Interest rates have fallen over the seven years since a $1,000 par, 10-year bond was issued with a coupon of 7%. What is the present value of this bond if the required rate of return is currently four and one-half percent? (For simplicity, assume annual payments.) 
 
  
 
Each of the remaining cash flows on the bond is discounted at the annual rate of 4.5%. 
| 
 Period   | 
 Payment   | 
 Discount   | 
 PV   |  
| 
  1   | 
 $1,000 × 7% = $70   | 
 (1.045)1   | 
 $ 66.99   |  
| 
  2   | 
 $1,000 × 7% = $70   | 
 (1.045)2   | 
 $ 64.10   |  
| 
  3   | 
 $1,000 × 7% = $70   | 
 (1.045)3   | 
 $ 61.34   |  
| 
  3   | 
 $1,000 principal   | 
 (1.045)3   | 
 $ 876.30   |  
| 
 Total Present Value of Cash Flows   | 
 $1,068.73   |    
The present value can also be determined with a financial calculator. N = 3, I = 4.5%, PMT = $1,000 × 7%, FV = $1,000. Solve for PV = $1,068.724.   
  |