Chapter 20, Problem 4MC

1.

Summary Introduction

Case Study:

Company E is developing educational software for the primary and secondary school markets. In order to maintain the market place the owner entrusted the financial manager with the task to increase the market share which raises the capital requirements. Person P after observing the market trends analyze that the stock price of the company may rise in future thus, cannot raise the new capital and also due to the high interest rates and B rating of the firm it cannot issue the debt instruments. Person P came up with three alternatives, preferred stock, bonds with warrants and convertible bonds and required to make choice out of these three financial alternatives.

To determine:

Conversion price of bond

Explanation of Solution

Formula to calculate conversion price:

$\text{Conversion}\text{price}=\frac{\text{Par}\text{value}}{\text{Shares}\text{received}}$

Substitute the value of par value: $1,000 and shares received: 40 shares in the above formula.

$\begin{array}{c}\text{Conversion}\text{price}=\frac{\$1,000}{40\text{shares}}\\ =\$25\text{per}\text{share}\end{array}$

Therefore, the conversion price is $25 per share.

2.

Summary Introduction

To determine:

Convertible’s straight debt value and implied value of convertibility feature.

Explanation of Solution

Formula to calculate straight debt-value:

$\text{Straight}\text{debt-value}=\text{Annual}\text{Interest}\times \text{PVIFA}\left(\text{Rate,}\text{Years}\right)+Parvalue\times \text{PVIFA}\left(\text{Rate,}\text{Years}\right)$

Substitute the value of Annual interest: $85,par value: $1,000, rate: 10% and number of years are 20 in the above formula.

Calculation of straight debt-value:

$\begin{array}{c}\text{Straight}\text{debt-value}=\$85\times \text{PVIFA}\left(\text{10\%,}\text{20}\right)+\$1,000\times \text{PVIFA}\left(10\%,20\right)\\ =\$872.30\end{array}$

Formula to calculate implied value:

$\text{Implied}\text{Value}=\text{Future}\text{Value}-\text{Value}\text{of}\text{straight}\text{debt}$

Substitute the future value: $1,000 and value of straight debt: $872.30 in the above formula.

$\begin{array}{c}\text{Implied}\text{Value}=\$1,000-\$872.30\\ =\$127.70\end{array}$

Therefore, the straight debt value is $872.30 and implied value of convertibility feature is $127.70.

3.

Summary Introduction

To determine:

Formula for expected conversion value of bond in any year. Conversion value at the end of year 0 and year 10.

Explanation of Solution

Formula to calculate conversion value:

$\text{Conversion}\text{Value}=\text{CR}\times \left({\text{P}}_0\right){\left(1+g\right)}^{\text{t}}$

Substitute the above equation where CR is the number of shares the bonds can be converted into: 40 shares, P₀ is the current stock price: $20, g is the growth rate: 8% and t is time: 0 years in the above formula.

Calculation of conversion value at the end of year 0:

$\begin{array}{c}\text{Conversion}{\text{Value}}_o=\text{40}\times \$20{\left(1+0.08\right)}^o\\ =\$800\end{array}$

Substitute the above equation where CR is the number of shares the bonds can be converted into: 40 shares, P₀ is the current stock price: $20, g is the growth rate: 8% and t is time: 10 years in the above formula.

Calculation of conversion value at the end of year 10:

$\begin{array}{c}\text{Conversion}{\text{Value}}_{10}=\text{40}\times \$20{\left(1+0.08\right)}^{10}\\ =\$1,727.14\end{array}$

Therefore, the conversion value at the end of year 0 is $800 and at the end of year 10 is $1,727.14.

4.

Summary Introduction

To explain:

The meaning of Floor value. Also, Floor value of convertible at the end of year 0 and year 10

Explanation of Solution

The floor value refers to the higher value among the straight-debt value and the conversion value. The conversion value is $800 and the straight debt value is $872.30 at the year 0. So the floor value would be $872.30. at year 10, the  conversion value is $1,727 which is higher than the straight debt value. So the floor value is $1,727 at the end of year 10.

5.

Summary Introduction

To determine:

Expected year when the issue would be called.

