Corporate Finance –
LECTURE 04
BOND
Bond is a contract between an investor and the issuer – a company. It is a debt instrument that
a company uses to raise the capital and in return pay interest to the investors at per the terms of
contract. Bonds are redeemable – it means that after a period of time the company (issuer)
returns the money to the investors and liquidates its liability. The rate at which issuer pays
interest to investors is known as coupon rate.
Features of Bond:
Coupon Interest: stated interest payments per
period Face value: also Par value or the principal
amount Coupon rate: interest payments stated in
annualized term.
Duration or maturity date: The date on which company returns the principal amount back
to investors. Current yield: Annual coupon payments divided by bond price.
Discount Bond: A bond which is sold less than the face or par value is discount
bond. Premium Bond: A bond which is sold more than the face or par value is
premium bond.
Interest Rate Risk & Bonds
The risk arising from fluctuating interest rate is known as interest rate risk.
Interest rate risk depends on how sensitive bond price is to interest rate change.
This sensitivity depends upon two things:
- Time to maturity
- Coupon rate
A small change in interest rate will have greater impact on the on YTM and bond value.
BOND VALUATION:
Bond valuation is the process of determining the fair price of a bond. As with any security, the
fair value of a bond is the present value of the stream of cash flows it is expected to generate.
Hence, the price or value of a bond is determined by discounting the bond's expected cash
flows to the present using the appropriate discount rate.
¾ General relationships
¾ Bond pricing
1) General relationships:
a) The present value relationship:
The fair price of a straight bond is determined by discounting the expected
cash flows: Cash flows:
The periodic coupon payments C, each of which is made once every
period; The par or face value F, which is payable at maturity of the bond
after T periods.
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Discount rate:
r is the market interest rate for new bond issues with similar risk ratings
Bond Price =
Because the price is the present value of the cash flows, there is an inverse relationship between
price and discount rate: the higher the discount rates the lower the value of the bond (and vice
versa). A bond trading below its face value is trading at a discount; a bond trading above its
face value is at a premium.
b) Coupon yield:
The coupon yield is simply the coupon payment (C) as a percentage of the face value (F).
Coupon yield is also called nominal yield.
Coupon yield = C / F
c) Current yield:
The current yield is simply the coupon payment (C) as a percentage of the bond
price (P). Current yield = C / P0
d) Yield to Maturity:
The yield to maturity (YTM), is the discount rate which returns the market price of the bond.
It is thus the internal rate of return of an investment in the bond made at the observed price.
YTM can also be used to price a bond, where it is used as the required return on the bond.
Solve for YTM where
Market Price =
To achieve a return equal to YTM, the bond owner must invest each coupon received at this rate.
Points to remember:
For a bond selling above the face value is said to sell at premium. It means investor who buys
it at a premium face a capital loss over the life of bond. So return on bond will be less than the
current yield. For a bond selling below the face value is said to sell at discount. This means
capital gain at maturity. The return on this bond is greater than its current yield.
If interest rates do not change, the bond price changes with time so that total return on the bond
is equal to yield to maturity.
If YTM increases, the rate of return will be less than yield.
If the YTM decreases, the rate of return will be greater than yield.
2) Bond pricing:
a) Relative price approach:
Here the bond will be priced relative to a benchmark, usually a government security. The
discount rate used to value the bond is determined based on the bond's rating relative to a
government security with similar maturity. The better the quality of the bond, the smaller the
spread between its required return and the YTM of the benchmark. This required return is then
used to discount the bond cash flows.
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b) Arbitrage free pricing approach:
In this approach, the bond price will reflect its arbitrage free price. Here, each cash flow is
priced separately and is discounted at the same rate as the corresponding government issue Zero
coupon bond. Since each bond cash flow is known with certainty, the bond price today must be
equal to the sum of each of its cash flows discounted at the corresponding risk free rate - i.e. the
corresponding government security.
Here the discount rate per cash flow, rt, must match that of the corresponding zero coupon bond's
rate.
Bond Price =
TERM STRUCTURE OF INTEREST RATES
The relationship between long term & short-term rates is known as Term Structure.
Interest rates in short & long terms are different. Term structure tells us nominal interest
rate on default free securities. When long-term rate is greater than short term then the
term structure will be upward sloping and when short-term rate is greater than the long
term, the term structure will be downward sloping.
The term structure of interest rates, also known as the yield curve, is a very common
bond valuation method.
There are three main patterns created by the term structure of interest rates:
1) Normal Yield Curve:
As its name indicates, this is the yield curve shape that forms during normal market
conditions, wherein investors generally believe that there will be no significant changes in the
economy, such as in inflation rates, and that the economy will continue to grow at a normal
rate. During such conditions, investors expect higher yields for fixed income instruments with
long-term maturities that occur farther into the future. In other words, the market expects
long-term fixed income securities to offer higher yields than short-term fixed income
securities. This is a normal expectation of the market because short-term instruments
generally hold less risk than long-term instruments; the farther into the future the bond's
maturity, the more time and, therefore, uncertainty the bondholder faces before being paid
back the principal. To invest in one instrument for a longer period of time, an investor needs
to be compensated for undertaking the additional risk.
