Chapter 10, Problem 35PS

a(ii)

Summary Introduction

To examine:

Why YTM of par bond is higher than the YTM of the discount bond where,

The first bond was issued at a deep discount with an interest rate$4\%$with a price of$\$580$and YTM is$8.4\%$.

The second bond was issued at par with a coupon rate of$8.75\%$

Introduction:

The yield to maturity symbolized as YTM − it is regarded as the single interest rate which equalizes the present value of a security's cash flows to that of its price.

Answer to Problem 35PS

There is a gain only$5\%$by increasing in price up to$\$1050$.

Explanation of Solution

Given Information:

The first bond was issued at deep discount and the second was issued at par.

If the bond was issued at par then it is more beneficial for the bondholder because the rate of this bond is less than or equal to market yields and price of this bond would also be below the call price i.e.$\$1050$.

So, there is a gain only$5\%$by increasing in price up to$\$1050$.

Summary Introduction

(b)

To calculate:

Total gain on both bonds if price subsequently falls down in the next two year where,

The first bond was issued at a deep discount with an interest rate of$4\%$with price of$\$580$and yield to maturity is$8.4\%$.

The second bond was issued at par with a coupon rate of$8.75\%$

Introduction:

The yield to maturity symbolized as YTM − it is regarded as the single interest rate which equalizes the present value of a security's cash flows to that of its price.

Answer to Problem 35PS

The deep discount bond was providing higher return to investor.

Explanation of Solution

The present value of bond issued at par is

  $\begin{array}{c}\text{PV of Bond }\left(\text{issue at par}\right)={\displaystyle \sum _{\text{t=1}}^{20}\frac{\text{PMT}}{{\left(1+\text{r}\right)}^1}}+\frac{\text{FV}}{{\left(1+\text{r}\right)}^{20}}\\ ={\displaystyle \sum _{\text{t=1}}^{20}\frac{\$87.5}{{\left(1.0875\right)}^1}}+\frac{\$1000}{{\left(1.0875\right)}^{20}}\\ =\$1000\end{array}$

The present value of bond deeply discount bond is

  $\begin{array}{c}\text{PV of Deep Discount Bond}={\displaystyle \sum _{\text{t=1}}^{20}\frac{\text{PMT}}{{\left(1+\text{r}\right)}^1}}+\frac{\text{FV}}{{\left(1+\text{r}\right)}^{20}}\\ ={\displaystyle \sum _{\text{t=1}}^{20}\frac{\$40}{{\left(1.084\right)}^1}}+\frac{\$1000}{{\left(1.084\right)}^{20}}\\ =\$580.55\end{array}$

If YTM is decrease by$4\%$for both bonds in next two years then

The present value for bond issue at par for remaining$18$years is

  $\begin{array}{c}\text{PV of Bond}={\displaystyle \sum _{\text{t=1}}^{18}\frac{\text{PMT}}{{\left(1+\text{r}\right)}^1}}+\frac{\text{FV}}{{\left(1+\text{r}\right)}^{18}}\\ ={\displaystyle \sum _{\text{t=1}}^{18}\frac{\$87.5}{{\left(1.0475\right)}^1}}+\frac{\$1000}{{\left(1.0475\right)}^{18}}\\ =\$1476.85\end{array}$

The present value of bond deeply discount bond for remaining$18$years is

  $\begin{array}{c}\text{PV of Deep Discount Bond}={\displaystyle \sum _{\text{t=1}}^{18}\frac{\text{PMT}}{{\left(1+\text{r}\right)}^1}}+\frac{\text{FV}}{{\left(1+\text{r}\right)}^{18}}\\ ={\displaystyle \sum _{\text{t=1}}^{18}\frac{\$40}{{\left(1.044\right)}^1}}+\frac{\$1000}{{\left(1.044\right)}^{18}}\\ =\$950.97\end{array}$

Total coupon income on bond issued at par for two year is

  $\begin{array}{c}\text{Income}=\$87.5+\$87.5\\ =\$175\end{array}$

Total coupon income on deeply discount bond for two year is

  $\begin{array}{c}\text{Income}=\$40+\$40\\ =\$80\end{array}$

Total return on bond issued at par is

  $\begin{array}{c}\text{Return}=\frac{\left(\$1476.85-\$1000\right)+\$175}{\$1000}\\ =65.19\%\end{array}$

Total return on deeply discount bond is

  $\begin{array}{c}\text{Return}=\frac{\left(\$950.97-\$580.55\right)+\$80}{\$580.55}\\ =77.59\%\end{array}$

The deeply discount bond is given higher return to the investor.

Summary Introduction

(c)

To determine:

Implicit call protection provided by a deeply discount bond.

Introduction:

Bonds frequently are issued in call protection with a period.The selling price of a deeply discount bond is lesser than the call price which is implicit call protection.

Answer to Problem 35PS

The bond was issued with implicit call protection for compensating and giving an offer to the investor.

Explanation of Solution

For reducing the cost of debt on calling the bond before maturity, the bond was issued with call protection by the issuer. Forthis, the company is also giving a premium on call to bondholders for compensating the investor.

The selling price of a bond is lower from the call price so this bond was issued with implicit call protection for giving an offer to the investor.