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Bond Valuation


The price of a bond is given in per cent of the nominal amount. If the price (also called "market price") of a bond is 101.25%, for example, you would have to pay the nominal amount plus 1.25% when buying it. You would also have to pay the so-called "accrued interest":

Example  
Nominal value of the bond CHF 5'000
Bond price 101.25%
Accrued interest CHF 88.12

Payable amount (not including bank fees): CHF 5'000 x 101.25% + CHF 88.12 = CHF 5'150.62

Discounted cash-flow valuation

A bond consists of several payment flows. These are the periodically recurring interest payments, plus the repayment of the principal when the bond matures. All future payment flows have a value in the present. Determining this present value is called discounting.

The price of a bond is the sum of the discounted payment flows (interest payments and redemption). To determine the price, all future payment flows are divided by the discount factor (1 + discount rate). The discount rate is based on the market interest rate appropriate for the duration. The yield curve gives an indication of the interest rate to be applied.

The resulting price is called the cash value or present value, because it applies to the present.

Example  
Bond price 102.50%
Duration 2 years
Coupon 5%
Discount rate (market rate) 6%

In this example, the current price of the bond is 98.166%. This simplified example assumes that there are no differences in interest rates for different durations (a flat yield curve).

The purpose of a precise analysis must be to assign to each payment a discount factor which is appropriate for the duration; in other words, in the final analysis it must provide a structure of interest rates. The yield curve is of key significance in this regard because it supplies the required interest rates.

General formula for calculating cash value:

Zi : payment at point in time i
IRR: interest rate at point in time i

By the same token, the yield of a bond can be inferred from its price. Because most bonds are bought and sold in the course of the duration, there are so-called "broken periods" that have to be taken into account in calculating the yield.

Calculation of accrued interest

If you buy a bond in between two interest payments, you will receive the entire coupon (interest) for the interest period in question. However, the previous owner is entitled to the interest accrued before the purchase and will therefore need to be compensated accordingly at the time of purchase.

The payable compensation (also called "accrued interest") depends on the coupon, the purchase date, the interest date, the coupon frequency and the interest-calculation method.

  • The purchase date and therefore the settlement date (normally the trade day plus three bank working days) determine the point in time from which the interest is due to another party.
  • The previous interest date is important for calculating the period which has elapsed since the last coupon payment.
  • The coupon frequency is important in determining the next coupon date and hence in knowing the payment date for the entire interest for this period.
  • The interest-calculation method varies from one bond issue to the next and is used to calculate the days on which there is an entitlement to interest.
Example  
Nominal value of the bond CHF 5'000
Coupon 5%
Interest-calculation method 2 years
Accrued-interest days 129

Calculation of accrued interest: