CHAPTER 5

Mathematics of Individual Finance

[Mathematics of Individual Finance Page 1] [Time Value Of Money][Future Values] [More Frequent Compounding] [Effective Annual Interest Rate] [Present Value]
[Annuities] [Present Value Of An Annuity] [Annuities Due] [Future Value Of An Annuity] [Determining Payments] [Bond Valuation]
[Uneven Cash Flows] [Amortization Schedule] [Household Capital Budgeting] [Duration] [Summary] [Discussion Questions]
[Problems]

Bond Valuation

A regular bond is an instrument that pays a fixed rate of interest, generally called the "coupon," until maturity when it also repays the principal, which is usually $1,000 per bond. Therefore, the value of a bond is equal to the present value of the coupon payments, which is an annuity, plus the present value of the future lump sum repayment of principal.

Example 5-17

Barbara owns a Treasury bond which pays a semi-annual coupon of $45. The bond will mature in 7 years and will repay the principal of $1,000 at maturity. If the yield curve shows that 7 year Treasuries have yields of 8% at the current time, how much is Barbara's bond worth?

Solution 5-17

The bond will make 14 annuity payments of $45 each and then will pay out the principal of $1,000. Using the Treasury yield curve annual discount rate of 8% which becomes a semi-annual rate of (8%/2 = 4%), the present value of the annuity is $475.34. The value of the $1,000 in 14 periods at 4% is $1,000/(1.04)14 = $1,000/1.7317 = $577.48. Adding the two components together gives us $1,052.82. Note that this bond is worth more than its $1,000 par value because the discount rate of 8% is below the annual coupon rate of 9%. This bond is said to be selling at a "premium" to par value. If the discount rate were above the coupon rate, the bond would sell at a "discount" to par value.

Most financial calculators will solve the value of a bond in one step [14 N 4 %i 45 PMT 1000 FV CPT PV] = $1,052.82. Using the financial tables or LOTUS, the solution will have to be done in two parts. In LOTUS it would be @PV(45,.04,14)+(1000/1.04^14).

[Uneven Cash Flows]

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