Question

a. What is the difference between coupon rate and yield to maturity? How do you use the coupon rate to calculate the periodic payment received from a bond?

b. What is the price of a bond that is currently trading at a yield of 10% and has a face value of $1,000? This bond still has exactly 5 years to maturity. This bond pays semi-annual coupon at an annual rate of 8% (i.e., each coupon is 4%). Show how you found the value. Solving this in a calculator or at some other website that allows you to solve this kind of questions and just putting the value is not going to be an acceptable answer.

c. What is meant by duration of a bond? Describe the steps followed in finding the duration of a bond in Excel when built-in Excel functions are not used.

d. Calculate modi?ed Duration of a bond that pays annual coupon at a rate of 6% and matures in 2 years. This bond has face value of 1,000 and is currently selling at a yield of 8%. Show calculations. Using just modified duration, if yield changes by 0.5%, what is the expected change in the price of the bond? Show calculations. Solving this in a calculator or at some other website that allows you to solve this kind of questions and just putting the value is not going to be an acceptable answer.

Answer 1

a. What is the difference between coupon rate and yield to maturity? How do you use the coupon rate to calculate the periodic payment received from a bond?

Coupon rate is fixed payment which a bond holder receives for holding a bond. Yield to Maturity is prevailing market interest rate on bond and it is a annualize market return on bond.

Coupon calculation = Coupon rate x Face value x Frequency of coupon in year / Year

Frequency of coupon if annual is = 1; Semiannual = 2 ; Quarterly = 4; Monthly = 12

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b. What is the price of a bond that is currently trading at a yield of 10% and has a face value of $1,000? This bond still has exactly 5 years to maturity. This bond pays semi-annual coupon at an annual rate of 8% (i.e., each coupon is 4%). Show how you found the value. Solving this in a calculator or at some other website that allows you to solve this kind of questions and just putting the value is not going to be an acceptable answer.

F = Face value =	$1,000.00
C = Coupon rate =	4.00%
R = Yield = YTM =	5.00%
N = Number of coupon payments till maturity =	10
Formula for bond value = (C x F x ((1-((1+R)^-N)) / R) + (F/(1+R)^N)
Bond Value = ((4%)*1000*((1-((1+(5%))^-10))/(5%))+(1000/(1+(5%))^10))
Bond Value = ((4%)*1000*((1-((1+(5%))^-10))/(5%))+(1000/(1+(5%))^10))	$922.78

c. What is meant by duration of a bond? Describe the steps followed in finding the duration of a bond in Excel when built-in Excel functions are not used.

Bond duration is sensitivity of the bond which is obtained by combination of fixed payment, yield and term of the bond. It denotes the price sensitivity of the bond.

Calculation of bond duration:

1.       Calculate the present value of each node of cash flows of bond

2.       If we give each node equal weight then the sum of each present value will make Bond price today

3.       Now, if we give each node a time weight then we will get weight cash flow of the bond that will become our weighted present value of the bond

4.       Finally, divided point 3 / Point 2 this will throw a bond duration in years.

d. Calculate modi?ed Duration of a bond that pays annual coupon at a rate of 6% and matures in 2 years. This bond has face value of 1,000 and is currently selling at a yield of 8%. Show calculations. Using just modified duration, if yield changes by 0.5%, what is the expected change in the price of the bond? Show calculations. Solving this in a calculator or at some other website that allows you to solve this kind of questions and just putting the value is not going to be an acceptable answer.

	YTM 8%	YTM 8.5%
F = Face value =	$1,000.00	$1,000.00
C = Coupon rate =	6.00%	6.00%
R = Yield = YTM =	8.00%	8.50%
N = Number of coupon payments till maturity =	2	2
Formula for bond Price = (C x F x ((1-((1+R)^-N)) / R) + (F/(1+R)^N)
Bond Value =	$964.33	$955.72

Expected change in price = 955.72-964.33 = -$8.61 (For rise in yield by 0.5%

Modified duration = D* ; ?y = Change in yield ; ?P = Change in price; P = Initial price

?P/P = -D*(?y)

(955.72-964.33)/964.33 = -D*(0.50%)

D* = 0.008928479/0.50%

D*= 1.78570