Remember that as general current interest rates increase, the price of a bond will decrease
and its yield will increase.
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2) Flat Yield Curve:
These curves indicate that the market environment is sending mixed signals to investors, who are
interpreting interest rate movements in various ways. During such an environment, it is difficult
for the market to determine whether interest rates will move significantly in either direction
farther into the future. A flat yield curve usually occurs when the market is making a transition
that emits different but simultaneous indications of what interest rates will do. In other words,
there may be some signals that short-term interest rates will raise and other signals that long-term
interest rates will fall. This condition will create a curve that is flatter than its normal positive
slope. When the yield curve is flat, investors can maximize their risk/return tradeoff by choosing
fixed-income securities with the least risk, or highest credit quality. In the rare instances wherein
long-term interest rates decline, a flat curve can sometimes lead to an inverted curve.
3) Inverted Yield Curve:
These yield curves are rare, and they form during extraordinary market conditions wherein
the expectations of investors are completely the inverse of those demonstrated by the normal
yield curve. In such abnormal market environments, bonds with maturity dates further into
the future are expected to offer lower yields than bonds with shorter maturities. The inverted
yield curve indicates that the market currently expects interest rates to decline as time moves
farther into the future, which in turn means the market expects yields of long-term bonds to
decline. Remember, also, that as interest rates decrease, bond prices increase and yields
decline.
You may be wondering why investors would choose to purchase long-term fixed-income
investments when there is an inverted yield curve, which indicates that investors expect to
receive less compensation for taking on more risk. Some investors, however, interpret an
inverted curve as an indication that the economy will soon experience a slowdown, which
causes future interest rates to give even lower yields. Before a slowdown, it is better to lock
money into long-term investments at present prevailing yields, because future yields will be
even lower.
REAL VS NOMINAL INTEREST RATES:
The nominal interest rate is the amount, in money terms, of interest payable.
For example, suppose household deposits $100 with a bank for 1 year and they receive
interest of $10. At the end of the year their balance is $110. In this case, the nominal
interest rate is 10% per annum.
The real interest rate, which measures the purchasing power of interest receipts, is
calculated by adjusting the nominal rate charged to take inflation into account.
If inflation in the economy has been 10% in the year, then the $110 in the account at the
end of the year buys the same amount as the $100 did a year ago. The real interest rate,
in this case, is zero. After the fact, the 'realized' real interest rate, which has actually
occurred, is:
ir = in-p
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where p = the actual inflation rate over the year.
The expected real returns on an investment, before it is
made, are:
ir = in- pe
where:
in = nominal interest
rate ir = real interest
rate
pe = expected or projected inflation over the year.
Market interest rates
There is a market for investments which ultimately includes the money market, bond
market, stock market and currency market as well as retail financial institutions like
banks.
Exactly how these markets function is a complex question. However, economists
generally agree that the interest rates yielded by any investment take into account:
The risk-free cost of capital
Inflationary expectations
The level of risk in the investment
The costs of the transaction
Risk-free cost of capital
The risk-free cost of capital is the real interest on a risk-free loan. While no loan is ever
entirely risk-free, bills issued by major nations are generally regarded as risk-free
benchmarks.
This rate incorporates the deferred consumption and alternative investments elements of
interest.
Inflationary expectations
According to the theory of rational expectations, people form an expectation of what will
happen to inflation in the future. They then ensure that they offer or ask a nominal interest
rate that means they have the appropriate real interest rate on their investment.
This is given by the
formula: in = ir + pe
Where:
in = offered nominal interest
rate ir = desired real interest
rate
pe = inflationary expectations
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Risk
The level of risk in investments is taken into consideration. This is why very volatile
investments like shares and junk bonds have higher returns than safer ones like
government bonds.
The extra interest charged on a risky investment is the risk premium. The required risk
premium is dependent on the risk preferences of the lender.
If an investment is 50% likely to go bankrupt, a risk-neutral lender will require their returns
to double. So for an investment normally returning $100 they would require $200 back. A
risk-averse lender would require more than $200 back and a risk-loving lender less than
$200. Evidence suggests that most lenders are in fact risk-averse.
Generally speaking a longer -term investment carries a maturity risk premium, because
long-term loans are exposed to more risk of default during their duration.
Liquidity preference
Most investors prefer their money to be in cash than in less fungible investments. Cash is on
hand to be spent immediately if the need arises, but some investments require time or effort to
transfer into spend able
form. This is known as liquidity preference. A 10- year loan, for instance, is very illiquid
compared to a 1-year loan. A 10-year US Treasury bond, however, is liquid because it can easily
be sold on the market.
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