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Valuing Financial Assets Using Spot and Forward Rates

More About Present Values. Valuing Financial Assets Using Spot and Forward Rates. Valuing a Bond - Simple Approach. Bond Prices and Yields. Price. Yield. YTM (r). 1981. 1987 & Normal. 1976. Year. 1 5 10 20 30. Term Structure of Interest Rates.

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Valuing Financial Assets Using Spot and Forward Rates

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  1. More AboutPresent Values Valuing Financial Assets Using Spot and Forward Rates Fußzeile

  2. Valuing a Bond - Simple Approach Fußzeile

  3. Bond Prices and Yields Price Yield Fußzeile

  4. YTM (r) 1981 1987 & Normal 1976 Year 1 5 10 20 30 Term Structure of Interest Rates Interest Rate - the interest rate according to the term structureSpot 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

  5. Term Structure of Interest Rates What Determines the Shape of the TS? 1 - Unbiased Expectations Theory 2 - Liquidity Premium Theory Term Structure & Capital Budgeting • CF should be discounted using Term Structure info • Since the spot rate incorporates all forward rates, then you should use the spot rate that equals the term of your project. • If you believe in other theories take advantage of the arbitrage.

  6. Term – Structure of Interest Rates Germany Fußzeile

  7. - 1 × 40.000 1,07 - 2 × 40.000 1,07 - 3 × 1.040.000 1,07 Valuation - Spot Rates (Flat Rate) t t t t 0 1 2 3 40.000,00 40.000,00 1.040.000,00 Market Value 37.383,18 34.937,55 848.949,79 921.270,52

  8. - 1 × 40.000 1,05 - 2 × 40.000 1,06 - 3 × 1.040.000 1,07 ValuationInterest Rates (Yields) t t t t 0 1 2 3 40.000,00 40.000,00 1.040.000,00 Marktwert ? 38.095,24 35.599,86 848.949,79 922.644,89 Fußzeile

  9. t t t t 0 1 2 3 Valuation - Spot RatesDuplication-Portfolio 40.000,00 40.000,00 1.040.000,00 Market Value ? 971.962,62 - Loan: interest 7 % Interest 7 % interest 7 % 971962,62 - 68.037,38 - 68.037,38 - 68.037,38 Difference: 0 Difference: - 28.037,38 + 26.450,36 Investment: interest 6 % interest 6 % - 26.450,36 + 1.587,02 + 1.587,02 Difference: 0 Difference: - 26.450,36 25.190,82 Investment: Interest: 5 % 1.259,54 - 25.190,82 Difference: 0 920.321,44 Fußzeile

  10. Valuation Mode Result (P.V.) Which Priceis the Right One ? 3y Interest Rate flat (7%) 921.270,52 € Term – Structure of Interest Rates (5,6,7%) 922.644,89 € Replication of Cash Flows 920.321,44 € Three approaches lead to three results: But which is the right one ?????? Fußzeile

  11. 1 2 3 Use Spot Rates to Valuate the Price of a Bond Yield 5% 6% 7% Spot Rates 5% 6,03% 7,1% Proof : Fußzeile

  12. Term – Structure of Interest Rates and related Spot Rates (Calculation) Example: Fußzeile

  13. t0 t1 t2 Forward Rates A financial contract that does not start immediately but at a specified date in the future is called a Foward Contract.Example: Due to an expected future business development your corporate needs a 1-year loan of 10 Mio €. The loan should be available 1 year from now. Fußzeile

  14. Spot Rates and related Forward Rates To solve the problem you can fix a rate using a Forward Contract. The rate, that can be locked in today, results from a simple model: The cost of borrowing now for two years must equal the cost of borrowing now for one year with an obligation to extend the loan for a second year. Using the spot – rates from the example above and solving the equation for rf,1,1 results in: Fußzeile

  15. Spot Rates and relatedForward Rates Fußzeile

  16. Forward Rates (F.R.A. - Application) To contract a Forward-Rate means to lock in an interest rate concerning a future period. Your corporation might use an F.R.A. (= Forward Rate Agreement) to make sure, that her future costs of financing a 1-year 10 Mio € loan will not exceed 3,30 %. Fixed Rate: 3,30% Maturity of F.R.A. Time to Market Fußzeile

  17. Forward Rates(F.R.A. - Application) Profit Locked-in Rate: 3,3% Loss Scenario 1:Short rate in t1 is at 5%. Financing costs will be 500 T€. Compensations on F.R.A. will be (5%-3,3%)x10 Mio = +170 T€. Total costs: (500-170)=330 T€ (= 3,3%) Long F.R.A. Scenario 2:Short rate in t1 is at 2%. Financing costs will be 200 T€. Payments on F.R.A. will be (2%-3,3%)x10 Mio = -130 T€. Total costs: (200 +130)=330 T€ (= 3,3%) Fußzeile

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