Chapter 20, Problem 14IC

a.

Summary Introduction

To discuss: The preferred stock differs from debt and common equity.

Introduction:

Stock is a type of security in a company that denotes ownership. The company can raise the capital by issuing stocks.

Explanation of Solution

The preferred stock differs from debt and common equity is as follows:

Preferred stock can be termed as hybrid stock because it is similar characteristically with common equity and debt. The preferred payments made to the investors remain contractually stable resembling debt whereas like common equity the non-payment of dividend does amount to default and bankruptcy.

Even most preferred stock prohibits paying common dividends when there are arrears in preferred. Moreover, their dividends are cumulative until a level. The dividend on common stock is not paid just in case of non-payment of dividend on preferred stock.

b.

Summary Introduction

To discuss: The meaning of adjustable-rate preferred.

Explanation of Solution

The meaning of adjustable-rate preferred is as follows:

A particular form of preferred stock wherein the dividends issued varies with a benchmark such as Treasury-bill rate is termed as adjustable-rate preferred. This is the best short-term corporate investment since only 30 percent of the dividends are taxable to corporations and even the floating rate keeps the issue trading at the par value. Moreover, the adjustable-rate preferred stock will have price instability mostly for the liquid portfolios of numerous corporate investors.

c.

Summary Introduction

To discuss: The knowledge of call options helps people to understand convertibles and warrants.

Introduction:

Option is a contract to purchase a financial asset from one party and sell it to another party on an agreed price for a future date. There are two types of options, which are as follows:

• An option that buys an asset called call option
• An option that sells an asset called put option

Explanation of Solution

The knowledge of call options helps people to understand convertibles and warrants is as follows:

Both the convertibles and warrants are two forms of call options. The understanding of options will help a company’s financial managers to make decision on convertible and warrant issues.

d.1.

Summary Introduction

To determine: The coupon rate that is set on the bond with warrants.

Introduction:

A warrant is securities that give the bondholder the right, yet not the obligation, to purchase a specific number of securities at a specific cost before a particular period.

Explanation of Solution

Given information:

Person M (financial manager) of the F Company decided to issue a bond with warrants. The current stock price of the company is $10 and cost of 20-years annual coupon debt is 12 percent without warrants. Later, the banker has recommends to assign 50 warrants for every bond of the company. The exercise price of the warrant is $12.50 and the value of every warrant when detached and trade separately is $1.50.

The formula to compute the value of package is as follows:

$\text{Value of package}=\text{ Value of bond}+\text{ Value of warrant}$

Compute the value of warrant:

Note: Assume the entire package is to sell for the price of $1,000.

$\begin{array}{c}\text{Value of warrant}=\text{Number of warrant}\times \text{Value per warrant}\\ =50\times \$1.50\\ =\$75\end{array}$

Hence, the value of warrant is $75.

Compute the value of bond using the value of package formula:

$\begin{array}{c}\text{Value of package}=\text{ Value of bond}+\text{ Value of warrant}\\ \$1,000=\text{Value of bond}+\$75\\ \$1,000-\$75=\text{Value of bond}\\ \$925=\text{Value of bond}\end{array}$

Hence, the value of bond is $925.

Compute the PTM

The table below shows the Excel formula to compute the PTM:

The table below shows the calculated value of PTM:

Hence, the PTM is $109.96. The bonds will have a value of $925 and the package of one bond plus 50 warrants will cost $1,000 at 12 percent coupon rate.

d.2.

Summary Introduction

To discuss: The implication of terms of issues and whether the company loses or wins.

Explanation of Solution

The implication of terms of issues and determine whether the company loses or wins are as follows:

The company issues bonds and warrants directly trade for $2.50 each for 50 warrants. The total worth of 50 warrants will be $125 $\left(\$2.50\times 50\right)$. However, the package will actually worth $1,050 $\left(\$925+\$125\right)$. On selling the bonds worth $1,050 for $1,000 imposes a $50 per bond cost on the F Company’s shareholders. It is because the package will have sold with a lower-coupon rate bond. As a result, it indicates lower future interest payments. Therefore, the company will lose because the company is paying more in the interest expenses.

d.3.

Summary Introduction

To discuss: The expected period when the warrants to be exercised.

