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# THEORY OF FINANCE EXAM NOTES.docx

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University of Guelph

Economics

ECON 2560

Nancy Bower

Fall

Description

Chapter 1
Corporations are taxed twice
Chapter 5
• There are two types of interest money can earn
o Simple interest
Interest is earned only on the investment
o compound interest
Interest is earned on the value of money that is in the account at the
beginning of the period.
Interest earned on the investment from the previous period then has a
chance to earn interest on top of that
FV = Value today * (1 + r)^t
• E.g you invest $2000 today paying compound interest at the rate
of 8% per year. How much will the account be worth in 5 years?
o FV = 2000*(1+0.08)^5
o FV= 2938.66
PV = FV after t periods/(1 + r)^t
• E.G You have been offered 1 million dollars five years from now. If
the interest rate is expected to be 4% per year, how much is the
prize worth to you today in dollars?
• PV = 1 000 000/(1+0.04)^5
• PV = 821 927.11
Finding the interest rate
• 680.58 = 1000 / (1 + r)^5
• 680.58*(1+r)^5 = 1000
• 1+r^5 = 1000/680.58
• R^5 = 1.4693-1 =.4693 • R= 5√.4693
Future value of multiple cash flows
• You invest 1000 dollars today, 1200 dollars a year later and 1400
dollars the next year. If your bank offers you an 8% interest rate
what is the future value after 3 years
o FV= 1000*(1.08)+ 1200*(1.08)^2+ 1400*(1.08)^3
o FV= 4172
• Your car dealer offers you the option of paying 30000 today or
8000 now, 12 000 a year later and 12 000 a year after that. Which
is the better deal? At a discount rate of 8%
o 8000+ 12000/(1.08)+12000/(1.08)^2 = 29 399, take the
second option
o Level Cash Flows: perpetuities and annuities
Annuities
• Cash flows of equal amount every period for a limited number of
periods
o E.g loan payments for automobiles, periodic earnings from
the lottery
• Present value: The present value of t period annuity with cash flow
C and discount rate R is given by –
o PV of t-period annuity = C*(1/r – 1/r[1+r]^t)
o E.g you are purchasing a car. You are scheduled to make
3 annual installments of 12 000 per year with the first
payment one year from now. Given a rate of interest of 6%,
what is the price you are paying for the car?
o PV = 12 000 * (1/.06 – 1/.06(1.06)^3
o PV = 32 076.14
Perpetuities • Cash flows of equal amount every period for an unlimited number
of periods
o E.g property tax payments, preferred stocks
• Present value of perpetuity
o PV = C/R
o E.g in order to create an endowment that pays 150 000 per
year for ever how much needs to be set aside today if the
rate is 5%
o PV = 150 000/0.05
o PV= 3 000 000
o E.g If the first perpetuity payment wont be received until
four years from today, how much money needs to be set
aside today?
o PV = 3 000 000/(1.05)^3
o PV= 2 591 513
• Present value of a growing perpetuity
o PV of growing P = C/R – G
o PV of growing Annuity = C/r-g(1-[1+g/1+r]^t)
Inflation and the time value of money
• Inflation: Rate at which prices as a whole are increasing
• Nominal interest rate: Rate at which money invested grows
• Real interest rate: Rate at which the purchasing power of an
investment grows
o 1+real rate = 1+nominal rate/1+inflation rate
Effective Annual Interest rates
• Effective annual interest rate
o Interest rate that is annualized using compound interest
• Annual percentage rate o Interest rate that is annualized using simple interest
• If m is the number of compounding periods per year, then
o EAR= (1 + APR/m)^m – 1
• Summary of chapter 5
o Future value is the amount to which an investment will grow after earning interest
o The present value of a future cash payment is the amount you would have to
invest today to create that future cash payment
o You can calculate the interest or discount rate and time periods as well
o A level stream of payments which continue forever is called a perpetuity
o A level stream of payments for a limited number of years is an annuity
o You can use the FV and PV formulas to calculate their value
o You need to distinguish between real and nominal cash flows that are affected by
inflation
o Effective Annual Rates annualize using compound interest
Chapter 6
• Bonds and the bond market
Governments and corporations borrow money for the long time by issuing
securities called bonds
The interest payment paid to the bond hold is called the coupon
The payment at the maturity of the bond is called the face value, principal
or par value
The date on which the loan will be paid off is the maturity date
The coupon rate is the annual interest payment divided by the face value
of the bond
The interest rate or discount rate is the rate at which the cash flows from
the bond is discounted to determine its present value
o Interest rates and bond prices The price of a bond is the present value of its coupon payments plus the
price of a bond
• E.g calculate the current price of a 7.0% annual coupon bond, with
a $1000 face value which matures in 3 years. Assume a required
return of 5%
o 1000 * .07 = $70 in year 1 and $70 in year 2 then 70$ +
the price of the bond
70 + 70 + 70 + 1000 = 1210
When the coupon rate is equal to the required return the bond sells at
