth
Partnerships:
General partnership – business in which any two or more partners agree to
provide some fraction of the work and cash to share the profits and losses. Each
partner liable for debts
Limited partnership – permit the liability of some of the partners to be
limited to the amount of cash each has contributed to the partnership.
-partnerships are inexpensive & easy to form, have life the length of any general
partner, taxed as personal income, difficult to raise large amounts of cash
Corporation – a business that is a distinct legal entity that can issue stocks, does not
hold any shareholder personally liable, has a perpetual life, and has corporately
taxed income
Agency costs – the costs of resolving the conflicts of interest between managers and
shareholders
Direct agency costs – costs of things like job perks (corporate jet), monitoring – you
are spending $$ Indirect agency costs – costs of a missed opportunity i.e. management buys the CEO
an expensive painting, missing the opportunity of a profitable investment
-managerial goals are different from those as shareholders – the principal hires the
agent (management) to represent his interest, but agents have a tendency to be
motivated by their expenses (like company cars, company dinners etc) which
definitely don’t maximize shareholder wealth
-shareholder wealth maximization is considered the most appropriate goal to guide
agents (NOT accounting profit maximization, since it changes with depreciation and
ignores timing)
-shareholders (owners) don’t necessarily control managers; depends on the costs of
monitoring management, the costs of implementing control devices, and the
benefits of control
How can you address the conflict of interest?
a) Compensation plans – i.e. stock options
b) Have a board of directors – chosen by shareholders, choose the management
team
c) Market discipline – i.e. lay-off, hostile takeover
Financial Institutions – facilitate flows of funds from savers to borrowers i.e.
banks, insurance companies, etc.
Financial Markets – markets where you can trade financial instruments (or
claims/securities)
- short-term debt securities are bought and sold in money markets
- long-term debt and shares of stock are sold in capital markets
Primary markets – refer to the original sale of securities by governments and
corporations (i.e. an IPO)
Secondary markets – markets where these securities are bought and sold after the
original sale, either in an exchange or over the counter in a dealer market
Foreign exchange market – the market where one country’s currency is traded for
another
Direct financing involves financial intermediaries, whereas indirect financing does
not
2 Major Categories of Financial Securities
Debt Instruments Equity Instruments
Commerical Paper Common stock
T-bills and notes Preferred stock
Mortgage loans
Bonds
Chapter 4/Lecture 2
Financial intermediaries – institutions that match borrowers and lenders
(traders)
Market clearing – the total amount of people who wish to lend to the market must
equal the total amount of people that wish to borrow from the market. If lenders
wish to lend more than the borrowers wish to borrow, the interest rate is too high, and vice versa. The interest rate that clears the market is the equilibrium rate of
interest.
Investment Rule – Basic Principle – an investment must be at least as desirable as
the opportunities available in the financial markets (i.e. you won’t take on an
investment whose return is 5% if the interest rate in the markets is 7%)
A Competitive market has three qualities:
1) trading is costless
2) information about borrowing and lending opportunities is readily available
to all market participants
3) there are many traders, and no individual can move market prices (price
takers)
Example 1. A person has an income of $50 000 this year and $60 000 next year. The
interest rate r = 10%. The figure shows all possible consumption opportunities open
to the person through borrowing and lending
Point A represents consuming nothing this year (lending $50,000), and everything
(second year income & proceeds from the loan) next year:
A = 60,000 + 50,000 (1 + .10)
Point B represents spending everything this year, including taking out a loan to
spend next year’s income:
B = 50,000 + 60,000/1.10
Point C represents spending $40,000 of this year’s income this year and saving
$10,000
-next year you would be able to spend $60,000 + 10,000(1.10)
The line has a slope of –(1+r), so that for each additional dollar spent today, (1+r)
less dollars can be spent next year Example 2. A person has income of 50k this year and 60k next year when the
interest rate r = 10%. The person has the chance to undertake an investment that
will require a 30k outlay of cash and will return 40k to the investor next year
At point B, the person has decided to undertake the investment decision, where the
