Valuing Financial Assets

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Presentation transcript:

Valuing Financial Assets More About Present Values Valuing Financial Assets Using Spot and Forward Rates Berlin, 04.01.2006 Fußzeile

Valuing a Bond - Simple Approach Berlin, 04.01.2006 Fußzeile

Bond Prices and Yields Price Yield Berlin, 04.01.2006 Fußzeile

Term Structure of Interest Rates YTM (r) Year 1981 1987 & Normal 1976 1 5 10 20 30 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 Berlin,

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. Berlin,

Term – Structure of Interest Rates Germany Berlin, 04.01.2006 Fußzeile

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

Valuation Interest Rates (Yields) t t t t 1 2 3 40.000,00 40.000,00 1.040.000,00 Marktwert ? 1 1,05 40.000 - × 38.095,24 2 - × 1,06 40.000 35.599,86 3 - × 1,07 1.040.000 848.949,79 922.644,89 Berlin, 04.01.2006 Fußzeile

Valuation - Spot Rates Duplication-Portfolio t 1 t 2 t 3 Market Value ? 40.000,00 40.000,00 1.040.000,00 Loan: 971.962,62 - interest 7 % Interest 7 % interest 7 % 971962,62 - 68.037,38 - 68.037,38 - 68.037,38 Difference: 0 Difference: - 28.037,38 Investment: + 26.450,36 interest 6 % interest 6 % - 26.450,36 + 1.587,02 + 1.587,02 Difference: 0 Difference: - 26.450,36 Investment: 25.190,82 Interest: 5 % 1.259,54 - 25.190,82 Difference: 0 920.321,44 Berlin, 04.01.2006 Fußzeile

Which Price is the Right One ? Three approaches lead to three results: Valuation Mode Result (P.V.) 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 € But which is the right one ?????? Berlin, 04.01.2006 Fußzeile

Use Spot Rates to Valuate the Price of a Bond 1 2 3 Yield 5% 6% 7% Spot Rates 6,03% 7,1% Proof : Berlin, 04.01.2006 Fußzeile

Term – Structure of Interest Rates and related Spot Rates (Calculation) Example: Berlin, 04.01.2006 Fußzeile

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. t0 t1 t2 Berlin, 04.01.2006 Fußzeile

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: Berlin, 04.01.2006 Fußzeile

Spot Rates and related Forward Rates Berlin, 04.01.2006 Fußzeile

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% Time to Market Maturity of F.R.A. Berlin, 04.01.2006 Fußzeile

Forward Rates (F.R.A. - Application) Locked-in Rate: 3,3% Profit 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%) Berlin, 04.01.2006 Fußzeile