For example, consider a bond with a face value of 1000, 5 years to maturity and an annual coupon rate of 5% (paid on an annual basis). The future cash flows in year 1 to year 4 will then be 5% of 1000: 50. The cash flow in the fifth year will be equal to 1050 since the principal is then also repaid. Suppose the market discount rate is 4% a year (in every year). The value of the bond will then equal 1044.52, which is higher than the face value of a 1000. This is because the market discount rate today (4%) is lower than the coupon rate (5%) received on the bond. Therefore, the value of the bond goes up such that an investor who wants to buy this bond will only have a (effective rate of) return of 4%.

Bond valuation and the yield curve

Of course in real life, most of the time it is not the case the market discount rate is the same for all maturities. Most of the time, the so-called yield curve is upward rising. This means that the annual market interest rate for 1 year may be 1%, while the annual market interest rate for 2 years may be 3%, for 3 years 4% and so on. In that case, the interest rate that is plugged in the denominator will vary year from year.