An investor buys a 3.8% annual payment bond with 8 years to maturity. The bond is...

An investor buys a 3.8% annual payment bond with 8 years to maturity. The bond is priced at a yield-to-maturity of 5.6%. What is the bond’s Macaulay duration?

Expert Solution

Calculation of Macaulay duration of the bond

Maturity Period =	8 years
Face value (assumed) =	$1,000
Coupon Rate =	3.80%
Coupon payment at 3.8% of face value	$38.00
Yield-to-maturity	5.60%

Year (t)	Cash Flow from coupon payments and maturity amount (CF)	Present value (PV) discounted at 5.6% [=CF/(1+5.6%)^t]	PV *t
1	$38.00	$35.98	$35.98
2	$38.00	$34.08	$68.15
3	$38.00	$32.27	$96.81
4	$38.00	$30.56	$122.23
5	$38.00	$28.94	$144.69
6	$38.00	$27.40	$164.42
7	$38.00	$25.95	$181.65
8	$1,038.00	$671.25	$5,370.02
sum		$886.43	$6,183.96
		Bond's Price↑
	Macaulay duration = sum of (PV*t)/sum of PVs =	$6183.96/$886.43	6.98	Years

Macaulay duration of the bond is 6.98 years

Formulas used in excel calculation:

jeff jeffy answered 4 months ago

. An investor buys a 10 year, 8% annual coupon bond at par (so the yield-to-maturity...

. An investor buys a 10 year, 8% annual coupon bond at par (so the yield-to-maturity must be 8%), and sells it after three years (just after the coupon is recieved). Interest rates rise immediately after the purchase, and the bond’s yield-to-maturity jumps to 10% and remains there for the rest of the three year period. Assume coupons are reinvested at the new yield-to-maturity. Show the components of the investor’s “total return,” or portfolio value at the end of the...

An investor buys 6% semi-annual coupon paying bond with six years to maturity and $1000 par...

An investor buys 6% semi-annual coupon paying bond with six years to maturity and $1000 par value at $906.15.The bond has a YTM of 8%. For all the calculations ,keep four digits after the decimal place b)Calculate the bond's modified duration c)If the interest rate increases by 20 basis points, what is the approximate value of the bond by using modified duration? d)What is the real value of the bond after the change (using the bond pricing formula )?

An investor buys a bond with the following characteristics: Maturity - 10 years Coupon - 4.5%,...

An investor buys a bond with the following characteristics: Maturity - 10 years Coupon - 4.5%, paid once per year Nominal Value - £100 The yield to maturity at the time of purchase is 8.50%. The investor sells the bond immediately after the sixth coupon payment, when the yield to maturity rises to 9.50%. c.Use the modified Macaulay duration to calculate what the price of the above bond would have been immediately after purchase, if the yield to maturity had...

A firm has a bond with 12 years to maturity, and pays an annual coupon payment...

A firm has a bond with 12 years to maturity, and pays an annual coupon payment of 8%. The bond is currently selling for $1,122.40. When the company issues a new bond, there will be administrative costs and flotation costs estimated at $25 per bond. If the firm decides to issue new 10-year bonds today, what would be the effective cost of the new bonds, assuming a 35% marginal tax rate? A. 6.85 percent B. 6.94 percent C. 7.19 percent...

An investor owned a 9 percent annual payment coupon bond for six years that was originally...

An investor owned a 9 percent annual payment coupon bond for six years that was originally purchased at a 9 percent required return. She did not reinvest any coupons (she kept the money under her mattress). She redeemed the bond at par. What was her annual realized rate of return? What if she did reinvest the coupons but only earned 5 percent on each coupon? Why are your answers not equal to 9 percent?

For a semi-annual coupon bond with 3 years to maturity, an annual coupon of 8% (paid...

For a semi-annual coupon bond with 3 years to maturity, an annual coupon of 8% (paid 4% each six-month period), and a current yield to maturity of 4.5%, What is the Macauley duration of this bond? What is the modified duration of this bond? An investor owns $100M (market value or price NOT face or par) of these bonds, what is the Dollar Duration of this position? What is the price elasticity of this bond for a 1bp increase in...

A bond is issued with 15 years to maturity and an annual coupon of 8%. Similar bonds...

A bond is issued with 15 years to maturity and an annual coupon of 8%. Similar bonds are yielding 7%. Calculate the current price of the bond.

Bond X is noncallable and has 20 years to maturity, an 8% annual coupon, and a...

Bond X is noncallable and has 20 years to maturity, an 8% annual coupon, and a $1,000 par value. Your required return on Bond X is 9%; if you buy it, you plan to hold it for 5 years. You (and the market) have expectations that in 5 years, the yield to maturity on a 15-year bond with similar risk will be 6.5%. How much should you be willing to pay for Bond X today? (Hint: You will need to...

Bond X is noncallable and has 20 years to maturity, a 8% annual coupon, and a...

Bond X is noncallable and has 20 years to maturity, a 8% annual coupon, and a $1,000 par value. Your required return on Bond X is 9%; if you buy it, you plan to hold it for 5 years. You (and the market) have expectations that in 5 years, the yield to maturity on a 15-year bond with similar risk will be 10%. How much should you be willing to pay for Bond X today? (Hint: You will need to...

A bond has four years to maturity, an 8% annual coupon and a par value of...

A bond has four years to maturity, an 8% annual coupon and a par value of $100. The bond pays a continuously compounded interest of 5%. a. What would the actual percentage change in the price of the bond be if the interest rate goes up from 5% to 6%? b. What would be the percentage change in the price of the bond implied by the duration approximation? c. What would be the percentage change in the price of the...

Question