Flashcards in Stock and Bond Valuation Deck (54):
What is the time value of money (TVM)?
The concept that a dollar received in the present is not worth the same as a dollar received in the future; future amounts must include a premium to be equal in value
What are the two different kinds of TVM problems?
Lump sums (paid all at once) and annuities (paid periodically)
What are two different kinds of annuities?
(1) ordinary annuities (annuities in arrears) -- paid at the end of a period
(2) annuities due (annuities in advance) -- paid at the beginning of a period
How is the future value (FV) of an amount calculated?
The present value (PV) of the amount is multiplied as if it were earning interest until the point in the future: FV = PV x (1+r)^n
Thus, if the interest rate (also called the "discount rate") is deemed to be 10%, then the FV of $100 for two years in the future would be $100 x (1.10)^2 = $121 -- but these problems tend to be much more complicated, and the CPA exam usually provides the factors you will need to multiply or divide the amounts by
How is the PV of an amount calculated?
It is the exact opposite as finding the FV -- the FV amount is divided by the interest rate (discount rate) to arrive at the PV: PV = FV / (1+r)^n
Thus, the PV of $121 received two years in the future, with a 10% discount rate, is $121 / (1.10)^2 = $121 / 1.21 = $100
How are FV or PV factors normally determined?
Not by formulas -- there are tables that list the PV or FV of $1 at given interest rates and given durations of time
On the CPA exam, though, usually the test will provide a few factors and require you to choose which one applies to the problem
How do PV and FV interest factors relate to each other?
Future value interest factors (FVIFs) and present value interest factors (PVIFs) are reciprocals -- for any given discount rate and duration of time, FVIF x PVIF = 1
How do annuities complicate TVM problems?
Since they involve a number of payments in the future, their calculation is more complicated, but it can generally be accomplished through the factors provided on the test questions -- knowing the formulas is helpful but not necessary
What are the formulas for PV and FV of annuities?
FV = [(1+r)^n - 1] / r
PV = [1 - (1+r)^(-n)] / r
What is the most important thing to remember for TVM problems involving annuities?
Keeping straight the exact timing of payments, so that the proper interest factor (PVIF or FVIF) is correctly selected and not off by one time period
Do all TVM problems involve yearly compounding periods?
No, some can involve interest paid every six months, every quarter, every month, or some other period
In problems like these, the interest rate must be proportionately reduced (e.g. divided by 12 if payments are made monthly) and the number of compounding periods ("n" in the formulas) must be increased accordingly (e.g. multipled by 12 if payments are made monthly) -- otherwise the calculation is exactly the same
For a bond, what is the par value, maturity date, and coupon rate?
(1) par value = face amount of bond (usually $1,000)
(2) maturity date = date at which the principal of the bond (its par value) is paid back to the bondholder
(3) coupon rate = interest rate; determines amount of periodic interest payments to the bondholder
For a bond, what is the difference between a new issue and an outstanding issue?
Right after it is issued (approximately two weeks), a bond is called a new issue; otherwise it is termed an outstanding issue, or a seasoned issue
What is the general model for valuating a bond?
The PV of all its future payments
Bond value = PV of principal + PV of coupon payments
What are bond discounts and premiums?
Given that bond coupon rates can differ from the prevailing market interest rate, different bonds can sell on the market at a price higher than their face value or lower than their face value
-If market price > face value, it sells at a premium
-If market price < face value, it sells at a discount
What is the difference between the coupon rate and the effective interest rate?
Coupon rate = rate at which actual interest payments are made
Effective rate = the market rate when the bond was obtained -- basically, the true interest rate of the bond after the discount or premium is taken into account (and other factors, e.g. risk premiums)
How is the effective interest rate relevant when valuating bonds?
Effective rate determines the discount rate at which PV is calculated
The coupon rate determines the amount of periodic interest payments which will then be discounted to PV
How do you calculate a return on investment for a bond?
These two things must be added:
(1) the total interest earned to date
(2) the capital gain or loss on the bond -- i.e. its PV compared to the amount initially paid for it (e.g. if it was initially purchased at a discount, then it may have increased in value, which is a capital gain)
(1) + (2) will be the total return, and the total return divided by the initial price paid for the bond will be the return on investment
What is a bond's yield to maturity (YTM)?
The rate of return for a bond if it is held to maturity
Assumes that periodic interest payments will be reinvested at the same rate
What is another way to understand yield to maturity (YTM)?
