Interest Rates and Bond Valuation

1
Interest Rates and Bond Valuation

• Chapter 7

2
Bond Features

• Bond - a loan made by investors to the issuer.
  In return for funds, the investors receive a
  legal claim on future cash flows of the borrower.
• Bond Features
• regular coupon payments
• payment of face/par/principal at maturity
• restrictions
• attached options
• Default - breach of the above mentioned
  contractual obligations exposes the issuer to
  legal action on behalf of the lenders
  (bondholders)

3
Basic Bond Terminology

• Coupon Rate Annual Coupon Pmt./Face
• Current Yield Annual Coupon Pmt./Price
• Yield-to-Maturity Implied discount rate setting
  the present value of coupons equal to price
• Default Risk Premium The extra yield required
  by investors to compensate for default risk
• Selling at a Premium - P gt Face Value
• Selling at a Discount - P lt Face Value
• Selling at Par - P Face Value
• Payment Frequency - in most cases semi-annually

4
Types of Traded Debt

• Money Market Debt (maturity lt 1 year)
• U.S. Treasury Bills Commercial Paper Bank CDs
• Capital Market Debt (maturity gt 1 year)
• U.S. Treasury Notes and Bonds Strips
  (Zero-coupon Bonds) Municipal Notes and Bonds
  Corporate Notes and Bonds Mortgages
  Mortgage-Backed Securities other Asset-Backed
  Securities
• Bond Markets
• Primary vs. secondary markets
• Direct placement vs. Publicly traded
• Exchanges vs. OTC
• Individual investors vs. Institutional Investors

5
Valuing Bonds

• GE has a AA-rated 3-year bond with a
  yield-to-maturity of 7 (APR with semi-annual
  compounding), and a coupon rate of 8 (with
  semi-annual payments). What is the price of the
  bond?
• Alternatively n 6 half-years PMT 40 FV
  1000I 3.5 --gt PV -1,026.64

6
Finding Yield-to-Maturity

• GE has a AA-rated 3-year bond selling for 950,
  and a coupon rate of 8 (with semi-annual
  payments). What is the yield-to-maturity of the
  bond?
• Note that yields are are derived from the pricing
  equation.

7
Bond Price Sensitivity to YTM(Both bonds have
10 Coupon Rates)
8
Bond Pricing Theorems

• 1. Bond prices and market interest rates move in
  opposite directions
• 2. When a bonds coupon rate is (greater
  than/equal to/less than) the YTM, the market
  value will sell at (a discount/par value/a
  premium)
• 3. Ceteris paribus, the price of a longer-term
  bond will change more (in percentage terms) than
  that of the shorter-term bond, for a given change
  in yields
• 4. Ceteris paribus, the price of a lower-coupon
  bond will change more (in percentage terms) than
  that of the higher-coupon bond, for a given ?y

9
The Bond Indenture

• Three-party contract between the issuer, the
  bondholders, and the trustee.
• Trustees are hired by the issuer to protect
  bondholders interests
• What do you think would happen if an issuer
  refused to hire a trustee?
• Included in the indenture
• total -amount of bonds issued
• payment arrangement
• collateral/seniority
• call provisions
• details of protective covenants

10
Term Structure of Rates

• Relationship between maturity and yields
• Characteristics
• almost always slopes upward
• short-term and long-term tend to move in same
  direction
• short-term rates are more volatile than long-term
  rates
• shape can be inverted, humped or very steep
• inverted yield curves signal weak future economy
• steep yield curves signal strong future economy

11
Components of the Yield Curve
12
The Yield Curve as Economic Predictor

• Estrella and Mishkin (1998) Predicting U.S.
  Recessions Financial Variables as Leading
  Indicators, Review of Economics and Statistics,
  45-61.
• Hypothesis
• the slope of the yield curve embeds the markets
  expectations of the future economy
• consistent with economic theory, a downward
  sloping yield curve forecasts recession due to
  ...
• lower real rates as economic expansion slows
• lower inflation premiums as deflationary
  pressures mount
• Using data from 1960-1995 EM conducted an
  analysis to forecast recession probability

13
Findings
14
Stock Valuation

• Chapter 8

15
Features of Common and Preferred Stock

• Common Stock
• voting rights proportional share of dividends
  proportional share of liquidation value
  preemptive rights
• Preferred Stock
• Preference over common stock - dividends
  liquidation dividend arrearages
  stated/liquidating value
• Stock Markets
• Primary vs. secondary markets
• Exchanges vs. OTC (Nasdaq)
• Individual Investors vs. Institutional Investors

16
Dividend Discount ModelsJohn Burr Williams
Fundamental Theory of Valuation

• Lets recall the stock return formula and do a
  little algebra

17
Stock Value is the present value of an infinite
stream of non-constant dividends
18
Dividends should be interpreted loosely as Cash
Flow to Equity Holders

• Some companies dont pay dividends, but they do
  repurchase shares
• These are cash flows to shareholders so they
  should be included in valuation models

19
Constant Growth DDM

• If dividends are expected to grow at a constant
  rate, g, then the Pricing Model simplifies to
• Example Suppose ACME just paid a 5 dividend.
  The dividends are projected to grow at 5 per
  year indefinitely. If the required return is 9,
  then P0 ?
• By the way, where does R come from?

20
Using the CGDDM to infer R

• Rearrange and solve for R
• Example SP 500 Dividend Yield 1.5. How much
  must the perpetual growth rate be in order to be
  consistent with 10 returns? 10 1.5 8.5

21
What is g?

• The growth rate, g, is the steady-state (that is,
  long-long-run) growth rate in dividends
• In the very long run g cannot grow faster than
  the economy as a whole. Why not?
• Reasonable Assumptions for g 5-7 g real GDP
  growth Inflation

22
Caveats to the CGDDM

• The growth rate must be less than R. Why?
• Model is useful only for mature firms with steady
  growth.
• Value is very sensitive in small changes in
  inputs.
• MOST STOCKS DO NOT PAY DIVIDENDS!!!!

23
Price Sensitivity to R and g
Steady-state Growth Rates
R

3
4
5
6
7
8
103.00
130.00
175.00
265.00
535.00
9
85.83
104.00
131.25
176.67
267.50
10
73.57
86.67
105.00
132.50
178.33
11
64.38
74.29
87.50
106.00
133.75
12
57.22
65.00
75.00
88.33
107.00
13
51.50
57.78
65.63
75.71
89.17
14
46.82
52.00
58.33
66.25
76.43
15
42.92
47.27
52.50
58.89
66.88
24
What about stocks that dont pay dividends?

• These stocks still have value. Why?
• They may make alternative payments to
  shareholders
• They WILL make payments eventually, even if to
  liquidate its assets
• If they NEVER paid money out to shareholders and
  NEVER WILL, youve bought yourself an asset that
  never matures and never pays out cash. How much
  is such an asset worth?
• How do we value such stocks (e.g., Microsoft)?
• Multiple-stage DDMs
• Value the Firm, then subtract Debt, leaving
  equity value (warning this involves WACC and
  FCFF)
• Use of Multiples
• Lets devote all of next weeks lecture to these
  subjects