Finance 300 Financial Markets Lecture 8 Professor J. Petry, Fall, 2002©

2 Housekeeping Equity projects due October 3 rd. You should be done with the numerical analysis, now focusing on writing the text. Form investment challenge teams this week for start on October 1 st. Next exam is October 15 th, will cover chapters IV and V. Class on October 10 th may have to be cancelled. I will keep you posted.

3 Debt Markets & Interest Rates Bond A certificate which is evidence of a debt obligation Specifies the rate of interest, and other terms of the loan Interest Interest rate: the factor by which money today can be exchanged for money tomorrow; the price or cost of money; the compensation necessary to induce putting off consumption from today to tomorrow.

4 Debt Markets & Interest Rates Real & Nominal Rates of Interest Fisher’s Law states that the nominal interest rate is the real interest rate adjusted for inflation. Adjusting the real interest rate for inflation, keeps the inter-temporal dollars whole—we care about how much it can buy, not its nominal value. The real rate is the actual payment for delaying consumption. Example: nominal interest rates are 6% Inflation is 2.5% Therefore, real interest rate is approximately 3.5% (1+ r) = (1+ i ) / (1 + π); r = ( i – π ) / ( 1 + π ) r = real rate of interest; i = nominal rate of interest; π = inflation rate (book uses p-prime for inflation).

5 Debt Markets & Interest Rates Example: (1+ r) = (1+ i ) / (1 + π); (1+ r) = (1+.06 ) / ( ) = 1.06/1.025 = = 3.41% r = ( i – π ) / ( 1 + π ) r = (.06 –.025 ) / ( ) = / = 3.41% Example 2: Find r (using both calculations) if inflation is 20%, and nominal interest rate is 26%.

6 Debt Markets & Interest Rates Compounding & Discounting Much of financial analysis involves cash flows which occur at different times. Future value = the value of cash flows translated into future dollars. To find a future value we compound Example: What is the real future value of $500 in 4 years at a 3% real interest rate? 500 * (1.03) 4 = 500 * = $ What is the nominal future value of $1000 in 5 years at 6% nominal interest rate?

7 Debt Markets & Interest Rates Compounding & Discounting Present Value = the value of cash flows translated into present dollars. To find a present value we discount future cash flows. Example: What is a cash flow of $500 in 10 years worth this year if interest rates are 5%? $500 / (1.05) 10 = 500 / = $ What is the present value of $1000 in 5 years at 6% nominal interest rate?

8 Debt Markets & Interest Rates Things to Do IV –1 You win the Investment Challenge and the prize is $1600: $100 in 2003; $200 in 2004, $300 in 2005 and $1000 in All prizes are paid out on May 1. Calculate how much money the Investment Challenge Administration should have put aside on May 1, 2002 to pay these prizes. (present value) Calculate how much money you would have in the bank on May 1, 2006 if you put each payment in the bank when you received it and the bank paid 3% interest. (future value) Calculate the future and present value of the same cash flows if the expected interest rates are 3% in 02/03, 4% in 03/04, 5% in 04/05 and 6% in 05/06 with interest rates valid from May 1 to May 1.

9 Debt Markets & Interest Rates Bonds A bond is a loan. The borrower will issue a certificate which promises a specific interest rate (coupon), plus a guarantee of repayment of the principal amount at some future specified maturity date. Coupon—the rate of interest on the bond when issued at par. Bonds were issued as bearer bonds (who ever had it in their possession could cut off the coupon, and send it in for payment on the appropriate day). Now almost all bonds are registered bonds—whoever is the registered owner gets the payment automatically. Principal—The principal payment is the amount of the loan on which interest is calculated. Often referred to as the face value, it is generally repaid at the end of the loan on the maturity date. Maturity Date—The date at which the final payment is made on the loan and the bond contract expires. The coupon rate, principal value and maturity date are engraved on the bond and thus never change for the life of the bond. If this is true, how do interest rates adjust to economic conditions over time? Don’t interest rates change over time?

10 Debt Markets & Interest Rates Bonds Negotiable—A security which may be bought or sold in the secondary market. This is the defining characteristic of bonds vs. loans. Premium —When a bond sells for more than its face value, it sells at a premium. If you buy a bond at a premium, it will yield less than the coupon rate if you hold it to maturity. –10 year bond originally issued at $100 face value, with 8% coupon. Market interest rates go to 5%. Is this bond worth $100? What happens to its interest rate? Discount—When a bond sells for less than its face value it sells at a discount. If you buy a bond at a discount, it will yield more than its coupon rate if you hold to maturity. –10 year bond originally issued at $100 face value, with 8% coupon. Market interest rates go to 12%. Is this bond worth $100? What happens to its interest rate? Par—When a bond sells for precisely its face value, it sells for par. If you buy a bond at par it will yield exactly its coupon rate if you hold it to maturity. –If you buy & hold to maturity the 10 year bond, what is your interest rate?

11 Bond Pricing

12 Bond Pricing The price of a bond is given by:

13 Bond Pricing Where: C t = coupon rate x principal/2 = $30,000 = (.06 x $1,000,000)/2 P = Principal; Yd = Market Yield n = Maturity; Term to maturity in years Which is nothing more than the sum of the net present values of the amounts paid Price yield calculation assumes semi-annual compounding because in US almost all bonds pay twice a year. The first formula is most easily applied when using excel, while the second version can be completed with calculator. We will also use the calculator to find these numbers for us.

14 Bond Pricing So what is our bond worth to us at issuance if mkt yld = 6%? Which equals? Now do the calculations using the second formula.

15 Bond Pricing Or using the calculator to find the same answer...