# Zero coupon bonds Essay

## Zero coupon bonds

These bonds do not have explicit rate of interest on their face rather they provide a lump sum amount at a future date in exchange for the current price of the bond. It follows then that the return of these bonds is the difference between the face value and the purchase price. This return is also called yield to maturity (Thau, 2000). The face value of these bonds is calculated using the market yield which is the market interest rate. Zero coupon bonds involve one single payment which is usually the face value at maturity. If his amount (face value) is the discounted, the bond value is achieved.

Value of zero coupon bond=present value of amount on maturity Vb=par value at period n (1+Kd)^n Where; Vb= value of bond Kd= yield to maturity n=maturity period (Thau,2000). 2. Current yield Current yield looks at the market price of the bond relative to the annual cash inflows if the bond is held for one year (Rhamesh, 2000) Current yield=annual cash inflows x 100% Current market price = 7%*1000*100% 1115 =6. 28% Coupon yield This is the return on the principal amount of the bond. It is usually the interest rate stated on the face of the bond. In is the amount of income from the bond.

The coupon yield is 7% Yield to maturity It includes all the aspects of the bond i. e. all the cash inflows, coupon and capital gains or losses (Rhamesh, 2000) YTM=coupon payments+(par value-market value/periods to maturity) (Par value + market value/2) =70+(1000-1115/2) (1000+1115/2) =1. 18% Yield to call This is the annual rate of return that investors receive at the date that the bond is called. Yield to call =coupon payment +(callable amount –market value/ maturity period) (Callable amount –market value/2) =70+(1100-1115/2) (1100+1115)/2 =5. 64% 3. Bond prices and inflation

The bond cash flows are normally discounted using the bond yield to arrive at the par value. Inflation affects interest rate movements which consequently affects the discount rate used in calculating bond prices. If inflation increases, the bond discount rate increases as well thus reducing the bond price and vice versa (Faerber, 2001) The bond yields with varying maturities can be used to predict the future behavior of the economy. This is possible through the use of the yield curve Maturity bond and inflation The yield of the bond is affected by the maturity period. The longer the maturity period, the higher the yield because .

of the uncertainty in the future. Changes in the short term interest rates affects short term bonds more than long term bonds while changes in long term interest rates affects long term bonds more than short term bonds (Faerber, 2001) Yield curve Yield curve shows the interest rates of bonds with equal credit rating but varying maturity periods at a give point in time. The shape of the curve can be used as a predictor of the future interest rate changes as well as economic activity. The gradient of the yield curve is also important because it shows the gap between short term and long term rates (Baumohl 2007)

The yield curve shape can be normal, inverted, or flat. Normal yield curve depicts longer maturity bonds with higher yields while inverted shows short term yields which are higher than longer term yields. Inverted yield curve shows a possibility of an economic slowdown. Flat yield curve occurs when the shorter and longer term yields are very close to each other. Flat yield curve shows the possibility of an economic transition (Baumohl 2007) 4. Duration The prices of bond are sensitive to changes in interest rates. The extent of this sensitivity depends on the maturity if the bond as well as the coupon interest rate.

Bonds with longer maturity periods are highly sensitive to interest rate changes. Low coupon bonds are also more sensitive to interest rte changes (Pandey, 2005: 47). Sensitivity of the price of the bond can be adequately estimated using the bond duration which is measured as weighted average of times of each cash flow i. e. interest payments or principal repayment. There are our types of duration; key rate duration, effective duration, modified duration and Macaulay duration. The duration of a bond is negatively related to the yield to maturity i. e. the higher the yield to maturity, the lower the duration and vice versa

The duration of the bond enables an investor to consider the timing of the cash flows in the sense that the weights are determined as the present value of the cash flow to the bond time. Therefore it can be noted that two bonds with similar maturity periods but different coupon rates and cash flow patterns will have different durations (Pandey, 2005: 48). The bond duration concepts helps an investor to understand the bonds price volatility which is important in the determination of the best strategy to take advantage of interest rate movements hat can affect the return of the bond (Pandey, 2005: 487).

The duration of the bond also helps an investor to protect his investment portfolio from interest rate by using bond duration concepts to establish an optimal bond portfolio. References Thau, A. (2000). The Bond Book. New York. Mc Graw Professional Pandey, I. (2005). Valuation of bonds and shares in Financial Management. 9th Ed. New Delhi. Vikal Publishing House: 47-48 Rhamesh, R. (2000). Financial Analysts Indispensable Pocket Guide. New York. Mc Graw Professional Faerber, E. (2001). Fundamentals of Bond Market. New York. Mc Graw Professional Baumohl, B. (2007). The Secrets of Economic Indicators. Chicago. Wharton School Publishing