Explanation of Solution

The expected time when the warrant to be exercised is discussed below:

A warrant is sold for premium beyond exercise value in an open market. Every investor will sell warrants in specific place than exercising it; on stock selling at price more than exercise price. However, few warrants comprise of step-up provisions of exercise price in which exercise price raises than warrant’s life period. It is because the warrant value drops when the exercise price increases.

As a result, the step-up provision will support holders for exercising their warrants. Therefore, the warrants holder would voluntarily exercise when there is higher dividend. Moreover, the higher dividends will raise the attraction of stock from warrants.

d.4.

Summary Introduction

To discuss: Whether the warrants will bring in additional capital when exercised and determine the type of capital.

Explanation of Solution

Determine whether the warrants will bring in additional capital when exercised and determine the types of capital are as follows:

At the time when a warrant is exercised, it will bring in exercise price or additional capital of $12.50 (equity capital). As a result, the holder will receive a share of common stock per warrant.  Here, let assume that the exercise price is set at 10 percent to 30 percent above the current price of stock. In this case, a higher-growth company will set the exercise price to a higher-end range and vice-versa.

d.5.

Summary Introduction

To discuss: Whether all the debt been issued with warrants when the warrants lower the cost of debt and determine the expected cost of the bond with warrants.

Explanation of Solution

Determine whether all the debt been issued with warrants when the warrants lower the cost of debt and determine the expected cost of the bond with warrants are as follows:

The overall cost of the issue will be higher than straight debt even though the coupon rate on the debt is lower. Few returns are contractual in nature for the investors while the remaining return is related to price of stock movements. As a result, the cost will be much higher as compared to the debt. Therefore, the overall cost and risk is greater as compared to the cost of debt.

At the time when the warrants are exercised in 5-years, then the price of stock will be $17.50. Then the F Company will exchange stock worth $17.50 for one warrant plus $12.50. Therefore, the company will realize an opportunity cost of $5 on every warrants because every bond has 50 warrants and the total cost per bond will be $250$\left(\$5\times 50\right)$.

Summary Introduction

To discuss: The comparison on the cost of bond with warrants by the cost of straight debt and cost of common stock.

Explanation of Solution

Given information:

Person M (financial manager) of the F Company decided to issue a bond with warrants. The current stock price of the company is $10 and cost of 20-years annual coupon debt is 12 percent without warrants. Later, the banker has recommends to assign 50 warrants for every bond of the company. The exercise price of the warrant is $12.50 and the value of every warrant when detached and trade separately is $1.50.

Note: The F Company will make interest payments over the 20-year life of bonds and repay the principal after 20-years.

Compute the IRR:

The table below shows the Excel formula to compute the IRR:

The table below shows the calculated value of IRR:

Hence, the IRR is 12.93%. The IRR from this cash flows stream is higher than the 12 percent cost of straight debt. It is because the issue is riskier as compared to the straight debt as per the investor point of view.  However, the bonds with warrants will be less risky as compared to the common stock. Therefore, the bonds with warrants will have a lower cost than common stock.

e.1.

Summary Introduction

To determine: The conversion price and whether ot is implied in the convertible’s terms.

Explanation of Solution

Given information:

Person M is considering convertible bonds. As per the investment banker estimates, the F Company will sell a 20-years bond for 10 percent coupon rate. The callable convertible bond’s face value is $1,000 and straight-debt issue will need a 12% coupon rate. The F Company’s current price of stock is $10 and its last year’s dividends are $0.74. The constant growth rate of dividend is 8 percent and it’s converted in 80 shares of F Company’s stock at the position of owner.

The formula to compute the conversion price is as follows:

$\text{Conversion price}=\frac{\text{Par value}}{\text{Number of share received}}$

Compute the conversion price:

$\begin{array}{c}\text{Conversion price}=\frac{\text{Par value}}{\text{Number of share received}}\\ =\frac{\$1,000}{80}\\ =\$12.50\end{array}$

Hence, the conversion price is $12.50. Here, the conversion price can be assumed as the convertible’s exercise price, even though it has already paid out. Therefore, the conversion price is set at 20 percent to 30 percent above the prevailing stock price as with the warrants.

e.2.

