Question

# What is the price of a 4-year bond with a coupon rate of 10% and face...

What is the price of a 4-year bond with a coupon rate of 10% and face value of \$1,000? Assume the bond is trading at 10% yield, and that coupons are paid semi-annually. Assume semi-annual compounding.

What is the yield of a 3-year bond with a coupon rate of 9% and face value of \$100? Assume the bond is currently trading at a price of \$100, and that coupons are paid semi-annually. Assume semi-annual compounding.

Sol:

Calculation of Bond Price:

Here,

C = coupon rate = 1000 * 10/100 = 100

Kd = Yield rate = 10%

M = maturity value or face value = \$1000

n = periods = 4

Bond price = = C / 2 x PVIFA(Kd/2 %,2n) + M x PVIF (Kd/2 % , 2n ) [PVIFA = Present Value Interest Factor of Annuity]

= 100/2 x PVIFA(K10/2 %,2*4) + \$1000 x PVIF (K10/2 % , 2*4 ) [ PVIF = Present Value Interest Factor]

= 50 x  PVIFA(K 5%,8) + \$1000 x PVIF (K 5 % , 8 )

= 50 x 6.46 + \$1000 x 0.68

= \$1003

Calculation Of Bond Yield:

Here,

C = coupon rate = 100 * 9/100 = 9

Coupon rate semi annually = 9/2= 4.5

Current price = \$100

M = maturity value or face value = \$100

Bond Yield = Annual Interest or coupon rate(Semi annual) / Current market price

= 4.5 / \$100

= 0.045 or 4.5 %

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