Key features of bonds
Bonds valuation
Measuring yield
Assessing risk
In accounting, you discuss more on bonds payable and investment in bonds. But this discussion is more
on financial management of bonds.
What is bonds?
A long-term debt instrument in which a borrower agrees to make payments of principal and interest, on
specific dates, to the holders of the bond.
Primarily traded in the over-the-counter market.
Traded among large financial institutions.
Key features of a bond:
Par Value: face amount of the bond, which is paid at maturity (assume $1,000).
Coupon interest rate: stated interest rate (generally fixed) paid by the issuer. Multiply by par
value to get dollar payment of interest.
o If you are the bond holder, you will earn in terms of interest. The issuer will pay interest.
Maturity date: years until the bond must be repaid.
Issue date: when the bond was issued.
Yield to maturity: rate of return earned on a bond held until maturity (also called “promise
yield”).
Effects of a call provision
Allows issuer to refund the bond issue if rates decline (helps the issuer, but hurts the investor)
Bond investors require higher yields on callable bonds.
In many cases, callable bonds include a deferred call provision and a declining call premium.
In terms of bonds, it’s important for us to know the sinking fund.
You save money to pay for a specific thing. In this discussion, to pay for bonds.
Provision to pay off a loan over its life rather than all at maturity.
Similar to amortization of a loan.
Reduces risk to investor, shortens average maturity.
Before the discussion of bonds valuation, review the future value, present value, NPV, and IRR.
Simple Example:
What if a company sells you a piece of paper for $1,000 and promises to pay the buyer 5% of $1,000 (or
$50) per year, every year, for three years. And promises to pay back the whole $1,000 at the end of 3
years (in addition to the promised $50 at the end of 3 years) --- this is called a bond. (bond = promise)
In this case, the FV is $1,000, and the coupon rate is 5%.
But what if after the company sells it to the original buyer for $1,000, that original buyer sells it to
someone else for another price… say, $913. Is the new bond value $1,000 or $913?
Answer: BOTH! $1,000 is the FV (always), and $913 is the Market Value.
Another question: if the new owner is still getting $50 per year (5% of the FV), is he still getting 5%?
Of course, the answer is NO.
So, what is the new percentage? 5.48%. So now, is the coupon rate still 5% or 5.48%?
The coupon rate is still 5%, but the current yield is 5.48%. The coupon rate does not change, it is always
based on the face value of the bond. Coupon rate = face value, current yield = market value.
Another question: What if you buy it in the beginning of the 2 nd year (so the bond will still live for 2 more
years) for only $913 (but you still get 5% of $1,000 = $50 per year); and you’ll still get the full $1,000 in
the end. What is your rate of return?
0 = -$913(1.r)-0 + $50(1.r)-1 + $50(1.r)-2 + $1,000(1.r)-2
To get the IRR, we will guess what is the “r” until the NPV becomes zero.
Answer: the rate of return is 10%.
So now, is this 10% a coupon rate or a current yield? This 10% is called Yield to Maturity. Or simply
“yield” for short.
Another question: What if your coupon rate is 5%, your current yield is 5.48%, and your yield to maturity
is 10%, but the banks or the government is giving 4% on deposits. What is this 4% rate called? --- this is
called the market rate or discount rate or interest rate.
Before you proceed to calculating bond value, you must know 1st the difference between these things:
1. Difference between bond’s face value, market value, and fair value.
2. Difference between coupon rate, current yield, yield to maturity or “yield”, and
market/discount/interest rate.
Bond Valuation for a Coupon Bond
Example:
CBA Corp issued a 3-year bond with a Face Value and a 5% Coupon Rate, with coupons paid once a year
at the end of every year. It is now the beginning of its second year and the first coupon has already been
paid. Banks are now giving 4% interest for deposits. The Bond’s Market Value is $913. What is the
bond’s coupon payment?
Coupon payment = Face Value x Coupon Rate
Coupon payment = $1,000 x 0.05
Coupon payment = $50
Given the same situation, what is the Bond’s Yield?
We use the IRR formula:
0 = -$913(1.r)-0 + $50(1.r)-1 + $50(1.r)-2 + $1,000(1.r)-2
The yield is 10%.
Given the same situation, with additional information of the yield, what is the bond’s fair value?
We use the NPV formula:
Bond fair value = $50(1.04)-1 + $50(1.04)-2 + $1,000(1.04)-2
Bond fair value = $1,018.86
If bank interest rates went up to 6%.
Bond fair value = $50(1.06)-1 + $50(1.06)-2 + $1,000(1.06)-2
Bond fair value = $981.67
If interest rates went down, bond fair value would go up. So, bond fair value and interest rates go
opposite directions.
Another Example:
CBA Corp issued a 3-year bond with a Face Value and a 5% Coupon Rate, with coupons paid once a year
at the end of every year. It is now the beginning of its second year and the first coupon has already been
paid. Banks are now giving 4% interest for deposits. Yield is 10%. What is the bond’s market value?
Use the NPV formula differently:
Bond market value = $50(1.10)-1 + $50(1.10)-2 + $1,000(1.10)-2
Bond market value = $913.22
When the market rate is greater than the coupon rate, the bond is at discount. The market is paying
more than what you’re getting. Otherwise, the bond is at premium, meaning the market is lower than
what the company is paying you.
