07CashFlowAnalysisBonds-2013.pdf-Bond Valuation • Yield to maturityshowing page 10-17 out of 26

Page 10
Bond Valuation
Yield to maturity (return on investment) = actual interest
earned from a bond over the holding period (equivalent to
IRR calculations as we will see later)
When considering buying or selling bonds, the yield (NOT
to be confused with the coupon rate) is the fundamental
consideration and this depends on a number of issues and
is determined by the market:
Current yields for that type of security (economy dependent)
Inflation rate (usually included in the yield by market forces)
Investors’ tax positions
Foreign exchange risk if you invest in other currencies
The actual price of a bond, even at issue, is very unlikely to
be the face value, except at redemption.

Page 11
Note the items:
Coupon rate
Maturity Date
Bid Price
These are very
important concepts
for bonds. Note how
yeild rates vary due
to risk issues.

Page 12
Bond Problems
Types on bond problems you will find
encompass different approaches to the
You may be required to calculate any of the
The current price of the bond
The current yield rate
An appropriate coupon rate
Other: face value

Page 13
Bond Example 1
A $500,000 5 yr bond is offered for purchase.
It has an 8% coupon rate, payable semi-
The yield rate today is 10%.
Calculate what you would be willing to pay for
it today.
Yield rates on bonds are typically quoted based on
coupon payment frequency – so if coupon paid semi-
annually, the 6-month rate is 10%/2 = 5%
The face value will be paid 5 years from now

Page 14
Example 2 on Bonds
A 15 year bond was issued 5 years ago:
Has a coupon rate of 8% on a $1000 face value,
paid semi-annually
It’s yield is quoted to be 12%
What price should we offer for the bond?

Page 15
Bond example 3
A $10,000 bond was bought that will mature in 8
years, it has a 12% coupon payable quarterly. The
yield rate at the time of issue was 11%. If the
yield rate is currently 10%, how much would you
pay for the Bond if it was for sale?
Note: Just as a "sanity check" if the discount rate is
(lower) than the coupon rate, the purchase
price must be
(greater) than the face value - look
at this when working on a problem to check if you are

Page 16
Bond example 4
How much would you pay for a bond with a
face value of $10,000 and a coupon rate of
10% per year, payable quarterly and it will
mature in 15 years.
You want to make 4% per
P = 250*(P/A, 4%, 60) + 10,000*(P/F, 4%, 60)
P =

Page 17
Bond example 5
A company issued a mortgage bond for
$10,000,000 with a 20 year maturity.
rate was 8% per year, payable quarterly.
issuing expenses and brokerage fees paid by
the company were $250,000 what is the
present worth of the bond after 10 years if the
owners would like to sell it and interest rates
rose to 12% per year in the market place for
the given perceived risk?

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