Chapter 22, Problem 6P

a.

Summary Introduction

To calculate: Company FS pre-merger unlevered horizon value. Also, the Year 0 unlevered value.

Explanation of Solution

Given information:

Company FS pre-merger unlevered cost of equity: 8%

Pre-tax cost of debt: 6%

Tax rate: 25%

Terminal growth rate of free cash flow: 5%

Company FS outstanding shares: 800 million

Calculation of Horizon value of unlevered operations (HVUL) pre-merger:

Formula to calculate HVUL:

$\text{HVUL}=\frac{\text{Free cash flow in Year}4\times \left(\text{1}+\text{terminal}\text{growth}\text{rate}\text{of}\text{free}\text{cash}\text{flow}\right)}{{\text{r}}_{\text{U}}-\text{terminal}\text{growth}\text{rate}\text{of}\text{free}\text{cash}\text{flow}}$

Substitute $2,000 for free cash flow in year 4, 5% for terminal growth rate of free cash flow and 8% for $\left({\text{r}}_{\text{U}}\right)$ to calculate HVUL.

$\begin{array}{c}\text{HVUL}=\frac{\text{\$2,000}\times \left(\text{1}+5\text{\%}\right)}{\text{8\%}-5\text{\%}}\\ =\frac{\$2,100}{3\%}\\ =\$70,000\end{array}$

Hence, the HVUL is $70,000.

Calculation of year 0 unlevered value:

$\begin{array}{c}{\text{Value}}_{\text{UL}}=\left[\frac{\text{Free}\text{cash flows}}{{\left(1+\text{Unlevered cost of equity}\right)}^{\text{N}}}\right]\\ =\left[\frac{\$1,600}{\left(1+8\%\right)}+\frac{\$1,800}{{\left(1+8\%\right)}^2}+\frac{\$1,900}{{\left(1+8\%\right)}^3}+\frac{\$2,000+\$70,000}{{\left(1+8\%\right)}^4}\right]\\ =\$57,455.122\end{array}$

b.

Summary Introduction

To calculate: Company FS pre-merger horizon value tax shield. Also, calculate year 0 tax shield value.

Explanation of Solution

Calculation of tax shield:

Particulars	Year 1($)	Year 2($)	Year 3($)	Year 4($)
Interest	474	486	492	498
Tax shield $\left(\begin{array}{l}\text{Interest}\times \text{Tax rate of Company}\\ \text{ ACC after merger}\end{array}\right)$	118.50	121.50	123.00	124.50

Calculation of Horizon value of tax shield (HVTS):

Formula to calculate HVTS:

$\text{HVTS}=\frac{\text{Tax}\text{shield}\times \left(\text{1}+\text{terminal}\text{growth}\text{rate}\text{of}\text{free}\text{cash}\text{flow}\right)}{{\text{r}}_{\text{U}}-\text{terminal}\text{growth}\text{rate}\text{of}\text{free}\text{cash}\text{flow}}$

Substitute $124.50 for tax shield, 5% for terminal growth rate of free cash flow and 8% for $\left({\text{r}}_{\text{U}}\right)$ to calculate HVTS.

$\begin{array}{c}\text{HVTS}=\frac{\text{\$124}\text{.50}\times \left(\text{1}+5\text{\%}\right)}{\text{8\%}-5\text{\%}}\\ =\$4,357.50\end{array}$

Hence, the HVTS is $4,357.50.

Calculation of year 0 tax shield value:

$\begin{array}{c}{\text{Value}}_{\text{TS}}=\left[\frac{\text{Tax shield}}{{\left(1+\text{Unlevered cost of equity}\right)}^{\text{N}}}\right]\\ =\left[\frac{\$118.5}{\left(1+8\%\right)}+\frac{\$121.5}{{\left(1+8\%\right)}^2}+\frac{\$123}{{\left(1+8\%\right)}^3}+\frac{\$124.5+\$4,357.5}{{\left(1+8\%\right)}^4}\right]\\ =\$3,605.93\end{array}$

c.

Summary Introduction

To calculate: Company FS pre-merger value of levered operations and value of equity. Also compute the minimum stock price.

Explanation of Solution

Calculation of value of levered operations:

$\begin{array}{c}\text{Value}\text{of}\text{levered}\text{operations}=\text{Unlevered}\text{opertaions}+\text{Value of tax shield}\\ =\$57,455.12+\$3,605.93\\ =\$61,061.05\end{array}$

Hence, value of levered operations is $61,061.05.

