1. Valuing Financial Assets
More About Present Values
Valuing Financial Assets
Using Spot and Forward
Rates
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2. Valuing a Bond - Simple Approach
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3. Bond Prices and Yields
Price
Yield
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4. Term Structure of Interest Rates
YTM (r)
Year
1981
1987 & Normal
1976
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
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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.
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6. Term – Structure of Interest Rates Germany
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7. Valuation - Spot Rates (Flat Rate)1 2 3
40.000,00
40.000,00
,00
Market Value 1
1,07
40.000 - ×
37.383,18 2 - ×
1,07
40.000
34.937,55
,79 3 - ×
1,07
,52
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8. Valuation Interest Rates (Yields)t t t t 1 2 3
40.000,00
40.000,00
,00
Marktwert ? 1
1,05
40.000 - ×
38.095,24 2 - ×
1,06
40.000
35.599,86 3 - ×
1,07
,79
,89
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9. Valuation - Spot Rates Duplication-Portfoliot 1 t 2 t 3
Market Value ?
40.000,00
40.000,00
,00
Loan:
,62 -
interest 7 %
Interest 7 %
interest 7 %
971962,62
,38
,38
,38
Difference: 0
Difference:
,38
Investment:
,36
interest 6 %
interest 6 %
,36
,02
,02
Difference: 0
Difference:
,36
Investment:
25.190,82
Interest: 5 %
1.259,54
,82
Difference: 0
,44
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10. Which Price is the Right One ?
Three approaches lead to three results:
Valuation Mode
Result (P.V.)
3y Interest Rate flat (7%)
,52 €
Term – Structure of Interest Rates (5,6,7%)
,89 €
Replication of Cash Flows
,44 €
But which is the right one ??????
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11. Use Spot Rates to Valuate the Price of a Bond1 2 3
Yield 5% 6% 7%
Spot Rates
6,03%
7,1%
Proof :
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12. Term – Structure of Interest Rates and related Spot Rates (Calculation)
Example:
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13. 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
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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:
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15. Spot Rates and related Forward Rates
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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%
Time to Market
Maturity of F.R.A.
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17. 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: ( )=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: ( )=330 T€ (= 3,3%)
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