# Corporate Finance

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Corporate Finance ­FIN 622
VU
Lesson 05
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.
General relationships
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.
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
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Corporate Finance ­FIN 622
VU
d) Yield to Maturity:
The yield to maturity (YTM), is the discount rate which returns the maket 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.
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 =
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