Chapter 11, Problem 3CP

Summary Introduction

(A)

Bonds:

A bond is defined as a debt instrument which is usually created for the purpose of raising capital. Bonds are also known as fixed- income securities.

This is an agreement between an investor and a bond issuer, wherein the issuer of the bond is under obligation to pay a specified amount at a future date specified.

To determine:

To evaluate specific bond issues using the given information provided.

1. The price and yield behavior of the two bonds under each scenario
2. Strong Economic recovery with rising inflation expectations
3. Economic recession with reduced inflation expectations.

Explanation of Solution

Monticello Corporation Bond Information:

	Bond A( Callable)	Bond B( Non-Callable)
Maturity	2022	2022
Coupon	11.05%	7.25%
Current price	125.75	100.00
Yield to Maturity	7.70%	7.25%
Modified duration to maturity	6.20	6.80
Call date	2016	-
Call Price	105	-
Yield to call	5.10%	-
Modified Duration to call	3.10	-

1. Based on information and Yield and Duration of two bond A and bond B provided in tabular Comparison of price and yield of a bond is mentioned below:
2. The market interest rate and yield in case of strong economic recovery with rising inflation on the bond will increase.

If the market rates of return will increase then the Price of both the bonds will decrease. The probability of call of Bond A will decrease, when the price of bond will decrease.

So both will behave in the same manner whether it is callable or a non-callable bond.

Again, the duration of bond A is slightly less than duration of bond B, it means that the bond A is performing somewhat better than Bond B.

3. In case of economic recession with reducing inflation the market interest rate and yield on bond will decrease. If market rate of return will decrease then Price of both bonds will increase. If the price of the bond will increase then the probability of call of Bond A will increase. The relevant duration calculation for the callable bond is now its modified duration to call.

Summary Introduction

(B)

Bonds:

A bond is defined as a debt instrument which is usually created for the purpose of raising capital. Bonds are also known as fixed- income securities.

This is an agreement between an investor and a bond issuer, wherein the issuer of the bond is under obligation to pay a specified amount at a future date specified.

To determine:

The projected price change for bond B if the yield-to-maturity for this bond falls by 75 basis points

Answer to Problem 3CP

Hence, projected price change of bond B with change in YTM of bond is $5.10\%$ and Price of callable bond = Price of non - callable bond - price of option.

Explanation of Solution

Monticello Corporation Bond Information:

	Bond A( Callable)	Bond B( Non-Callable)
Maturity	2022	2022
Coupon	11.05%	7.25%
Current price	125.75	100.00
Yield to Maturity	7.70%	7.25%
Modified duration to maturity	6.20	6.80
Call date	2016	-
Call Price	105	-
Yield to call	5.10%	-
Modified Duration to call	3.10	-

YTM of Bond B = 7.25%

Modified duration for Bond b = 6.80%

Change in YTM = 0.75%

Projected price change of bond B with change in YTM of bond is calculated below using following formula:

$\begin{array}{l}\text{Projected}\text{price}\text{change=Modified}\text{duration×Change}\text{in}\text{YTM}\\ \text{=6}\text{.80×0}\text{.75\%}\\ \text{=5}\text{.10\%}\end{array}$

Hence, projected price change of bond B with change in YTM of bond is $5.10\%$ .

Summary Introduction

(C)

Bonds:

A bond is defined as a debt instrument which is usually created for the purpose of raising capital. Bonds are also known as fixed- income securities.

This is an agreement between an investor and a bond issuer, wherein the issuer of the bond is under obligation to pay a specified amount at a future date specified.

To determine:

The shortcoming of analyzing bond A strictly to call or to maturity

Explanation of Solution

Monticello Corporation Bond Information:

	Bond A( Callable)	Bond B( Non-Callable)
Maturity	2022	2022
Coupon	11.05%	7.25%
Current price	125.75	100.00
Yield to Maturity	7.70%	7.25%
Modified duration to maturity	6.20	6.80
Call date	2016	-
Call Price	105	-
Yield to call	5.10%	-
Modified Duration to call	3.10	-

Bond A has a feature of call that is the issuer can call the bond anytime during the life.

So the future cash flow for Bond A is uncertain. The duration of bond A is very long and the yields obtained are also very high.

And if one treats the premium bond selling above the call price on a "to call" basis then the duration is impractically short and the yields are very low.

The callable bond can be categorized into two separate securities: the first one is a non-callable bond and the 2^nd is an option.

So, therefore we can say that the

Price of a callable bond is equal to the difference between the Price of a non - callable bond and the price of an option.