Explanation of Solution

Formula to calculate number of years:

$\text{Future}\text{value}=\text{Present}\text{value}\times {\left(1+\text{rate}\right)}^n$

Substitute the future value: $1,200, present value: $800, rate: 0.08 and n represents number of years in the above formula.

Calculation of number of years:

$\begin{array}{c}1,200=800\times {\left(1+0.08\right)}^n\\ {\left(1.08\right)}^n=1.5\\ n=5.27\end{array}$

Since call must occur on anniversary date, that is why the answer is rounded to 6. So, the bond should be called after 6 years.

6.

Summary Introduction

To determine:

Expected cost of capital of the convertible and whether this cost is consistent with the riskiness of the issue.

Explanation of Solution

$\text{Net}\text{cash}\text{flows}=\text{Shares}\text{converted}\times \text{Current}\text{stock}\text{price}\times {\left(1+\text{rate}\right)}^n+\text{Coupon}\text{payment}$

Substitute the value of shares converted: 40, current stock price: $20, rate: 0.08 and n represents number of years in the above formula.

$\begin{array}{c}\text{Net}\text{cash}\text{flows}=40\times \$20\times {\left(1+0.08\right)}^6+\$85\\ =800\times {\left(1.08\right)}^6+\$85\\ =\$1,354.50\end{array}$

Formula to calculate NPV_LR  and NPV_HR :

${\text{NPV}}_{\text{Rate}}=\frac{\text{Net}\text{cash}\text{flows}}{{\left(1+\text{rate}\right)}^n}$

Substitute the value of rate with lower rate which is assumed as: 11%, net cash flows: $1,354.50 and n is number of years: 6 in the above formula.

Calculation of NPV:

$\begin{array}{c}{\text{NPV}}_{LR}=\frac{\$1,269.50}{{\left(1+0.11\right)}^6}\\ =\$678.726\end{array}$

Substitute the value of rate with higher rate which is assumed as: 12%, net cash flows: $1,354.50 and n: 6 in the above formula.

$\begin{array}{c}{\text{NPV}}_{HR}=\frac{\$1,269.50}{{\left(1+0.12\right)}^6}\\ =\$643.168\end{array}$

Formula to calculate internal rate of return (IRR) is calculated by using trial and error method:

$\text{IRR=LR+}\frac{{\text{NPV}}_{LR}}{{\text{NPV}}_{LR}-{\text{NPV}}_{HR}}\times \left(\text{HR}-L\text{R}\right)$

Substitute the values of Lower rate (LR): 11%, higher rate (HR): 12%, NPV_LR: $678.726 and NPV_HR: $643.168 in the above formula.

Calculation of IRR:

$\begin{array}{c}\text{IRR}=11\%+\frac{\$678.726}{678.726-643.168}\times \left(12\%-11\%\right)\\ =11\%+1.91\%\\ =12.91\%\end{array}$

Formula to calculate cost of equity:

$\text{Cost}\text{of}\text{equity}=\frac{D_0\times \left(1+r\right)}{P_0}+r$

Substitute the value of D₀: $1, r: 0.08 and P₀: $20 in the above formula.

Calculation of cost of equity:

$\begin{array}{c}\text{Cost}\text{of}\text{equity}=\frac{\$1\times \left(1+0.08\right)}{\$20}+0.08\\ =13.4\%\end{array}$

The firm’s convertible bond has risk which is a blend of the cost of debt (10%) and the cost of equity (13.40%), so Cost of capital should fall between the cost of debt and equity. So, the 12.91 percent cost appears reasonable.

Since the cost of capital is between Cost of debt and cost of equity, the costs are consistent with the risk.

7.

Summary Introduction

To compute:

After tax cost of the bond

Explanation of Solution

Formula to calculate after tax cost:

$\text{After}\text{tax}\text{cost}=\text{Coupon}\text{rate}\times \left(\text{Bond}\text{value}\right)\times \left(1-\text{tax}\text{rate}\right)$

Substitute the Coupon rate: 8.5%, bond value: $1,000 and tax rate: 0.25 in the above formula.

Calculation of after tax cost:

$\begin{array}{c}\text{After}\text{tax}\text{cost}=8.5\%\times \$1,000\times \left(1-0.25\right)\\ =\$63.75\end{array}$

Therefore, after tax cost of the bond is $63.75.