face value or par
When the coupon rate is higher than the required return, the bond sells
above face value (at a premium)
When the coupon rate is lower than the required return the bond sells
below face value (At a discount)
Yield to maturity = interest rate for which the present value of the bonds
payments equal the price
• E.g a 3-year, 8% annual coupon bond, with face value of 1000
sells for 1053.46
o PV = 80/(1+.08)^1 + 80/(1.08)^2+80+1000/(1.08)^3
Rate of return is the earnings per period per dollar invested
• You buy $1000 par, 3-year 8% annual coupon bond for 1053.46.
one year later you sell it for 1100
o Rate of return = coupon income + price change /
investment
o Rate of return = 80 + 46.54 / 1053.46
o Rate of return = 0.1201 or 12.01%
o The yield curve
Real return bond – the bonds with variable nominal coupon payments,
determined by a fixed real coupon payment and the inflation rate
Fisher effect – the nominal interest rate is determined by the real interest
rate and expected rate of inflation Expectations theory – an explanatory theory that shows why there are
different shapes of the yield curve
o Corporate bonds and the risk of default
Interest rate risk is the risk in bond prices due to fluctuations in interest
rates
Different bonds are affected differently by interest rate risks
• Longer term bonds get hit harder than shorter term bonds and
lower coupon rate bonds get hit harder than higher
• Default risk or credit risk is the risk that a bond issuer defaults on
its debts
• The default premium or credit spread is the difference between the
promised yield on a corporate bond and the promised yield on a
government of Canada bond given the same coupon and maturity
• The safety of a corporate bond can be judged from its bond rating
• Bond ratings are provided by companies like
o Dominion bond rating service (DBRS)
o Moody’s
o Standard and Poors
• Bonds are BBB and above are called investment grade bonds
• Bonds rated BB and below are called speculative grade, high
yield, or junk bonds
• Summary of Chapter 6
o Coupon rate is the bonds rate divided by its face value
o Current yield is the bonds coupon rate divided by its current price
o Yield to maturity measures the average return to an investor who purchases the
bond and holds it until maturity
o Bond prices and yield to maturity vary inversely
o Bond prices vary in response to interest rates. The risk of price change is called
interest rate risk Long term bonds have greater interest rate risks than short term bonds
o Investors use bond ratings to determine the risk of default on a bond
o The additional return that investors demand for bearing credit risk is called the
default premium
Chapter 7
• Common stock : ownership shares in a publicly held company
• Primary market: place where the sale of new stock first occurs
• Initial public offering: first offering of stock to the general public
• Seasoned issue: sale of new shares by a firm that has already been through its IPO
• Secondary market: market in which already issued securities are traded by investors
• P/E: price per share divided by earnings per share
• Dividend: periodic cash distribution from the firm to its investors
o Dividends represent that share of the firms profits that are redistributed
• Retained Earnings: Profits that are retained in the firm and reinvested in operations
• Liquidation value – net proceeds that would be realized by selling off the firms assets
and paying off its creditors
• Market value balance sheet: financial statement that uses market value of assets and
liabilities
• Expected return : the percentage yield that an investor forecasts from a specific
investment over a set period of time
o Expected return = Div1 / P0 + P1-P0/P0 or expected return = dividend yield +
capital gains yield
• Price and intrinsic value
o The dividend discount model: share value equals the present value of all
expected future dividends. If the discount rate is ‘r’ it can be written as
DDM = Div1/(1+r)^t + Div2/(1+r)^t+Div3/(1+r)^t
o Simplifying the dividend discount model
Zero Growth Case • If the dividend paid by the company is not expected to change
then the payment is treated as a perpetuity , the present value of
all dividends is then P0 = Div1/r
Constant Growth Case
• If the dividend paid by the stock is expected to grow at a constant
rate, then the cash flows are treated like perpetual flows with a
growth rate. In this case the PV of cash flows = Div1/r-g
Non-constant growth case
• Many companies grow at rapid or irregular rates for many years
before slowing down
o Before the growth settles down each dividend must be
calculated separately
o When the growth rate does settle down, we can find the
future stock price using the constant growth formula
o At the end, we have to find the present values of all the
dividends and the future stock price
o Growth stocks and income stocks
• The fraction of earnings retained by the firm is called the plowback
ratio
• The fraction of earnings a company pays out in dividends is called
the pay out ratio
• The growth rate for a company can be determined by multiplying
the return on equity by the plowback ratio
• G = ROE * Plowback ratio