person can consume 20k (50,000-30,000) this year and 100k (60,000+40,000) next
year. B is on the new line because there are new possibilities available with the
investment. The lines are parallel since the interest rate is constant
The total amount available to consume today without the investment is:
=$50,000 + $60,000/1.1 = $104,545
The total amount available to consume today with the investment is:
=$50,000 - $30,000 + ($60,000+$40,000)/(1+.01)
=$20,000 + $100,000/1.10 = $110,909
The difference between these amounts, $110,909-$104,545 = $6364 = the Net
Present Value (NPV)
It can also be calculated by converting all consumption values to the present, on a
standalone basis from the investment itself:
-$30,000 + $40,000/1.1 = $6364
-if the NPV is positive, the investment is worth taking on
Fisher Separation theorem – all investors will want to accept or reject the same
investment projects by using the NPV rule, regardless of their personal preferences,
-same for shareholder’s and the firm’s NPV decisions
-so investment decision making is separated from the owners and handled by the
managers -an individual’s preference for consumption will not impact an NPV decision
Chapter 5 / Lectures 3 & 4
Present Value of Investment = PV = C1
1 + r
where C 1s the cash flow at date 1 and r is the interest rate
Net present value (NPV) – the value of the investment after stating all the benefits
and all the costs as of date 0
Compounding – the process of leaving money in the capital market and lending it
for another year
-compounding may not make a big difference in the short run, but can make a huge
difference over a long period of time
-involves interest on interest (i.e. r , exponential growth) [versus simple interest
over two years, 2 x r]
Future value of an investment = FV = C x (0 + r) T
Where C i0 the cash to be invested at date 0, r is the interest rate, and T is the
number of periods over which the cash is invested
Discounting – the process of calculating the present value of a future cash flow – is
the opposite of compounding
Present value factor – the factor used to calculate the present value of a future cash
T
flow (the 1/(1+r) part)
Compounding an investment m times over one year provides end of year wealth of:
m
C o1 + r/m)
-where r is the stated annual interest rate (or annual percentage rate)
Annual percentage rate (APR) – the stated or quoted annual rate that gnored the
effects of compounding. It is computed by simply multiplying the periodic rate by
the number of periods in a year i.e. an investment pay 3% per quarter with
quarterly compounding. The APR will be 3 x 4 = 12% whereas the EAR will be
12.5509%
Effective annual interest rate (EAR) – the annual rate of return. Due to
compounding, the EAR will be greater than the stated rate
EAR = (1 + r/m) – 1
i.e. if the stated annual rate of interest, 8%, is compounded quarterly, what is the
EAR?
EAR = (1 + .08/4) – 1 = 0.0824 = 8.24%
Future Value with Compounding = FV = C (1 + r/m) mT
0
-where m is the number of times per year the investment is compounded, and T is
the number of years
r T
Continuous Compounding Present Value = C x e 0
-remember than e ln(= x
-if looking to solve for T, you made need to take the ln of both sides of an equation Perpetuity – a constant stream of cash flows without end i.e. consols
PV perpetuityC
r
i.e. consider a perpetuity paying $100 a year. If the interest rate = 0.08, what is the
value of the consol?
PV = 100/0.08 = $1250
Growing perpetuity – a constant, growing stream of cash flows that will grow
indefinitely
PV growing perpetuityC ,
r – g
-note that the numerator is the cash flow one period hence, not at date zero
-the interest rate must be greater than the growth rate, otherwise the denominator
gets infinitesimally small and the PV grows infinitely large; the PV will be undefined
when r is less than g
-assumes a regular and discrete pattern of cash flow
Annuity – a level stream of regular payments that lasts for a fixed number of
periods i.e. leases, mortgages, pension plans
Present Value of an annuity = PV = C [ 1 – 1 ]
r (1 + r)
-where C is the payment at date 1
T
(the FV would be the PV of an annuity times (1 + r)
i.e. a lady wins the lottery that pays $50k a year from now each year for 20 years. If
the interest rate is 8%, what is the true value of the lottery?
PV = 50000/0.08 (1 – (1/(1.08) ))20
PV = $490 905
Annuity factor – the term we used to compute the value of the stream of level
payments, denoted as A Tr
A = [ 1 – 1 ]
r T
r r(1 + r)
Mortgages – a common example of an annuity with monthly payments. Keep in
mind that although payments are monthly, mortgage rates are typically quotes with
semiannual compounding. You must convert the stated semi-annual rate to the EAR,
and then to the effective monthly rate.
i.e. a bank is offering a $100 000 25 year mortgage at a stated rate of 6%. What is the
monthly mortgage payment?
