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Tables
of bond yields or bond values which assist in computing bond yields to
maturity, or in calculating the price of value of a bond necessary to
afford a given yield to a given maturity. Various
types of tables are available. For
computing bond yields to maturity, the Rollins tables show the value to
the nearest cent of a bond of specified maturity bearing interest rates
of 2%, 2.5%, 3%, 3.5%, 4%, 4.5%, 5%, 6% and 7% and yielding from 2% to
7%. Appended is a sample from
the 20 years' maturity table, interest payable semi-annually.
It is apparent from the table that a 20-year 4% bond, interest
payable semi-annually, purchased at 103,50 will yield 3.75% to maturity. By
means of interpolation, or calculation based on proportion of differences,
exact yields not directly given by the table may be calculated.
For example, the yield to maturity of a 20-year 4% bond, interest
payable semi-annually, purchased at 104, is not directly given by the
table, However, the table
does show nearest prices of 104.21, at which yield to maturity is 3.70%,
and 103.50, at which yield to maturity is 3.75%.
The differences are 0.71 in price and 0.05% in yield.
Since the given purchase price, 104, is 0.50 greater than 103.50,
it will therefore yield 50/71 of 0.05% less than 3.75% and, conversely,
21/71 of 0.05% more than 3.70%. In
either case, the answer is 3.7148% or, rounded out, 3.72%. Similarly,
it may be desired to calculate the price or value of a 20-year 4% bond,
interest payable semi-annually, necessary to afford a 3.75% yield to maturity.
It is apparent from the table that the price is 103.50.
Where the exact price is not directly given by the table, it may
be calculated by means of interpolation.
For example, it may be desired to calculate the price or value
of a 20-year 4% bond, interest payable semi-annually, necessary to yield
4.85% to maturity. The nearest
prices given are 89.79, at which the yield is 4,80%, and 88.90, at which
the yield is 4.875%. The difference
of 0.075% in yield is equal to the difference of 0.89 in price,
Therefore, the difference of 0.05% between 4.890% and the required
yield of 4.85% is equal to a difference of 0.593 in price (0.05/0.075
of 0.89 or, expressed in ratio form, 0.075:0.89 as 0.05:0.593).
This indicates a price of approximately 89.25 (89.79 less 0.l593,
or 89.197). |