It is the discount rate by which the sum of all future cash flows for the bond (interest and principal), when discounted to PV, equals the amount actually paid for the bond
In this sense it is just like the effective interest rate
How are YTM problems typically solved?
Often by trial and error -- using an estimated discount rate to discount the total future payments back to PV, and altering the discount rate until the PV = the actual payment made
There are also bond yield tables which can give approximate YTMs
When would a bond issuer want to call its bonds before their maturity date?
If the prevailing market interest rates are lower than the coupon rates, then the bond issuer may want to call the bonds and reissue other bonds at a lower coupon rate
This can only occur if the bonds are callable, i.e. if the bond issuer has the right to call the bonds in the first place
What is a bond's yield to call (YTC)?
The same as YTM, except that the reference point is not the bond's maturity date, but the bond's call date
YTC is more significant for callable bonds than YTM
If a bond issuer can call a bond on different dates (rather than the maturity date, which is singular), how is the YTC calculated?
The YTC is ordinarily calculated using the earliest available call date
How do changes in market interest rates affect the prices of bonds with different maturity dates?
A change in market interest rates more powerfully affects the price of a longer-duration bond than for a shorter-duration one
Increase in market interest rates --> decrease in bond price, since the bonds would then be less valuable than other available interest rates
What are the general rights implicit in common stock?
(1) right to assets upon liquidation
(2) right to receive dividends
What is the difference between a realized and an unrealized capital gain or loss?
Realized = occurs when the stock is sold
Unrealized = occurs before the stock is sold
Capital gain/loss = difference between price when sold and price when initially purchased
What is the total return for a stock?
The sum of dividends received and the stock's capital gain or loss
How does stock valuation differ from bond valuation?
In both, the PV of all future cash flows must be determined
But stocks have no maturity date, and thus have a potentially infinite stream of cash flows
How is a stock's value determined if the stockholder intends to hold it indefinitely and there is no prospect of dissolution?
The PV of all future dividend payments
This would thus be a PV calculation for an infinite future cash flow stream
How is a stock's value determined if the stockholder intends to resell it?
The valuation is still the PV of an infinite stream of future cash flows (so long as the company's end does not loom near), and this value can change as time progresses
This is because when the stock changes hands, at that point it still has value for its future cash flows, and so at any point the infinite future cash flows (discounted to PV) are the relevant consideration in valuating the stock
What is a stock's growth rate?
The rate at which the dividends of the stock increases -- thus a stock with zero growth has constant dividends
How is the PV of a stock with a constant growth rate calculated?
Using the Gordon model (named after Myron Gordon):
PV = d / (k-g)
d = the dividend payment one year (or other period) in the FUTURE
k = discount rate
g = growth rate
How is the PV of a stock with zero growth calculated?
PV = d / k
d can be the dividends received in any year, since by definition those amounts do not change from year to year
How is the PV of a stock with uneven growth calculated?
Any stock presented with uneven growth will have specific amounts of growth for a number of years and then a growth that is assigned to all the remaining years unto infinity
Thus the normal lump-sum PV formulas will apply to all the years where the specific growth rate is known, and then the Gordon model will apply to the final available year where a growth rate is assumed to be constant from then on -- this final year must be discounted twice: once to arrive at the value of all future dividends at that date, and another to take that value and discount it to its PV
What is an example for calculating the PV of a stock with uneven growth?
A company pays year-end dividends of $5 in year 1, and is expected to have 2% growth in year 2, 3% growth in year 3, and 4% growth in year 4 and onward. The discount rate (k) is 8%.
dividend for year 2 = $5 x 1.02 = $5.10
yr 3 = $5.10 x 1.03 = $5.25
yr 4 = $5.25 x 1.04 = $5.46
PV of year 1 dividend = $5 x 0.9091 = $4.55
yr 2 = $5.10 x 0.8264 = $4.21
yr 3 = $5.25 x 0.7513 = $3.94
value of remaining dividends at end of year 3 = (yr 4 dividend) / (k-g) = $5.46 / (8% - 4%) = $136.50
-PV of this amount = $136.50 x .7513 = $102.55
value of stock = PV at year 0 = PV of all future dividends = $4.55 + $4.21 + $3.94 + $102.55 = $115.25
In matters of uncertainty, how is the expected rate of return for a stock calculated?
