Chapter 10, Problem 32PS

Summary Introduction

(A)

To calculate:

The yield to call on a$8\%$coupon bond having$30$-year maturity with paying coupons semiannually and is callable in$5$years at a call price of$\$1,100$.

Introduction:

A Callable bond is a bond issued by the company for making money funds adding a feature of calling that bond back at any time before maturity when the interest rates in the market are in decline mode.

Yield to maturity is the rate which determines the return on bond from the period it is bought till its maturity.

Yield to call is the rate which determines the return of the investor from the time it is bought till the time it is called back.

Answer to Problem 32PS

The yield to call on a$8\%$coupon bond withcallable in$5$years at a call price of$\$1,100$is$6.74\%$.

Given:

A$8\%$coupon bond having$30$-year maturity with paying coupons semiannually and is callable in$5$years at a call price of$\$1,100$. Its yield to maturity is$7\%$.

Explanation:

The formula for computing price of the bond as follows:

  $\text{PV}={\displaystyle \sum _{t=1}^n}\frac{\text{PMT}}{{(1+r)}^1}+\frac{\text{FV}}{{(1+r)}^n}$

Here,

PV is Current price of the bond

FV is Face value of the bond

  $r$is yield to maturity

  $n$is no. of periods

For computing yield to call, the following data is entered in the spreadsheet:

The following are the output results for the data entered in the spreadsheet:

Thus, the current price of the bond is$\$1,124.72$and the yield to call is$6.74\%$.

Explanation of Solution

Given:

A$8\%$coupon bond having$30$-year maturity with paying coupons semiannually and is callable in$5$years at a call price of$\$1,100$. Its yield to maturity is$7\%$.

The formula for computing price of the bond as follows:

  $\text{PV}={\displaystyle \sum _{t=1}^n}\frac{\text{PMT}}{{(1+r)}^1}+\frac{\text{FV}}{{(1+r)}^n}$

Here,

PV is Current price of the bond

FV is Face value of the bond

  $r$is yield to maturity

  $n$is no. of periods

For computing yield to call, the following data is entered in the spreadsheet:

The following are the output results for the data entered in the spreadsheet:

Thus, the current price of the bond is$\$1,124.72$and the yield to call is$6.74\%$.

Summary Introduction

(B)

To calculate:

The yield to call on a$8\%$coupon bond having$30$-year maturity with paying coupons semiannually and is callable in$5$years at a call price of$\$1,050$.

Introduction:

A Callable bond is a bond issued by the company for making money funds adding a feature of calling that bond back at any time before maturity when the interest rates in the market are in decline mode.

Yield to maturity is the rate which determines the return on bond from the period it is bought till its maturity.

Yield to call is the rate which determines the return of the investor from the time it is bought till the time it is called back.

Answer to Problem 32PS

The yield to call on a$8\%$coupon bond with callable in$5$years at a call price of$\$1,050$is$5.95\%$.

Given:

A$8\%$coupon bond having$30$-year maturity with paying coupons semiannually and is callable in$5$years at a call price of$\$1,050$. Its yield to maturity is$7\%$.

Explanation:

The formula for computing price of the bond as follows:

  $\text{PV}={\displaystyle \sum _{t=1}^n}\frac{\text{PMT}}{{(1+r)}^1}+\frac{\text{FV}}{{(1+r)}^n}$

Here,

PV is Current price of the bond

FV is Face value of the bond

  $r$is yield to maturity

  $n$is no. of periods

For computing yield to call, the following data is entered in the spreadsheet:

The following are the output results for the data entered in the spreadsheet:

Thus, the current price of the bond is$\$1,124.72$and the yield to call is$5.95\%$.

Explanation of Solution

Given:

A$8\%$coupon bond having$30$-year maturity with paying coupons semiannually and is callable in$5$years at a call price of$\$1,050$. Its yield to maturity is$7\%$.

The formula for computing price of the bond as follows:

  $\text{PV}={\displaystyle \sum _{t=1}^n}\frac{\text{PMT}}{{(1+r)}^1}+\frac{\text{FV}}{{(1+r)}^n}$

Here,

PV is Current price of the bond

FV is Face value of the bond

  $r$is yield to maturity

  $n$is no. of periods

For computing yield to call, the following data is entered in the spreadsheet:

The following are the output results for the data entered in the spreadsheet:

Thus, the current price of the bond is$\$1,124.72$and the yield to call is$5.95\%$.

Summary Introduction

(C)

To calculate:

The yield to call on a$8\%$coupon bond having$30$-year maturity with paying coupons semiannually and is callable in$2$years at a call price of$\$1,100$.

Introduction:

A Callable bond is a bond issued by the company for making money funds adding a feature of calling that bond back at any time before maturity when the interest rates in the market are in decline mode.

Yield to maturity is the rate which determines the return on bond from the period it is bought till its maturity.

Yield to call is the rate which determines the return of the investor from the time it is bought till the time it is called back.

Answer to Problem 32PS

The yield to call on a$8\%$coupon bond with callable in$2$years at a call price of$\$1,100$is$6.06\%$.

Given:

A$8\%$coupon bond having$30$-year maturity with paying coupons semiannually and is callable in$2$years at a call price of$\$1,100$. Its yield to maturity is$7\%$.

Explanation:

The formula for computing price of the bond as follows:

  $\text{PV}={\displaystyle \sum _{t=1}^n}\frac{\text{PMT}}{{(1+r)}^1}+\frac{\text{FV}}{{(1+r)}^n}$

Here,

PV is Current price of the bond

FV is Face value of the bond

  $r$is yield to maturity

  $n$is no. of periods

For computing yield to call, the following data is entered in the spreadsheet:

The following are the output results for the data entered in the spreadsheet:

Thus, the current price of the bond is$\$1,124.72$and the yield to call is$6.06\%$.

Explanation of Solution

Given:

A$8\%$coupon bond having$30$-year maturity with paying coupons semiannually and is callable in$2$years at a call price of$\$1,100$. Its yield to maturity is$7\%$.

The formula for computing price of the bond as follows:

  $\text{PV}={\displaystyle \sum _{t=1}^n}\frac{\text{PMT}}{{(1+r)}^1}+\frac{\text{FV}}{{(1+r)}^n}$

Here,

PV is Current price of the bond

FV is Face value of the bond

  $r$is yield to maturity

  $n$is no. of periods

For computing yield to call, the following data is entered in the spreadsheet:

The following are the output results for the data entered in the spreadsheet:

Thus, the current price of the bond is$\$1,124.72$and the yield to call is$6.06\%$.