Question

Bond A and bond B have the same maturity of 10 years and share identical risk features. Bond A has coupon rate of 5.7%, while bond B’s coupon rate is 6.7%. In each case the coupon is paid annually. If bond B is currently selling for $800, what should be bond A’s current price?

A. $864.78

B. $863.21

C. $862.20

D. $865.78

E. $740.81

F. $738.42

G. $737.41

H. $739.81

Answer 1

as both has identical risk features so the current price of bond should be the same.

suppose face value of both bond = $ 1000

Present value of bond = coupon rate*face value*PVIFA(x%,10years) + face value/maturity value*PVIF(X%,10year)

now put all the given values of Bond B in above equation:

800 = 0.067*1000*PVIFA(x%,10Years) + 1000*PVIF(X%,10year)

now the price of bond is less than its face value so the market rate of interest would be definately greater than its coupon rate.

so assume it would be 10% in that case

current value of bond = 67*PVIFA(10%,10years) + 1000*PVIF(10%,10year)

current value of bond = 67*6.144567 + 1000*0.385543

= 797.22

now assume it would be 9%

current value of bond = 67*PVIFA(9%,10years) + 1000*PVIF(9%,10year)

= 67*6.417 + 1000*0.422

= 429.98 + 422.41

= 852.39

now by intrapolation

(852.39 - 797.22) ---------------on 1%

(800-797.22) -------------------would be 1%/55.17*2.78

= 0.05%

so the market rate of interest is (10%-0.05%) = 9.95% (with rounding off diff.)

Now the current price of Bond A at market rate of interest 9.95% is as follows -

current market price of Bond A = 0.057*1000*PVIFA(9.95%, 10years) + 1000*PVIF(9.95%,10year)

= 57*6.157787 + 1000*0.3873

= 351 + 387.30

= 738.30 (Rounding off diff.)

so the correct option should be option (F) $ 738.42

Please check with your answer and let me know.