The rate of return can be established for different scenarios (e.g. company X will provide a return of only 3% if the economy is in a recession), and the different scenarios can be assigned different probabilities (e.g. there is a 25% chance that the economy will be in a recession)
The expected rate of return is the weighted average of the return for all possible scenarios multiplied by their respective probabilities
What is a probability distribution?
A listing of all possible events for an investment and the probability for each one
What are the two different kinds of risk for stocks?
(1) company-specific risk = risk that the particular company will fail or worsen
(2) market risk = risk due to changes in the whole stock market (e.g. a change in interest rates)
What is diversifiable risk?
Risk that can be avoided through diversifying one's portfolio, i.e. not having all your eggs in one basket, but investing in many different stocks
By definition, company-specific risk is diversifiable (i.e. nonsystematic), but market risk is not -- and is thus called systematic risk
How is a stock's risk generally measured?
After mapping out the expected rate of return with a probability distribution, the stock's risk is the volatility of that distribution -- specifically, a higher standard deviation (σ) in the distribution signifies higher risk
How is a stock's volatility with reference to the rest of the market measured?
With a beta coefficient: β
If β = 1.0 for a stock, then it moves perfectly with the rest of the market; a 7% increase in the market would be accompanied by a 7% increase in that particular stock
If β < 1.0, then the stock moves less than the rest of the market, and is thus less volatile
If β > 1.0, then the stock moves more than the rest of the market, and is thus more volatile
How does the beta coefficient (β) relate to the measurement of a portfolio's risk?
The portfolio's β is the weighted average of the β for each of the individual stocks in the portfolio
This measures the volatility of the portfolio in relation to the market overall, and thus measures the riskiness of the portfolio
What is the correlation coefficient (r) for various stocks?
r measures the way in which two stocks can move in relation to one another
They can have:
-a perfect positive correlation (+1.0), so that they move the same direction to the same degree
-a perfect negative correlation (-1.0), so that they move the opposite direction to the same degree,
-a correlation of 0, so that they do not move in relation to each other at all
-any other correlation between these amounts
What is the correlation coefficient (r) for most stocks?
Most have some positive coefficient between 0 and +1.0, i.e. a partial positive correlation
How does the correlation coefficient (r) relate to diversification?
Market risk is not lessened at all if a stockholder acquires stocks whose r = +1.0 in his portfolio, since they will act as a joint unit however they behave -- and so market risk cannot be diversified unless the correlation is less than +1.0
What is the capital asset pricing model (CAPM)?
A model that calculates the expected return of a stock by assuming that investors should be compensated for their investment in two ways:
(1) the time value of money -- investors should be paid for the fact that they are giving money to a corporation
(2) the risk premium -- investors should be compensated for the fact that they are placing their money in a riskier enterprise than risk-free ones (i.e. gov't bonds)
The CAPM gives a required rate of return, i.e. how much an average investor should expect to gain on the investment in order to see it as worthwhile
What is the CAPM formula?
Ra = Rf + β (Rm - Rf)
Ra = required rate of return on the asset (stock)
Rf = risk-free rate (i.e. interest rate for gov't bonds)
β = beta coefficient; measure of volatility
Rm = market rate of return
How is the CAPM formula structured?
The first part of the sum (Rf) refers to how investors are compensated for the time value of money, since, if nothing else, they could always invest their money to get that risk-free rate of return
The second part of the sum [β (Rm - Rf)] refers to how investors are compensated for the risk they undertake: they should be paid for a risk premium by investing in the market rather than risk-free bonds (Rm - Rf), and this premium is multiplied by the volatility of the stock (β)
Which government bonds typically provide the risk-free rate of return (Rf)?
Long-term U.S. Treasury bonds
What is a security market line (SML)?
A graphical representation of the CAPM:
-x-axis = β
-y-axis = required return
-slope = market risk premium (Rm - Rf)
What does a steeper security market line (SML) say about investors' risk aversion?
A steeper SML means that it has a higher slope and thus a higher market risk premium which investors require for their investments -- investors would thus be MORE averse to risk, since they would require more value (a higher premium) to compensate them for it
How does a security market line (SML) help investors select stocks to invest in?
Stocks with given levels of riskiness (β) and expected returns can be plotted on the graph
If they are above the SML, then their expected return is higher than the minimum required by the investor for that given level of risk, so they would be acceptable
-if below, then the expected return would not be worth the risk