Sustainable growth rate
• Steady rate at which a firm can grow
o G = Return on Equity * plowback ratio
Price earnings ratio
• Stock price / earnings per share
o Efficient market A market where prices reflect all available information
• Weak form efficiency
o A market where prices rapidly reflect all information
contained in the history of past prices and volumes
• Semi strong form efficiency
o A market where prices rapidly reflect all publicly available
information
• Strong form efficiency
o A market where prices reflect all information that could be
used to determine the real value of an asset
• Summary chapter 7
o Valuing a common stock
o PO = Div1/r
Chapter 11
• Measuring rates of return
o Percentage return = capital gain + dividend / initial share price
o Capital gain yield = capital gain/initial share price
o Dividend yield = dividend/initial share price
o 1 + real rate = 1 + nominal rate/1+inflation rate
• Investors receive a premium for risk
o Therefore, rate of return on any security = rate of return on t-bills + market risk
premium
• Measuring risk
o Volatility of returns is considered risk
Variance- the average value of squared deviations from the mean Standard deviation – the square root of the variance
o The risk-return trade off, T-bills have the lowest return and the lowest volatility.
Conversely common stocks have the highest return and the highest volatility
• Diversification and unique vs market risk
o Diversification reduces risk through…
spreading ones portfolio over many investments
Since stocks do not increase or decrease in value in exact harmony when
one stock is doing poorly the other is doing well
Reduction in risk of the portfolio also depends upon the correlation co-
efficient
• If you hold two stocks with a correlation coefficient that is less than
one you can reduce the amount of risk by holding them together
possible because of unique risk and market risk
Market risk vs Unique risk
• You cannot eliminate all risk from a portfolio by adding securities
• Typically once you get to 15 stocks adding more stocks does very
little to reduce the risk of a portfolio
• The risk that cannot be diversified away is called market risk
• For a reasonably well diversified portfolio only market risk matters
• Unique risk is minimized by diversifying a portfolio
• Market risks are macro risks
o E.g changes in interest rates, industrial production,
inflation
• Summary of chapter 11
o Standard deviation and variance are measures of risk
o Diversification reduces risk because stocks do not move in perfect contingency,
poor performance by one stock can be offset by good performance by the other o Correlation coefficient is a measure of how two variable move with respect to one
another
o Risk which can be eliminated with diversification is called unique risk
Chapter 12
o Is the sensitivity of a stocks return to the return on the market portfolio
Is a measure of risk
o There are two ways of measuring beta
Beta of stock j = Bj = cov(Rj,Rm)/µ^2m
Where COV(j,m)= covariance of the stocks return with the markets
return
µm= standard deviation of the market
o portfolio beta
the weighted average of the betas of individual assets; with the
weights being equal to the proportion of wealth invested in each
asset
the beta of a portfolio with two assets
st
• portfolio beta = (fraction of portfolio in asset 1 * beta of 1
asset) + (fraction of portfolio in asset 2 * beta of 2 asset)
o Capital Asset Pricing Model
The theory of the relationship between risk and return which
states that expected risk premium on any security equals its beta
times the market risk premium
According to the CAPM – E(Rj) = rf + Bj*(rm-rf)
Security Market Line
• Graph showing the relationship between the market risk of
the security and its expected return
• According to the CAPM expected rates of return for all
securities and portfolios fall on the SML Chapter 13
• WACC – Weighted Average Cost of Capital
o The weighted average of returns on debt and equity, with weights
depending on the relative market values of the two securities
o WACC = [D/V *(1-Tc)r debt]+[E/V *r equity]
o Three steps to calculating capital
1. Calculate the value of each security as a proportion of the
firms market value
2. Determine the required rate of return on each security
3. Calculate the weighted average of these required returns
E.g executive fruit has issued debt, preferred stock and common stock.
The market value of these securities are 4 mil, 6 mil and 2 mil. The
required returns are 6%, 12% and 18% respectively
WACC = 4/12(1-.35)(.06)+6/12(.12)+2/12(.18) = 12.3%
o When you can and cannot use the WACC
The WACC is the rate of return the firm must expect to earn on its
average risk investments in order to compensate its investors
• Thus WACC may be used to value assets that have the same risk
as the old ones
• Will support the same ratio of debt as the firm itself
o Issues with using the WACC
Changing the capital structure might affect the required returns
Increasing debt might increase the cost of equity
Changing the capital structure might affect beta
• Beta of the firm is the weighted average of the beta of its debt

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