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BOND VALUATION AND YIELD

In valuing a bond ( or any such security ) we are primarily concerned with discounting ( or capitalizing ) the cash flow stream that the investor would receive over the life of the instrument.

The discount ( capitalisation ) rate applied to the cash flow stream will differ among bonds depending on the risk structure of the bond issue.

Future Value and Present Value of an Annuity ( REVISION)

1.Ordinary Annuities.

If $10,000 is deposited each year in a savings account paying 15% p.a., how much will you have after 3 years?

We know : n

FVAn = PMT ∑ ( 1 + i )ⁿ-t

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e. 4 % interest after 6 months.

At the end of 1 year the future value of the deposit would be :

2

FV 1 = 100 ( 1 + [ 0.08/2 ] = $108.16

Additional interest of $0.16 is earned on the $100 for the year because of the semi- annual compounding- i.e. interest is earned on the interest paid after 6 months.

In general, the formula is :

mn

FV n = PMT ( 1 + [ i/m ] )

If interest were paid quarterly ( 4 times per year ) then the FV for a 3 year instrument would be given by :

(4)(3)

FV n = 100 ( 1 + [ 0.08/4 ] )

12

= 100 ( 1.02 ) = $126.82

The PRESENT VALUE calculations involving compounding more than once per year is the reciprocal of the future value calculations.

PV = FV n

-----------------

mn

( 1 + [ i/m ] )

= 100

------------ (4)(3)

( 1 + [ 0.08/4] )

= 100

---------- = $ 78.85

( 1 + 1.02 )12

CONTINUOUS COMPOUNDING

Interest is sometimes compounded continuously. As m, the number of times interest is compounded, approaches infinity ( ∞ ) we get continuous compounding and the term

mn i,n

( 1 + [ i/m ] ) approaches ℮ , where ℮ is approx. 2.71828.

Therefore the future value at the end of n years of an initial deposit PVo where interest is compounded continuously at a rate i % is :

i,n

FVn = PVo ( ℮ )

(0.08))(3)

= $100( ℮ )

(0.24)

= $100 ( 2.71828 )

= $ 127.12

The PRESENT VALUE of a continuously compounding instrument is the reciprocal of the above, i.e. :...

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