Summary Introduction

To determine: The straight-debt value of the convertible and implied value of the convertibility.

Explanation of Solution

Given information:

Person M is considering convertible bonds. As per the investment banker estimates, the F Company will sell a 20-years bond for 10 percent coupon rate. The callable convertible bond’s face value is $1,000 and straight-debt issue will need a 12% coupon rate. The F Company’s current price of stock is $10 and its last year’s dividends are $0.74. The constant growth rate of dividend is 8 percent and it’s converted in 80 shares of F Company’s stock at the position of owner.

The formula to compute the value of convertibility is as follows:

$\text{Value of convertibility}=\text{Convertible bond value}-\text{Value of straight bond}$

The formula to compute per share value of convertibility is as follows:

$\text{Per share value of convertibility}=\frac{\text{Value of convertibility}}{\text{Number of shares converted}}$

Compute the value of 10% annual coupon bonds (straight bond):

The table below shows the Excel formula to compute the value of 10% annual coupon bonds:

The table below shows the calculated value of 10% annual coupon bonds:

Hence, the value of 10% annual coupon bonds is $850.61.

Compute the value of convertibility:

Note: The convertible will sell at $1,000 (face value).

$\begin{array}{c}\text{Value of convertibility}=\text{Convertible bond value}-\text{Value of straight bond}\\ =\$1,000-\$850.61\\ =\$149.39\end{array}$

Hence, the value of convertibility is $149.39.

Compute the per share value of convertibility:

$\begin{array}{c}\text{Per share value of convertibility}=\frac{\text{Value of convertibility}}{\text{Number of shares converted}}\\ =\frac{\$149.39}{80}\\ =\$1.87\end{array}$

Hence, per share value of convertibility is $1.87.

e.3.

Summary Introduction

To determine: The formula for the conversion value of bond in any year and even compute the value of conversion at Year 0 and Year 10.

Explanation of Solution

The formula for the conversion value of bond in any year is as follows:

The value of the stock which is obtained by converting is termed as conversion value in any year. In the case of F Company, the stock price is expected to increase by “g” every year since it has a constant growth stock. Therefore, the formula for the conversion value of bond in any year is given below:

${\text{P}}_{\text{t}}={\text{ P}}_{\text{0}}{\left(1+\text{g}\right)}^{\text{t}}$

Where,

P_t refers to the price at conversion of bonds

P_o refers to the current stock price

g refers to the constant growth rate of stock

t refers to the number of years

Note: The value of converting at any year is denoted as CR(P_t). Here, CR refers to the number of share received.

Compute the value of conversion at Year 0:

$\begin{array}{c}\text{Value of conversion at Year }0={\text{CR(P}}_{\text{0}})\times {\left(1+\text{g}\right)}^{\text{t}}\\ =80\times \$10\times {\left(1+\frac{8}{100}\right)}^0\\ =\$800\times {\left(1.08\right)}^0\\ =\$800\times 1\\ =\$800\end{array}$

Hence, the value of conversion at Year 0 is $800.

Compute the value of conversion at Year 10:

$\begin{array}{c}\text{Value of conversion at Year 1}0={\text{CR(P}}_{\text{0}})\times {\left(1+\text{g}\right)}^{\text{t}}\\ =80\times \$10\times {\left(1+\frac{8}{100}\right)}^{10}\\ =\$800\times {\left(1.08\right)}^{10}\\ =\$800\times 2.1589\\ =\$1,727.12\end{array}$

Hence, the value of conversion at Year 10 is $1,727.12.

e.4.

Summary Introduction

To discuss: The meaning of the term floor value of a convertible and compute the convertible’s expected floor value in the Year 0 and Year 10.

Explanation of Solution

The meaning of term floor value of a convertible and even compute the convertible’s expected floor value in the Year 0 and Year 10 are as follows:

The higher of straight-debt value and higher value of conversion is termed as floor value of a convertible.

Compute the expected floor value of convertible in the Year 0:

The table below shows the Excel formula to compute the value of 10% annual coupon bonds:

The table below shows the calculated value of 10% annual coupon bonds:

Hence, the value of 10% annual coupon bonds is $850.61.  The straight-debt value in Year 0 is $850.61 when the conversion value is $800. Therefore, the floor value is $850.61.

