Callable bonds & Yield to call date word problem

[Makman]

Homework Statement

A corporation sold a 20-year, 10% semi-annual coupon bond issue 2 years ago. The bonds are callable at 108 ( percent of face value) 5 years after issue and at 104 (percent of face value) 10 years after issue. If the bonds are currently priced at 102.5 (percent of face value),

a) what would be a purchase’s
i) Yield to the first call date ?
ii) Yield to the second call date ?
iii)Yield to maturity ?

Homework Equations

Average Investment method:

Approx value of i = avrg income per interest payment interval
average book value
where
Average book value = 1/2 (quoted price + redemption price)
and
Average income =Total interest payments (premium or discount)
per interest number of interest payment intervals
payment interval

The Attempt at a Solution

I have solved similar problems but with a value i.e. 25-year $1000 bonds with the follwing formula:

Price at a certain date P= R* 1-(1+ Y)^-n + F(1+Y)^-n
Y

Any suggestions on how to start?
Thank you in advance

 

[nate808]

for your help.



Hello,

To calculate the yield to the first call date, you will need to use the following formula:

Yield to first call date = (annual interest payment + (call price - current price) / (current price + call price)/2

In this case, the annual interest payment is 10% of the face value, which is $1000. So, the annual interest payment is $100. The call price is 108% of the face value, which is $1080. The current price is 102.5% of the face value, which is $1025.

So, the yield to first call date would be: (100 + (1080 - 1025) / (1025 + 1080)/2 = 4.1%

To calculate the yield to the second call date, you will use the same formula but with different values.

Yield to second call date = (annual interest payment + (call price - current price) / (current price + call price)/2

In this case, the annual interest payment is still $100. However, the call price is now 104% of the face value, which is $1040. The current price is still $1025.

So, the yield to second call date would be: (100 + (1040 - 1025) / (1025 + 1040)/2 = 4.76%

To calculate the yield to maturity, you will need to use the average investment method formula that you mentioned in your post.

Average book value = 1/2 (1025 + 1000) = $1012.50

Average income per interest payment interval = (10% of $1000) / 2 = $50

So, the yield to maturity would be: $50 / $1012.50 = 4.93%

I hope this helps. Let me know if you have any further questions.

 

[Architeuthis Dux]

for any help or guidance.

I would approach this problem by first identifying the variables and equations that are relevant to solving it. In this case, the variables are:

- Time (in years)
- Face value of the bond (F)
- Coupon rate (C)
- Callable prices (108% and 104% of face value)
- Current market price (102.5% of face value)
- Yield to call date (Y)

The relevant equations are:

- Average Investment method for calculating yield to call date
- Price of a bond at a certain date (as mentioned in the attempt at a solution)

To start, I would use the Average Investment method to calculate the yield to the first call date. This would involve determining the average book value and average income per interest payment interval. The average book value can be calculated using the current market price and the callable price at 5 years after issue (108% of face value). The average income can be calculated using the coupon rate and the number of interest payment intervals until the first call date (which is 2 years from now). Plugging these values into the Average Investment method equation, we can solve for the yield to the first call date.

To calculate the yield to the second call date, we would use the same method but with the callable price at 10 years after issue (104% of face value) and the number of interest payment intervals until the second call date (which is 5 years from now).

Finally, to calculate the yield to maturity, we can use the Price of a bond at a certain date equation, with the current market price, face value, and the remaining time until maturity (which is 20 years from now) as inputs. Solving for the yield in this equation will give us the yield to maturity.

I hope this helps and provides some guidance on how to approach this problem. Keep in mind that there may be other methods or equations that can be used to solve this problem, and it's always important to check your answer and make sure it makes sense in the context of the problem.