Question

Suppose a bond has a 6% coupon rate and pays coupons semiannually, the current price is $883 and the par value is $1000. The bond has 4 years remaining until maturity.

a. what is the YTM of the bond?

b. What is the Macaulay duration of the bond?

c. what is the modified duration of the bond?

Answer 1

(a) Coupon Rate = 6 % per annum payable semi-annually, Current Price = Pm = $ 883, Par Value = P0 = $ 1000, Remaining Maturity = 4 years of 8 half-years

Let the YTM be 2R

Semi-Annual Coupon = 0.5 x 0.06 x 1000 = $30

883 = 30 x (1/R) x [1-{1/(1+R)^(8)}] + 1000 / (1+R)^(8)

Using EXCEL's Goal Seek Function to solve the above equation, we get:

R = 4.795% approximately

YTM = 2 x R = 2 x 4.795 = 9.59 %

(b) & (c)