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RSM332H1 Study Guide - Midterm Guide: General Motors Ev1, Net Present Value, Spot Contract

Rotman Commerce
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Annuity: cash flow starts at time 1 and lasts for T periods; Annuity factor: ; Constant annuity: ; Growing annuity at g: ; FV of ordinary annuity: ;
FV of annuity due:
Sum of geometric series (a, a2, a3, …) with lal<1: S=a+a2+a3+…+an, -aS=-a2-a3-…-an+1; then (1-a)S=a-an+1 and S=(a-an+1)/(1-a)
Mortgage loan: In Canada, quoted as annualized semi-annual rate, compounding monthly (monthly payment). Principal payment starts as
smaller portion of total payment and grows over time: “Outstanding Principal (just after a payment is made) = PV of all remaining payments”
Perpetuity: cash flow starts at t=1 and last forever; Constant perpetuity: ; Growing perpetuity at g: for r>g
Sum of geometric series (1, a, a2, a3, …) with lal<1: S=1+a+a2+a3+…, -aS=-a-a2-a3-…; then (1-a)S=1 and S=1/(1-a)
Quoted rates vs. Effective rates: Continuous compounding: , EAR=er-1
Bond: Pure discount bond: YTM = spot rate; Bond traded at par (at face value): YTM = coupon rate; YTM=r=discount rate=required ROR
; be careful to semi-annual coupon bonds
Coupon-YTM: P0 > F premium coupon rate > r; P0 = F par coupon rate = r; P0 < F discount coupon rate < r
, YTM (geometric mean) is the constant/average r that discounts bond cash flow to market price; HPR=(coupon payments + price when sell @ t
– P0)/P0;
default risk or liquid (short term, high rated) or seniority, required YTM; positive/negative covenants are things firms agree to do/not to do
(supply periodic financial statements, maintain certain ratios; restricts the amount of debt the firm can take on, prevents the frim from
acquiring/disposing of assets); investment grade (AAA, AA, A, BBB), junk/high yield (BB, B, CCC, CC, D, suspended); 6 factors in rating process:
core profitability, asset quality, strategy & management strength, balance sheet strength, business strength, miscellaneous issues; option
favors lender, risk premium
Linear interpolation: spot rates in a linear fashion between 2 points and estimate the uncertain yield from that
Term structure of r - yield curve: upward sloping (common), downward sloping, flat, humped
Expectations theory: long-term r is average of expected future short-term r [forward rate = expected spot rate, ]
Liquidity preference theory: investors must be paid a liquidity premium to hold less liquid, long-term debt [forward rate = expected spot rate +
liquidity premium, forward rate > expected spot rate]
Law of one price: fundamental economic argument that 2 assets offering same payoffs and probabilities should have the same price (violation
creates arbitrage opportunity, no arbitrage: same risks have same expected return)
Options and features: call feature (allows issuer to redeem/pay off bond prior to maturity usually at premium), retractable bonds (allows older
to sell bonds back to issuer b4 maturity), extendible bonds (allows holder to extend maturity of bond), convertible bonds (can be converted
into common stock at pre-determined conversion price), sinking funds (funds set aside by issuer to ensure firm is able to redeem bond at
maturity), collateralized bonds (have physical assets pledged against interest payments in event of default)
Interest rate (r) is different for every period; generally we expect longer term r to be higher than short term b/c higher risk associated with
lending money long term, hence lender requires higher returns.
Pricing regular bond using pure discount bonds:
Suppose: discount bond with F=1, t=maturity, . If a series of pure discount bonds from t=1 to t=5, each with F=1, we can price a coupon bond
with maturity=5: P0=C*DF1+C*DF2+C*DF3+C*DF4+(C+F)*DF5
Forward rate vs. Spot rate: or ; spot rate is annualized rate for a particular holding period today, forward rate is the current estimate of what
future spot rates will be
Duration and modified duration: measure the sensitivity of bond price w.r.t changes in interest rate (yield curve)
; ;
Stock valuation: Stock price = PV of all future cash flows = or where r = expected return on stock = risk free r + risk premium of stock; Return
of stock > return of bond since risk of stock > risk of bond
Gordon model: Zero growth [PV of perpetuity = ] where P/E=1/r; Constant growth [PV of growing perpetuity = ]; Differential growth [PV of N-
yr growing annuity @ g1 = , PLUS discounted value of growing perpetuity @ g2 starts in yr N+1 = where g2<g1]; Same g&r, dividend payout
ratio, then same P/E ratio; where =Dt/Et is dividend-payout ratio; If 2 firms both have constant earnings per share forever, and belong to the
same risk class (same r), they should have the same P/E, not same P
Expected dividend/earnings growth rate=g=b*ROE, b=earnings retention/plowback ratio=1-, ROE=return on (common) equity; EPS=E1
Earnings next yr = earnings this yr + retained earnings * return on retained earnings (divide both side by “earnings this yr” to get g-formula)
NPVGO=P0-E1/r=E[D1]/(r-g)-E1/r, P0 includes both existing and growth opportunity, E1/r is existing and NPVGO is growth opportunity
P/E ratio=price/EPS=P0/E1=(E1/r+NPVGO)/E1=1/r+NPVGO/E1 where P/E ratio is multiple; P0=estimated EPS1 * justified P/E ratio=EPS1*(P0/E1)
NPV of an investment is the PV of the expected cash flows, less the cost of the investment
Reasons for higher leading P/E ratio: lower cost of equity capital due to lower risk (lower r); higher growth rate; higher dividend payout ratio;
adoption of an accounting standard that leads to a lower accounting earnings; investors are overly optimistic about the future of the company
EX: D0=3, g1=16% for 2-yr, g2=10% for 2-yr, g3=0 for rest, r=10%, =D4/r-g3=48.84528, P0==46.53421488
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