2
EAR = (1 + 0.06/2) - 1
EAR = 6.09%
Effective monthly rate = EMR = (EAR + 1) 1/m – 1
1/12
= (1.0609) – 1
= 0.49% PV = $100,000 = C [ 1 – 1 ] = C [1 - 1 ]
r (1 + r) .0049 (1.0049) 300
= $636.99
*note that T = 300 payments come from 25 years x 12 payments per year
Delayed annuities – if an annuity begins on a date many periods into the future
(say, date n), you must calculate the annuity at date n – 1 and then discount the
present value at date n – 1 to date 0 using the simple present value formula
Annuity due – if the annuity begins at date zero, you can calculate the present value
by either using the same formula and then compounding it for one year, or by
calculating the value of the annuity for T – 1 years, and adding today’s payment to
that value without any discounting whatsoever
i.e. using the same example as before, the lady receives the lottery of $50 000
a year for 20 years, but is given the first payment immediately. The present value is:
19
$50 000 + $50 000 x A 0.08
payment at date 0 19 – year annuity (not 20!)
it could also be calculated as follows:
20
$50 000 x A 0.08= $490 905 as a 20 year annuity beginning at date 1
$490 905(1.08) = $530 177 compounded forward by one year
Infrequent annuities – determine the interest rate over the period the annuity is
payable
i.e. An annuity is $450 payable once every two years, over the next 20 years. The
first payment occurs at date 2, two years from today. The annual interest rate is 6%.
Determine the interest rate over a two year period:
= (1.06 x 1.06) – 1 = 12.36%
Now we want the value of an annuity over 10 periods, with an r = .1236
= $450/.1236 [1 - 1 ] = $2,505.57
(1.1236) 10
Equating the present values of two annuities
i.e. Two parents are saving for the university education of their baby. They estimate
school will cost $30k per year when she enters uni in 18 years. The annual return on
their investment account will be 14%. How much money should they deposit in
their bank each year so that they can withdraw tuition money each year beginning
on her 18 birthday. They will make equal deposits on each of her first 17 birthdays,
but no deposit at date 0.
1. Calculate the present value of the four years at university at date 17.
PV 17= $30000/.14 [1 - 1 ] = $87,411
(1.14) 4
2. Calculate the present value of the four years at university as of date 0
PV 0 87,411 = $9,422.91
(1.14) 17
3. Calculate an annual deposit that will yield a present value of all the the deposits of
$9,422.91 9,422.91 = C /.14 [1 - 1 ]
(1.14)17
C = $1478.59
Growing Annuity – a finite number of growing cash flows
PV growing annuity ( )
Chapter 6 145-151 / Lecture 5
Bond – a certificate showing that a borrower owes a specified sum. In order to
repay the money, the borrower makes interest and principal payments on
designated dates
- less than one year – Bills or papers i.e. treasury bills, commercial papers
- 1 year < maturity < 10 years – Notes
- Maturity > 10 years – Bonds
Treasury Bills – short term government debt obligations which mature within a
year. They are ALWAYS issued at a discount and mature at face value. They are
generally regarded as risk free
Price of a T-bill =
Where BEY = bond equivalent yield = x
Where P = market price of the t-bill, F = face value of the T-bill, and n = number of
days until maturity
i.e. What is the price of a $1 000 000 Canadian T-bill with 80 days to maturity and a
BEY of 4.5%?
Price = 1000000/(1.045(80/365)) = $990 233.33
Pure discount bonds/zero-coupon bonds – a bond that promises to make a single
payment at a fixed future date. The holder receives no cash payments until maturity.
Issued at a discount and matures at par/face value. Has no reinvestment rate risk
(since no coupons to be reinvested)
Maturity date – the date when the issuer of the bond makes the last payment
Face value – the payment at maturity
Value/Price of a zero-coupon bond = P = F ,
(1 + r)T
where F is the face value that is paid in T years
i.e. What is the market price of a $50000 zero coupon bond with 25 years to
maturity that is currently yielding 6%?
PZCB = = $11 650
Coupons – cash payments offered by bonds at regular times before maturity Level coupon bond – a bond that pays a coupon annually (or semi-annually) until
maturity when the face value is paid
Value of a level-coupon bond = PV = +
-in the above equation, the first term is the PV of the annuity of all the coupon
payments, and the second term is the PV of the lump sum face value payment
i.e. What is the market price of a 10 year, $1000 bond with a 5% annual coupon if
the bond’s YTM is 6%?
Coupon = .05 x 1000 = $50
Price = + = $926.39
For semi-annual coupons:
- Size of the coupon payment – divide by 2
- Number of periods – multiply by 2
- YTM – divide by 2
i.e. Suppose you want to value a five-year, $1000 bond with a 4% coupon in semi-
annual payments with a YTM of 6%?
Coupon = .04/2 = .02 x 1000 = $20
YTM = .06 / 2 = .03
Five years 10 years
Price = +

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