1. Understanding Interest Rate (Ch3) -- Fin331 1 Understanding Interest Rates 1. Present Value 2. Calculating Yield to Maturity for different types of debt 3. Other Measures of Interest Rates 4. Real Interest Rate 5. Rate of Return 6. Interest Rate Risk and Reinvestment Risk

2. Understanding Interest Rate (Ch3) -- Fin331 2 Present Value A loan of $1 at 10% interest Year123 n $1.10 $1.21 $1.33 $1x(1+i) n PV of future $1 = $1 (1+i) n

3. Understanding Interest Rate (Ch3) -- Fin331 3 Types of Loans 1. Simple loan 2. Fixed-payment loan 3. Coupon bond 4. Discount bond

4. Understanding Interest Rate (Ch3) -- Fin331 4 Simple Loan: a loan that borrower repays lender principal and interest payment at the maturity date. Fixed-Payment Loan: a loan that borrower repays lender same payment every month. Coupon Bond: a bond/loan that pays the owner of the bond a fixed interest payment every year until maturity, when a specified final amount is repaid. Discount Bond (Zero-Coupon Bond): a bond that is bought at a price below its face value, and face value is repaid at the maturity date.

5. Understanding Interest Rate (Ch3) -- Fin331 5 Yield to Maturity: Simple Loans Yield to maturity = interest rate that equates today's value with present value of all future payments 1. Simple Loan You borrowed $100 and agreed to return $110. Then the return is ___? i =

6. Understanding Interest Rate (Ch3) -- Fin331 6 2. Fixed Payment Loan (i =?) LV = FP + FP + FP +... + FP (1+i) (1+i) 2 (1+i) 3 (1+i) N $1000 = $126 + $126 + $126 +... + $126 (1+i) (1+i) 2 (1+i) 3 (1+i) 25 Yield to Maturity: Fixed Payment Loans

7. Understanding Interest Rate (Ch3) -- Fin331 7 You planned to buy a house for $350,000. You will pay 20 percent down payment. You will also arrange a 30-year 6% APR mortgage. What is your monthly payment?

8. Understanding Interest Rate (Ch3) -- Fin331 8 Yield to Maturity: Coupon Bonds 3. Coupon Bond (Coupon rate = 10% = C/F) P = $100 + $100 + $100 +... + $100 + $1000 (1+i) (1+i) 2 (1+i) 3 (1+i) 10 (1+i) 10 P = C + C + C +... + C + F (1+i) (1+i) 2 (1+i) 3 (1+i) N (1+i) N Fixed coupon payments of $C forever P = C i = C i P

9. Understanding Interest Rate (Ch3) -- Fin331 9 Relationship Between Price and Yield to Maturity Three Interesting Facts 1. When bond is at par, yield equals coupon rate 2. Price and yield are negatively related 3. Yield greater than coupon rate when bond price is below par value

10. Understanding Interest Rate (Ch3) -- Fin331 10 In-class Exercise Quantitative Problem 3, Page 69

11. Understanding Interest Rate (Ch3) -- Fin331 11 4. One-year Discount Bond (P = $900, F = $1000) i = F - P P i = Yield to Maturity: Discount Bonds

12. Understanding Interest Rate (Ch3) -- Fin331 12 Other Bonds Reporting 1.Current yield - Corporate Bonds 2.Yield on a discount basis - Treasury Bill

13. Understanding Interest Rate (Ch3) -- Fin331 13 Current Yield i c = C P Two Characteristics 1. Is better approximation to yield to maturity, nearer price is to par and longer is maturity of bond 2. Change in current yield always signals change in same direction as yield to maturity

14. Understanding Interest Rate (Ch3) -- Fin331 14 Yield on a Discount Basis Example: One-year bill, P = $900, F = $1000 Two Characteristics 1.Understates yield to maturity; longer the maturity, greater is understatement 2.Change in discount yield always signals change in same direction as yield to maturity

15. Understanding Interest Rate (Ch3) -- Fin331 15 Bond Page of the Newspaper

16. Understanding Interest Rate (Ch3) -- Fin331 16 Distinction Between Real and Nominal Interest Rates Real interest rate: Interest rate that is adjusted for expected changes in the price level i r = i - π e 1. Real interest rate more accurately reflects true cost of borrowing 2. When real rate is low, greater incentives to borrow and less to lend if i = 5% and π e = 0% then: i r = 5% - 0% = 5% if i = 10% and π e = 20% then i r = 10% - 20% = - 10%

17. Understanding Interest Rate (Ch3) -- Fin331 17 U.S. Real and Nominal Interest Rates

18. Understanding Interest Rate (Ch3) -- Fin331 18 Distinction Between Interest Rates and Returns

19. Understanding Interest Rate (Ch3) -- Fin331 19 Calculate One-year return for investing a 10 year 10% coupon rate bond when interest rise from 10% to 20% Formula: Assuming face value is $1000, then C = P(t) P(t+1)

20. Understanding Interest Rate (Ch3) -- Fin331 20 Key Facts about Relationship Between Rates and Returns

21. Understanding Interest Rate (Ch3) -- Fin331 21 Maturity and the Volatility of Bond Returns 1. Only bond whose return = yield is one with maturity = holding period 2. For bonds with maturity > holding period, i  P  implying capital loss 3. Longer is maturity, greater is price change associated with interest rate change 4. Longer is maturity, more return changes with change in interest rate 5. Bond with high initial interest rate can still have negative return if i 

22. Understanding Interest Rate (Ch3) -- Fin331 22 Maturity and the Volatility of Bond Returns Conclusion from Table 2 Analysis 1. Prices and returns more volatile for long-term bonds because have higher interest- rate risk 2. No interest-rate risk for any bond whose maturity equals holding period

23. Understanding Interest Rate (Ch3) -- Fin331 23 Reinvestment Risk 1. Occurs if hold series of short bonds over long holding period 2. i at which reinvest uncertain 3. Gain from i , lose when i 