B. Present Value of 13 Coupons @ 35 is $ 339.43
C. Present Value of Bond (A + B) : $903.02
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Basic Bond Valuation Model
A bond holder typically earns two kinds of income from the bond:
1) Coupon Payments at periodic intervals.
2) A lump sum payment at maturity (or earlier, if sold before maturity).
Accordingly the value of a bond (V )is equal to
Present Value of Coupon Payments + Present Value of Amount Receivable at Maturity
V(0) = Intrinsic or Present Value of the Bond
C = Value of Single Coupon Payment
I = Annual Interest payable on the bond
F = Amount repayable at Maturity time
n = Maturity period of the bond
kd= required rate of return
Valuation of a Bond with Smaller Interval Payments
In real world, most of the bonds pay coupon either half yearly, quarterly or at a different set of intervals.
As these intermittent payments can be reinvested by the bondholder, these bonds have more value than bonds with annual interest payments.
Not only do the bonds pay at smaller intervals, the compounding or discounting also takes place in the same interval. For example, if a treasury bond makes coupon payments half yearly, it will also discount the bond at half yearly frequency.
The bond valuation formula now needs to be modified as:
i) Annual Interest payment I divided by frequency(f) of payment
ii) N multiplied by f tp get the actual number of coupon payments over the period
iii) Discount rate divided by f to get the discount rate for the interval
Accordingly, the new equation becomes:
All other terms mean the same
f = frequency of payment (1 for annual, 2 for half yearly, 4 for quarterly etc.)