Question

Coupon 3% 9% Price ($) $939.98 1,300.10 Cash Payments ($) Year 1 Year 2 Years 3 to 6 $30 $30 $30 90 90 90 Year 7 $1,030 1,090 Calculate the duration and modified duration for the 3% bonds in the table shown above. Assume annual coupon payments and a yield to maturity of 4 percent. (Do not round intermediate calculations. Round your duration to 3 decimal places and the modified duration to 2 decimal places.) Duration Modified Duration 3% coupon bond

Answer 1

Macaulay Duration is calculated using DURATION function in Excel :

settlement = date today, which is 03/09/2020

maturity = maturity date, which is 7 years from now, or 03/09/2027

coupon = coupon rate = (annual coupon payment / face value) =   ($30 / $1,000), or 3%.

yld = yield to maturity, which is 4%

frequency = number of coupon payments per year, which is 1

DURATION is calculated to be 6.395

=DURATION(B11,B12, B13,B14,815) D E F B16 - X for А I B 11 settlement 3/9/2020 12 maturity 3/9/2027 13 coupon 3.00% 14 yld 4.00% 15 frequency 1.00 16 Macaulay Duration 6.395 17 Modified Duration 6.15

Modified Duration is calculated using DURATION function in Excel :

settlement = date today, which is 03/09/2020

maturity = maturity date, which is 7 years from now, or 03/09/2027

coupon = coupon rate = (annual coupon payment / face value) =   ($30 / $1,000), or 3%.

yld = yield to maturity, which is 4%

frequency = number of coupon payments per year, which is 1

MDURATION is calculated to be 6.15

B17 x fc =MDURATION(B11,112,113,114,815) C F 13 11 settlement maturity coupon 14 yld 15 frequency 16 Macaulay Duration 17 Modified Duration A B 3/9/2020 3/9/2027 3.00% 4.00% 1.00 6.395 6.15 19