Question

In: Finance

Consider a five-year, 8 percent annual coupon bond selling at par of $1,000. a. What is...

Consider a five-year, 8 percent annual coupon bond selling at par of $1,000.

a. What is the duration of this bond?

b. If interest rates increase by 20 basis points, what is the approximate change in the market price using the duration approximation?

Expert Solution

a

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($1,000.00)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	80.00	1.08	74.07	74.07
2	80.00	1.17	68.59	137.17
3	80.00	1.26	63.51	190.52
4	80.00	1.36	58.80	235.21
5	1,080.00	1.47	735.03	3,675.15
			Total	4,312.13

b

Macaulay duration =(∑ Duration calc)/(bond price*number of coupon per year)

=4312.13/(1000*1)

=4.312127

Modified duration = Macaulay duration/(1+YTM)

=4.31/(1+0.08)

=3.99271

Using only modified duration

Mod.duration prediction = -Mod. Duration*Yield_Change*Bond_Price

=-3.99*0.002*1000

=-7.99

%age change in bond price=Mod.duration prediction/bond price

=-7.99/1000

=-0.8%

New bond price = bond price+Modified duration prediction

=1000-7.99

=992.01

jeff jeffy answered 10 months ago

Calculate the duration for a $1,000, 4‐year bond with a 4.5 percent annual coupon, currently selling at par.

Calculate the duration for a $1,000, 4‐year bond with a 4.5 percent annual coupon, currently selling at par. Use the bond’s duration to estimate the percentage change in the bond’s price for a decrease in the market interest rate to 3.5 percent.

An 8-year $1,000 par Treasury bond pays a 7 percent semi-annual coupon. The bond has a...

An 8-year $1,000 par Treasury bond pays a 7 percent semi-annual coupon. The bond has a conversion factor of 1.025. The risk-free is 6 percent and the annual yield on the bond is 7 percent. The bond just made a coupon payment. The price of a 15-month futures contract is closest to: A. $1 049.32 B. $979.00 C. $983.32

What is the duration of a $1,000 par annual bond with an eight percent annual coupon...

What is the duration of a $1,000 par annual bond with an eight percent annual coupon maturing in five years given a yield to maturity of five percent? What is the duration of a $10,000 par semi-annual bond making payments of $300 semi-annually maturing in five and a half years given a yield to maturity of seven percent?

The Corner Grocer has an 8-year, 7 percent annual coupon bond outstanding with a $1,000 par...

The Corner Grocer has an 8-year, 7 percent annual coupon bond outstanding with a $1,000 par value. The bond has a yield to maturity of 6.4 percent. Which one of the following statements is correct if the yield to maturity suddenly increases to 7.3 percent? a. The bond price will decrease by $55.21. b. The bond price will increase by 5.25 percent. c. The bond price will decrease by 5.11 percent. d. The bond price will increase by $58.69. e....

The selling price for a bond with a $1,000 par value and a 9 percent annual...

The selling price for a bond with a $1,000 par value and a 9 percent annual coupon rate is $1,100. It will mature in 14 years, and annual coupon payments are made at the end of each year. Present annual yields on similar bonds are 10 percent. Please answer or calculate the following questions: 1. Are the bonds selling at par value, discount or premium? Explain 2. Are the bonds selling in the primary or secondary market? Explain 3. Mention two reason why...

Consider an annual-pay bond with a $1,000 par value and a 7 percent coupon rate, three...

Consider an annual-pay bond with a $1,000 par value and a 7 percent coupon rate, three years remaining to maturity, and a 9 percent yield to maturity. The duration of this bond is closest to: Group of answer choices 2.8 years 2.63 years 2.5 years

A bondholder purchased an 8 percent coupon, $1,000 par three-year bond at a 7 percent yield....

A bondholder purchased an 8 percent coupon, $1,000 par three-year bond at a 7 percent yield. Interest rates then immediately fell to 6 percent and his bond was called at a price of $1,040. He reinvested his money and earned 6 percent on the $1,040 for three years. a) Did the call help or hurt the bondholder? (20 marks) b) What was his three-year rate of return on his original investment? (5 marks)

Consider a five-year bond with a 10% coupon selling at a yield to maturity of 8%....

Consider a five-year bond with a 10% coupon selling at a yield to maturity of 8%. If interest rates remain constant, one year from now the price of this bond will be: A. Higher B. Lower C. The same D. Par

Bond XYZ is a 4-year, 8% annual coupon bond, with $1,000 par value. The required return...

Bond XYZ is a 4-year, 8% annual coupon bond, with $1,000 par value. The required return on the bond is 5.4%. 1)What is the duration, 2) What is the modified duration of this bond?

Consider a bond (with par value = $1,000) paying a coupon rate of 8% per year...

Consider a bond (with par value = $1,000) paying a coupon rate of 8% per year semiannually when the market interest rate is only 5% per half-year. The bond has three years until maturity. a. Find the bond's price today and six months from now after the next coupon is paid. (Round your answers to 2 decimal places.) Current price Price after 6 months b. What is the total (six-month) rate of return on the bond? (Do not round intermediate...