Question

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.

Round your answer to the nearest cent (2 decimal places).

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.

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

Answer 1

Sol:

Calculation of Bond Price:

Here,

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

K_d = Yield rate = 10%

M = maturity value or face value = $1000

n = periods = 4

Bond price =

= C / 2 x PVIFA(K_{d/2 %,2n}) + M x PVIF (K_{d/2 % , 2n} ) [PVIFA = Present Value Interest Factor of Annuity]

= 100/2 x PVIFA(K_{10/2 %,2*4}) + $1000 x PVIF (K_{10/2 % , 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 %