a) What is the value of a 10-year, $1,000 par value bond with a 10% coupon paid

Question

a) What is the value of a 10-year, $1,000 par value bond with a 10% coupon paid semi-annually if its required rate of return is 10%?

b) What would its value be if, just after it had been issued, the expected inflation rate rose by 3% causing investors to require a 13% return? Would it become a discount or premium bond?

c) What would its value be if, just after it had been issued, the expected inflation rate declined and investors require a 7% return? Would it become a discount or premium bond?

d) Suppose a 10-year, 10% semiannual coupon bond with a par value of $1,000 is currently selling for $1,135.90 producing a nominal YTM of 8%. However, the bond can be called after 5 years for a price of $1,050. What is its nominal YTC?

Explanation / Answer

a) Face value (FV) 1000 Coupon rate 10.00% Number of compounding periods per year 2 Interest per period (PMT)                                              50.00 Number of years to maturity 10 Number of compounding periods till maturity (NPER) 20 Market rate of return/Required rate of return 10.00% Market rate of return/Required rate of return per period (RATE) 5.00% Bond price PV(RATE,NPER,PMT,FV) Bond price $                                    1,000.00 PV(5%,20,50,1000)*-1 b) Face value (FV) 1000 Coupon rate 10.00% Number of compounding periods per year 2 Interest per period (PMT)                                              50.00 Number of years to maturity 10 Number of compounding periods till maturity (NPER) 20 Market rate of return/Required rate of return 13.00% Market rate of return/Required rate of return per period (RATE) 6.50% Bond price PV(RATE,NPER,PMT,FV) Bond price $                                        834.72 PV(6.5%,20,50,1000)*-1 It became disocunted bond c) Face value (FV) 1000 Coupon rate 10.00% Number of compounding periods per year 2 Interest per period (PMT)                                              50.00 Number of years to maturity 10 Number of compounding periods till maturity (NPER) 20 Market rate of return/Required rate of return 7.00% Market rate of return/Required rate of return per period (RATE) 3.50% Bond price PV(RATE,NPER,PMT,FV) Bond price $                                    1,213.19 PV(3.5%,20,50,1000)*-1 It became premium bond d) Call price (here it is FV) $                                    1,050.00 Coupon rate 10.00% Number of compounding periods per year 2 Interest per period (PMT)                                              50.00 Bond price (PV) $                                  -1,135.90 Number of years to call 5 Number of compounding periods till call (NPER) 10 Bond Yield to call RATE(NPER,PMT,PV,FV) Bond Yield to call 6.75% RATE(10,50,-1135.9,1000)*2

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