1. slide no.: 1 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Betriebswirtschaftliche Bewertungsmethoden Einsatz und Bewertung von Forward Rate Agreements Duration Prof. Dr. Rainer Stachuletz Corporate Finance

2. slide no.: 2 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Valuing a Bond - Simple Approach

3. slide no.: 3 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Example: n=number of periods C=coupon payment r=interest/ spot rate FV=Maturity/Face Value t=time period PV= Present Value of the Bond (Price) c < r  P < par (discount) c = r  P = par c > r  P > par (premium) Valuing a Bond - Simple Approach Generally Bond Pricing follows the PV-Approach:

4. slide no.: 4 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Straight Bond, 5yrs. To Maturity, 5,5 Coupon Rate, annual payment, market rate: 5% or Valuing a Bond - Simple Approach +

5. slide no.: 5 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Semi-annual Coupon Payments: Example: n= 10 C= 5,5% r= 5% FV= 1000 t= 5 Floating Interest Rates (1%/year): Example: n= 5 C= 5,5% r= 5-9% FV= 1000 t= 5 Valuing a Bond - Simple Approach +

6. slide no.: 6 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Zero Bonds: Example: r= 5% FV= 1000 t= 5 Example: r= ? FV= 1000 P= 783.53 t= 5 Valuing a Bond - Simple Approach

7. slide no.: 7 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Bond Prices and Yields Yield

8. slide no.: 8 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Interest Rate - the interest rate according to the term structure Spot Rate – implied rate to valuate future cash flows Forward Rate - The interest rate, fixed today for a future period Current Yield – Coupon payments on a security as a percentage of the security’s market price (gross of accrued interest) Yield To Maturity (YTM) - The IRR on an interest bearing instrument YTM (r) Year 1981 1987 & Normal 1976 1 5 10 20 30 Term – Structure of Interest Rates

9. slide no.: 9 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Term – Structure of Interest Rates Germany

10. slide no.: 10 Prof. Dr. Rainer Stachuletz – Berlin School of Economics THE DURATION OF A ZEROBOND 0,00 20,00 40,00 60,00 80,00 100,00 120,00 t 5 t 20 75,13 56,45 42,41 31,86 23,94 14,86 10% 37,69 78,35 67,68 55,68 48,10 5% 74,30 67,29 2% 100 Die Duration eines Zerobonds entspricht seiner Restlaufzeit

11. slide no.: 11 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Value of Reinvested Payments : 48,84 € Present Value of Future Payments : 92,42 € Interest payments from the bond: 8% / y. Interest rate in the market: 10% t 0 t 5 t 10 8 8 8 8 8 8 8 8 8 8 100 + Total Portfolio Value: 141,26 € Ex.: Calculation of Portfolio Values in t 5

12. slide no.: 12 Prof. Dr. Rainer Stachuletz – Berlin School of Economics The Duration of a 8% Long – term Bond (10 years to maturity)

13. slide no.: 13 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Example: Calculation of Duration