Consider a corporate bond with a face value of $1,000, 2 years to maturity and a

Question

Consider a corporate bond with a face value of $1,000, 2 years to maturity and a coupon rate of 5%. Coupons are paid semi-annually. The next coupon payment is to be made exactly 6 months from today. What is this bond's YTM assuming the following spot rate curve.

6-month spot rate: 4%.

12-month: 5%.

18-month: 5.5%.

24-month: 5.8%.

Round your answer to 4 decimal places. For example if your answer is 3.205%, then please write down 0.0321.

Hint: It is helpful to first compute the price, and then compute the YTM based on the bond price.

Keep in mind the definition that the stated spot rates are yields (YTM) on zero coupon Treasuries.

Explanation / Answer

Step1: Computation of the price of bond.We have,

Price of bond = C / (1+r)n + Face Value / (1+r)n

Where,

C = Coupon payment(Semi-annually) = 1,000 x 5/2 % = $ 25

Face Value = $ 1,000

n = Number of semi-annual year = 2 x 2 = 4

r = YTM( using the spot rate curve)

Putting these value in the above equation.We get:

Price of bond = 25/(1.04) + 25/(1.04)(1.05) + 25/( 1.04)(1.05)(1.055) + 25/ ( 1.04)(1.05)(1.055)(1.058)

+ 1,000 / ( 1.04)(1.05)(1.055)(1.058)

Price of bond = 24.04 + 22.89 + 21.70 + 20.51 + 820.43 = $ 909.57

Hence,the price of the bond is $ 909.57

Step2: Computation of the YTM of the bond using approximate YTM formula.We have,

YTM = [C + (M - P)/n] / ( 0.4M + 0.6P)

Where,

C = coupon payment = $ 25

M = Maturity value of bond = $ 1,000

P = Present price of the bond = $ 909.57

n = Semi-years to maturity = 4

putting these value on the above formula.We have,

YTM = [25 + (1,000 - 909.57)/4 ] / ( 0.4X 1,000 + 0.6 X 909.57)

YTM = (25 + 22.60) / ( 400 + 545.74)

YTM = 47.60 / 945.74 = 0.0503

Hence,the YTM of the bond is 0.0503

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