Question

A​ BBB-rated corporate bond has a yield to maturity of 4.9%. A U.S. treasury security has a yield to maturity of 3.5%. These yields are quoted as APRs with semiannual compounding. Both bonds pay​ semi-annual coupons at a rate of 4.1% and have five years to maturity.    

a. What is the price​ (expressed as a percentage of the face​ value) of the treasury​ bond?

b. What is the price​ (expressed as a percentage of the face​ value) of the​ BBB-rated corporate​ bond?

c. What is the credit spread on the BBB​ bonds?

Answer 1

Lets assume the face value of these bonds = 100

a)

Price of the bond = Sum of present values of all coupons + Present value of redemption value (face value)

Present value of all the coupons = C* (1- 1/(1+r)^n) / r

C = Coupon = 100 * 4.1% = 4.1

r = Yeild rate = 3.5%

n = Number of componding periods = 5*2 = 10

Present value of all the coupons = 4.1* (1- 1/(1+0.035)^10 ) / 0.035 = 34.09

Present value of redemption value = face value/(1+r)^n

face value = 100

r = Yeild rate = 3.5%

n = Number of componding periods = 5*2 = 10

Present value of redemption value = 100/(1+0.035)^10 = 70.89

Price of the bond = 34.09 + 70.89 = 104.98

Price as percentage of face value = 104.98%

b)

Price of the bond = Sum of present values of all coupons + Present value of redemption value (face value)

Present value of all the coupons = C* (1- 1/(1+r)^n) / r

C = Coupon = 100 * 4.1% = 4.1

r = Yeild rate = 4.9%

n = Number of componding periods = 5*2 = 10

Present value of all the coupons = 4.1* (1- 1/(1+0.049)^10 ) / 0.0349 = 31.81

Present value of redemption value = face value/(1+r)^n

face value = 100

r = Yeild rate = 4.9%

n = Number of componding periods = 5*2 = 10

Present value of redemption value = 100/(1+0.049)^10 = 61.98

Price of the bond = 31.81 + 61.98 = 93.79

Price as percentage of face value = 93.79%

c)

A credit spread refers to difference in yeild of two bonds with same maturity but different credi rating.

Credit spread of BBB bond = yeild on BBB rated corporate bond - yeild on US treasury security

= 4.9 - 3.5 = 1.4 % or 140 basis points