CA School of Business Calculating Fair Value of a Bond October 2011
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According to IFRS 7 Financial Instruments: Disclosures, paragraph 25 "Except as set out in
paragraph 29, for each class of financial assets and financial liabilities, an entity shall disclose the fair value of that class of assets and liabilities in a way that permits it to be compared with its carrying amount."
IAS 32 Financial Instruments: Presentation, paragraph 11 defines fair value as "The amount for which an asset could be exchanged, or a liability settled, between knowledgeable, willing parties in an arm's length transaction."
In general, the fair value of a bond is best measured using quoted market prices. When such values are not available, other techniques must be used. These include reference to the current market value of another bond that is substantially the same or discounted cash flow analysis.
Where bonds are publicly traded, quoted market values are commonly available.
Example: On January 1st , 2010, Able Ltd. (Able) purchased 100, $1,000 par value bonds of a public company at 99.125% of par. On December 31st , 2010, the bonds were trading at 102.625% of par. Price paid on January 1st , 2010: 100 x $1,000 x 99.125% $ 99,125 Fair value on December 31st , 2010: 100 x $1,000 x 102.625% 102,625
In this case, the market rate of interest must have gone down as the fair value of the bond increased.
When the financial instruments are not publicly traded, a discounted cash flow approach, using interest rates for bonds with similar risk characteristics, can be used to determine fair value.
Example: On January 1, 2010, Able Ltd. (Able) paid $100,000 to purchase a bond with a par value of $100,000 and a coupon rate of 5% from a privately owned company. The bond is due December 31st , 2019. The bond bears interest at 5% per annum, payable each December 31st . The market rate of interest for bonds with similar risk characteristics and maturity dates were as follows:
December 31st , 2010 6% December 31st , 2011 7%
Fair value of the bond as at December 31st , 2010
PV factor for an annuity due in 9 years at 6% 6.8017
PV factor for a lump sum due in 9 years at 6% .5919
Present value of interest payments: $5,000 x 6.8017 $ 34,009
Present value of principal 59,190 Fair value of the bond at December 31st , 2010 $ 93,199
Nine years is used to determine the present value factors because the bond is a 10 year bond and at the end of the first year, 9 years remain in the bond term.
The cash flows are the annual interest payment of $100,000 x .05 = $5,000 (based on the coupon rate of interest) and the principal payment at the end of the bond term of $100,000. These are both discounted using the current market rate of interest.
Because the market rate of interest has gone up, the fair value of the bond has gone down.
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Fair value of the bond as at December 31st , 2011
PV factor for an annuity due in 8 years at 7% 5.9713
PV factor for a lump sum due in 8 years at 7% .5820
Present value of interest payments: $5,000 x 5.9713 $ 29,857
Present value of principal: $100,000 x .5820 58,200 Fair value of the bond at December 31st , 2011 $ 88,057
Eight years is used to determine the present value factors because at December 31st , 2011, the remaining bond term is 8 years.
The market rate of interest has again gone up, so the fair value of the bond has gone down.。