Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Chapter 4 Interest Rates and Rates of Return
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4-2 Types of Bonds Categories of bonds are used to identify variations in the timing of payments Simple loan –Involves the principal (P) and interest ( i ) –Total payment = P + iP = P(1 + i ) Discount bond –Repays in a single payment –Repays the face value at maturity, but receives less than the face value initially.
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4-3 Types of Bonds, cont’d. Coupon bond –Borrowers make multiple payments of interest at regular intervals and repay the face value at maturity –Specifies the maturity date, face value, issuer, and coupon rate (equals the yearly payment divided by face value) Fixed-payment loan –Borrower makes regular periodic payments to the lender. –Payments include both interest and principal and no lump- sum payment at maturity.
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4-4 Present Value Comparing returns across debt types is difficult since timing of repayment differs. Solution is the concept of present value: to find a common measure for funds at different times, present each in today’s dollars. The present value of $1 received n years in the future is $1/(1 + i ) n.
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4-5 Figure 4.1 Time Lines for Credit Market Instrument Repayment
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4-6 Bond Yields The interest rate that equates the present value to price is the yield to maturity. Current yield = coupon/current price. Coupon rate = coupon/face value.0
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4-7 Current Price and Face Value If current price = face value, then yield to maturity = current yield = coupon rate. If current price current yield > coupon rate. If current price > face value, then yield to maturity < current yield < coupon rate.
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4-8 Figure 4.2 Sensitivity of Bond Prices to Changes in Interest Rates
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4-9 Total Rate of Return The total rate of return is the sum of current yield and actual capital gain or loss. Rate of return can differ from yield to maturity. The formula for total rate of return is: R = C/P t + (P t+1 - P t )/P t.
Copyright © 2008 Pearson Addison-Wesley. All rights reserved Real and Nominal Interest Rates Expected real interest rate = nominal interest rate - the expected rate of inflation. Fisher hypothesis: change in expected inflation = change in nominal interest rate. The real rate of return equals the nominal rate of return adjusted for expected inflation.
Copyright © 2008 Pearson Addison-Wesley. All rights reserved Figure 4.3 Real and Nominal Interest Rates, Three-Month Treasury Bills, 1960–2005