The conversion value of $1,727.12 is higher than the straight-debt value at the Year 10. Therefore, the conversion value sets at the floor price. The convertible would sell above its floor value in any period before the date of maturity. It is because the convertibility option carries extra values.

e.5.

Summary Introduction

To determine: The number of year or period when the issue is expected to callable.

Explanation of Solution

Given information:

Person M is considering convertible bonds. As per the investment banker estimates, the F Company will sell a 20-years bond for 10 percent coupon rate. The callable convertible bond’s face value is $1,000 and straight-debt issue will need a 12% coupon rate. The F Company’s current price of stock is $10 and its last year’s dividends are $0.74. The constant growth rate of dividend is 8 percent and it’s converted in 80 shares of F Company’s stock at the position of owner.

The formula for the conversion value of bond in any year is given below:

${\text{P}}_{\text{t}}={\text{ P}}_{\text{0}}{\left(1+\text{g}\right)}^{\text{t}}$

Where,

P_t refers to the price at conversion of bonds

P_o refers to the current stock price

g refers to the constant growth rate of stock

t refers to the number of years

Compute the number of years or period when the issue is expected to callable:

$\begin{array}{c}{\text{P}}_{\text{t}}={\text{ P}}_{\text{0}}{\left(1+\text{g}\right)}^{\text{t}}\\ \$1,200=80\times \$10{\left(1+\frac{8}{100}\right)}^{\text{t}}\\ \$1,200=\$800\times {\left(1.08\right)}^{\text{t}}\\ \frac{\$1,200}{\$800}={\left(1.08\right)}^{\text{t}}\\ 1.5={\left(1.08\right)}^{\text{t}}\\ \ln 1.50=\text{t ln(1}\text{.08)}\\ =\text{0}\text{.077 t}\\ \frac{0.4055}{\text{0}\text{.077 }}=\text{t}\\ \text{5}\text{.2678}=\text{t}\end{array}$

Hence, the number of year is 5.2678 years that is considered as 5-years.

e.6.

Summary Introduction

To determine: The expected cost of the convertible and whether the cost appears consistent with the risk of the issue.

Explanation of Solution

Given information:

Person M is considering convertible bonds. As per the investment banker estimates, the F Company will sell a 20-years bond for 10 percent coupon rate. The callable convertible bond’s face value is $1,000 and straight-debt issue will need a 12% coupon rate. The F Company’s current price of stock is $10 and its last year’s dividends are $0.74. The constant growth rate of dividend is 8 percent and it’s converted in 80 shares of F Company’s stock at the position of owner. The conversion value in Year 5 is $1,200.

Compute the IRR:

The table below shows the Excel formula to compute the IRR:

The table below shows the calculated value of IRR:

Hence, the IRR is 13.08% that is the cost of the convertible issue.

Compute the cost of equity:

$\begin{array}{c}\text{Cost of equity}=\frac{{\text{D}}_{\text{O}}\left(1+\text{g}\right)}{{\text{P}}_{\text{o}}}+\text{g}\\ =\frac{\$0.74\left(1+\frac{8}{100}\right)}{\$10}+\frac{8}{100}\\ =\frac{\$0.74\left(1+0.08\right)}{\$10}+0.08\\ =0.07992+0.08\\ =0.15992\end{array}$

Hence, the cost of equity is 0.15992 that is approximately is 16%. The convertible bond of firm has risk, which falls between the risk of its equity and debt. Therefore, the cost that appears consistent with the risk of the issue is 13.08 percent.

f.

Summary Introduction

To discuss: The factors that Person M as to consider on making decision between to securities.

Explanation of Solution

The factors that Person M as to consider on making decision between to securities are as follows:

• The Person M has to consider the future need for capital of the company. The warrants must be favorable because their exercise can bring in extra equity capital without retirement of the low-cost debt when the company anticipates continues need for capital. On the contrary, the convertible issue cannot bring in new funds at conversion.
• The second factor that Person M must consider is whether the Company wants to commit towards 20-year of debt at this period. Here, the conversion can remove off the debt issue but it does not occur on the exercise of warrants. In case, the F Company cannot increase over the period, then neither the warrants nor the convertibles will be exercised and debt will remain outstanding in the both case.