Arbitrage – same product different price Normal Market – no arbitrage opportunities
PV = 1000/(1+r) IF the price is not the same as that, arbitrage opportunity
No Arbitrage – If Security = Present Value AKA Price=PV
PV=CF0/(1+r)^n+CF1/(1+r)^n+……. (n=same as year| “today” means 0 years) Arbitrage = Security – CF0 - CF1-……..CF7 risk free
rate= (bond price/PV)-1
Arbitrage Portfolio – If a security has the same CF as the other securities in the portfolio, that security is equivalent to a portfolio or
combination of the other securities.
1
1
$800  $1400  $1100
2
Price of Risk – Calculate the PV for bond. 2
This is an example
Market return in Weak State = (800 – 1000) / 1000 = -20% Market return in Strong State = (1400 – 1000) / 1000 = 40% Expected
Return = ½ (-20%) + ½ (40%) = 10% Risk Premium = 10% - 4% = 6% The 4% is from the risk free rate
Public Corporate DEBT
Corporate Bonds – almost always pay semi-annually. 30 years or less in maturity. $1000 bond usually.
Registered Bond – Maintains a list of all holder. Coupon/principal payments only made to people on the list. Almost all bonds are
registered bonds.
Types of Public CD
Unsecured- in the event of bankruptcy, gives bondholders claim to asset which has not been pledged as collateral. Debentures and
notes are unsecured debt.
Secured- Specific assets are pledged as collateral. Asset-backed bonds and mortgage bonds are secured debt.
Tranches- Different classes of securities that compromise a single bond issue. Securities paid from same CF source.
Seniority- Claim assets not already securing other debt. Debentures contain clauses restricting the company from issuing a new debt
with equal or higher priority than existing debt. Subordinated Debentures.
Private Corporate DEBT
Has the advantage that it avoids the cost of registration but has the disadvantage of being illiquid. Term Loans: Term Loan, Syndicated
Bank Loan, Revolving Line of Credit.
Private Placement of Bonds- A bond issue that is sold to a small group of investors rather than the general public.
Bond Covenants – Restrictive clauses in a bond contract that limit the issuers from undercutting their ability to repay the bonds.
Examples: Restrict the ability of management to pay dividends. Restrict the level of further indebtedness. Specify that the issuer
must maintain a minimum amount of working capital.
Repayment Provisions – A bond issuer typically repays its bonds by making coupon and principal payments as specified in the bond
contract. However the issuer can: Repurchase a fraction of the outstanding bonds in the market (Sinking Fund Provision). Make a
tender offer for the entire issue. Exercise a call provision.
Call Provision – A call provision allows the issuer of the bond the right to retire all outstanding bonds on a specific date, for the call
price. The call price is generally set at or above, and expressed as a percentage of, the bonds face value.
A firm may choose to call a bond issue if rates fall. The issuer can lower its borrowing costs by exercising the call on the callable bond
and then immediately refinancing the issue at a lower rate. If rates rise after a bond is originally issued, there is no need to refinance.
Holders of the callable bonds understand that the issuer will exercise the call option only when the coupon rate of the bond exceeds
the prevailing market rate.
What happens to a bond that is callable at par on only specific date? On the call date: If the yield is less than the coupon, bond will
be called. If greater, than it wont be called.
When market yields are high relative to the bond coupon, investors anticipate that the
likelihood of exercising the call is low and the bond price is similar to an otherwise identical non-callable bond. When market yields
are low relative to the bond coupon, investors anticipate that the bond will likely be called, so its price is close to the price of a noncallable bond that matures on the call date.
Sinking Fund – A method of repaying a bond which a company makes regular payments into a fund administered by a trustee over
the life of the bond: These payments are then used to repurchase bonds. This allows the firm to retire some of the outstanding debt
without affecting the cash flows of the remaining bonds.
If the bonds are trading at a discount, the company will repurchase the bonds in the market. If the bonds are trading above face
value, the bonds are repurchased at par. Which bonds are repurchased is decided by a lottery.
Convertible Provision
Convertible Bond – A corporate bond with a provision that gives a bondholder an option to convert each bond owned into a fixed
number of shares of common stock.
Conversion Ratio – The number of shares received upon conversion of a convertible bond, usually stated per $1000 of face value.
Bond Valuation – If semi annual, divide coupon payment by 2 and Yield to maturity by 2. Multiply the amount of years by 2. YTM =
I/Y 1000=FV
YTM inversely related to bond price
Formula Sheet
PV = CF/(1+r)^n
BOND VALUATION: T1 BA11 + Calculator: (2nd)(CLRTVM) 1000(FV) 50(PMT) 10(N) 6(1/Y) (CPT) PV
𝐹𝑉
𝑷𝑽 =
(1 + 𝑌𝑇𝑀)𝑛
DETEREMINING YTM: TI BAII+ Calculator: (2nd) (CLRTVM) 30 (PMT) -1030 (PV) 1000 (FV) 40 (N) (CPT) (I/Y) = 2.87, then multiply by 2
to annualize
Calculate Yield to Call (YTC): IBM has just issued a callable (at par) five-year, 8% coupon bond with annual coupon payments. The
bond can be called at par in one year or anytime thereafter on a coupon payment date. It has a price of $103 per $100 face value.
What is the bond’s yield to maturity and yield to call?
Solution: Make a timeline and calculate YTM first(Year 5 = 108). (2nd) (CLRTVM) 8 (PMT) -103 (PV) 100 (FV) 5 (N) (CPT) (I/Y) = 7.26
103 =
108
(1+YTC ) Rearrange and solve for YTC.
…..
YTC: N = 1; PV = -1000; PMT = 60; FV = 1050; CPT I/Y = 11
P 
(1

FV
YTM n ) n
Zero Coupon Bonds
Zero Coupon Bonds YTM/Spot Rate = ((Face Value/Price)^1/n) -1
P  PV (Bond Cash Flows)

CPN
CPN


1  r1
(1  r2 ) 2

CPN  FV
(1  rn ) n
Post Money Valuation = Pre-money valuation + Amount Invested
Div3
Div1
Div2
P0 =
+
+
+ L
2
3
1
+
r
(1
+
r
)
(1
+
r
)
E
E
E
Dividend Discount Model
Constant Dividend Growth Model P0=
P0 
𝐷𝑖𝑣1
𝑟𝑐−𝑔
D3  P3
D1
D2
1.00
1.50
2.00  29.7143





 $25.31
1  re
(1  re ) 2
(1  re ) 3
1.11
1.112
1.113
where : P3 
D3 (1  g )
D4
2.00(1.04)


 $29.7143
re  g
re  g
0.11  0.04
A single shareholders, discounting the dividends the shareholder will receive:
P0 
P0  PV  Future Dividends per Share 
PV  Future Total Dividends and Repurchases 
Shares Outstanding 0
Total Payout Model
EPS, dividend, share price growth rate g = Re – D1 / P0
Enterprise Value  Market Value of Equity  Debt  Cash
V0  PV (Future Free Cash Flow of Firm)
P0 
V0  Cash 0  Debt 0
Shares Outstanding 0
2


Expected Return  E  R   R PR  R Var (R)  E  R  E  R   

PR   R  E  R  SD ( R ) 
2
R
Value of investment i
xi 
Total value of portfolio Portfolio Return RP  x1 R1  x2 R2 
Portfolio Weights
 xn Rn   i xi Ri
Var ( R)