Halfway done!
Feb. 1st, 2004 04:45 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
sinjunOkay, so far today, I have …
- washed the dishes,
- watered all the plants downstairs,
- cleaned the kitty litter,
- snuggled all three cats,
- put a load of laundry in the washer and then into the dryer,
- started my next load of laundry,
- talked on the phone to the 2 people who have called me,
- chatted on icq,
- and done at least some of my assignment.
So, here’s
Question 3
Find the value of a 40-year bond with the following features. The coupon rate for the first 20 years will be 6% of the face value of $1000. After 20 years, the coupon rate will be 7% for the remaining 20 years. The company is rated AA (AA rated bonds are trading at 0.50% premium over the treasury bond rate of 6.50%). Coupon payments are semi-annual.
Since this is an AA bond, the market rate is 7.0% (6.50% + 0.50% premium). To determine the face value of the bond, we need to find the present value of $1000, when
r = 3.5% = 7.0% per year / 2 periods per year and
t = 80 periods = 40 years * 2 periods per year.
Present value = C / (1 + r)**t
= 1000 / (1.035**80)
=63.79
For the first 20 years, we have a 6% coupon rate, which is 60$, but it’s paid semi-annually, which means we get $30 every 6 months, for 20*2 = 40 periods.
Annuity present value of the coupon = 30 * (1 – 1/1.035**40) / 0.035
= 640.65
For the remaining 20 years, we have a 7% coupon rate, which is 70$, but paid semi-annually, so we get $35 every 6 months, for 20*2 = 40 periods.
Annuity present value of the coupon = 35 * (1 – 1/1.035**40) / 0.035
= 747.43
The value of the bond is the sum of these three parts = 63.79 + 640.65 + 747.43 = 1,451.87
And just to prove the point, here’s .
Question 4
XYZ Company issued a bond on January 1, 1995. It has a 12% coupon rate and matures in 30 years. Coupon payments are made semi-annually.
a) What was the YTM on January 1, 1995?
YTM, as defined on page 194 of the textbook, is the market interest rate that equates a bond’s present value of interest payments and principal repayment with its price. In this case, we have a new bond, where the market interest = coupon rate. So, the YTM is 12%.
b) What was the price on January 1, 2000 if interest rates had fallen by 2% since the bond was issued?
r = Market rate = 12 – 2 = 10% which can be stated as 5% per 6 months.
t = 25 years which is 25 * 2 = 50 periods of 6 months
face value = 1,000
coupon = 120$ per year, which is paid out as $60 every 6 months.
Present value of the face amount = 1000 / 1.05**50 = $87.20
Present value of the coupons = 60 * [1 – (1/1.05**50)] / 0.05 = $1,095.36
Bond value = present value of the face amount + present value of the coupons
= $87.20 + $1,095.36
= $1,182.56
The price on January 1, 2000, if interest rates had fallen by 2%, was $1,182.56
c) You expect that on July 1, 2015 bonds with 9 to 10 years to maturity will have YTM’s of 6%. What will be the price of the bond then?
t = 9.5 years = 19 periods.;
YTM = 6%, so r = 3%;
Face value = 1000;
Coupon = $60 per 6 months;
Present value of the face amount = 1000 / 1.03**19 = $570.29
Present value of the coupons = 60 * [1 – (1/1.03**19)] / 0.03 = $859.43
Bond value = present value of the face amount + present value of the coupons
= $570.29 + $859.43 + 60
= $1,429.72
The price of the bond would be $1,429.72
- washed the dishes,
- watered all the plants downstairs,
- cleaned the kitty litter,
- snuggled all three cats,
- put a load of laundry in the washer and then into the dryer,
- started my next load of laundry,
- talked on the phone to the 2 people who have called me,
- chatted on icq,
- and done at least some of my assignment.
So, here’s
Question 3
Find the value of a 40-year bond with the following features. The coupon rate for the first 20 years will be 6% of the face value of $1000. After 20 years, the coupon rate will be 7% for the remaining 20 years. The company is rated AA (AA rated bonds are trading at 0.50% premium over the treasury bond rate of 6.50%). Coupon payments are semi-annual.
Since this is an AA bond, the market rate is 7.0% (6.50% + 0.50% premium). To determine the face value of the bond, we need to find the present value of $1000, when
r = 3.5% = 7.0% per year / 2 periods per year and
t = 80 periods = 40 years * 2 periods per year.
Present value = C / (1 + r)**t
= 1000 / (1.035**80)
=63.79
For the first 20 years, we have a 6% coupon rate, which is 60$, but it’s paid semi-annually, which means we get $30 every 6 months, for 20*2 = 40 periods.
Annuity present value of the coupon = 30 * (1 – 1/1.035**40) / 0.035
= 640.65
For the remaining 20 years, we have a 7% coupon rate, which is 70$, but paid semi-annually, so we get $35 every 6 months, for 20*2 = 40 periods.
Annuity present value of the coupon = 35 * (1 – 1/1.035**40) / 0.035
= 747.43
The value of the bond is the sum of these three parts = 63.79 + 640.65 + 747.43 = 1,451.87
And just to prove the point, here’s .
Question 4
XYZ Company issued a bond on January 1, 1995. It has a 12% coupon rate and matures in 30 years. Coupon payments are made semi-annually.
a) What was the YTM on January 1, 1995?
YTM, as defined on page 194 of the textbook, is the market interest rate that equates a bond’s present value of interest payments and principal repayment with its price. In this case, we have a new bond, where the market interest = coupon rate. So, the YTM is 12%.
b) What was the price on January 1, 2000 if interest rates had fallen by 2% since the bond was issued?
r = Market rate = 12 – 2 = 10% which can be stated as 5% per 6 months.
t = 25 years which is 25 * 2 = 50 periods of 6 months
face value = 1,000
coupon = 120$ per year, which is paid out as $60 every 6 months.
Present value of the face amount = 1000 / 1.05**50 = $87.20
Present value of the coupons = 60 * [1 – (1/1.05**50)] / 0.05 = $1,095.36
Bond value = present value of the face amount + present value of the coupons
= $87.20 + $1,095.36
= $1,182.56
The price on January 1, 2000, if interest rates had fallen by 2%, was $1,182.56
c) You expect that on July 1, 2015 bonds with 9 to 10 years to maturity will have YTM’s of 6%. What will be the price of the bond then?
t = 9.5 years = 19 periods.;
YTM = 6%, so r = 3%;
Face value = 1000;
Coupon = $60 per 6 months;
Present value of the face amount = 1000 / 1.03**19 = $570.29
Present value of the coupons = 60 * [1 – (1/1.03**19)] / 0.03 = $859.43
Bond value = present value of the face amount + present value of the coupons
= $570.29 + $859.43 + 60
= $1,429.72
The price of the bond would be $1,429.72