Calculation of value of equity:

$\begin{array}{c}\text{Value of Equity}=\left(\text{Value of levered operations}-\text{Value of pre-merger debt proportion}\right)\\ =\$61,061.05-\$7,700\\ =\$53,361.05\end{array}$

Hence, value of equity is $53,361.05.

Calculation of stock price:

$\begin{array}{c}\text{Stock}\text{price}=\frac{\text{Value}\text{of}\text{equity}}{\text{Outstanding}\text{Shares}}\\ =\frac{\$53,361.05}{800\text{Shares}}\\ =\$66.70\end{array}$

Hence, minimum stock price is $66.70 per share.

d.

Summary Introduction

To calculate: Company FS post-merger unlevered horizon value to Company CR. Also, compute year 0 unlevered value.

Explanation of Solution

Calculation of Horizon value of unlevered operations (HVUL) post-merger:

Formula to calculate HVUL:

$\text{HVUL}=\frac{\text{Free cash flow in Year}4\times \left(\text{1}+\text{terminal}\text{growth}\text{rate}\text{of}\text{free}\text{cash}\text{flow}\right)}{{\text{r}}_{\text{U}}-\text{terminal}\text{growth}\text{rate}\text{of}\text{free}\text{cash}\text{flow}}$

Substitute $2,200 for free cash flow in year 4, 5% for terminal growth rate of free cash flow and 8% for $\left({\text{r}}_{\text{U}}\right)$ to calculate HVUL.

$\begin{array}{c}\text{HVUL}=\frac{\text{\$2,200}\times \left(\text{1}+5\text{\%}\right)}{\text{8\%}-5\text{\%}}\\ =\$77,000\end{array}$

Hence, the HVUL is $77,000.

Calculation of year 0 unlevered value:

$\begin{array}{c}{\text{Value}}_{\text{UL}}=\left[\frac{\text{Free}\text{cash flows}}{{\left(1+\text{Unlevered cost of equity}\right)}^{\text{N}}}\right]\\ =\left[\frac{\$1,700}{\left(1+8\%\right)}+\frac{\$2,000}{{\left(1+8\%\right)}^2}+\frac{\$2,100}{{\left(1+8\%\right)}^3}+\frac{\$2,200+\$77,000}{{\left(1+8\%\right)}^4}\right]\\ =\$63,170.164\end{array}$

e.

Summary Introduction

To calculate: Company FS post-merger horizon value tax shield. Also, calculate year 0 tax shield value.

Explanation of Solution

Calculation of tax shield:

Particulars	Year 1($)	Year 2($)	Year 3($)	Year 4($)
Interest	1,320	1,338	1,344	1,350
Tax shield $\left(\begin{array}{l}\text{Interest}\times \text{Tax rate of Company}\\ \text{ ACC after merger}\end{array}\right)$	330.00	334.50	336.00	337.50

Calculation of Horizon value of tax shield (HVTS):

Formula to calculate HVTS:

$\text{HVTS}=\frac{\text{Tax}\text{shield}\times \left(\text{1}+\text{terminal}\text{growth}\text{rate}\text{of}\text{free}\text{cash}\text{flow}\right)}{{\text{r}}_{\text{U}}-\text{terminal}\text{growth}\text{rate}\text{of}\text{free}\text{cash}\text{flow}}$

Substitute $337.50 for tax shield, 5% for terminal growth rate of free cash flow and 8% for $\left({\text{r}}_{\text{U}}\right)$ to calculate HVTS.

$\begin{array}{c}\text{HVTS}=\frac{\$\text{337}.\text{5}0\times \left(\text{1}+5\text{\%}\right)}{\text{8\%}-5\text{\%}}\\ =\$11,812.50\end{array}$

Hence, the HVTS is $11,812.50.

Calculation of year 0 tax shield value:

$\begin{array}{c}{\text{Value}}_{\text{TS}}=\left[\frac{\text{Tax shield}}{{\left(1+\text{Unlevered cost of equity}\right)}^{\text{N}}}\right]\\ =\left[\frac{\$330}{\left(1+8\%\right)}+\frac{\$334.5}{{\left(1+8\%\right)}^2}+\frac{\$336}{{\left(1+8\%\right)}^3}+\frac{\$337.5+\$11,812.5}{{\left(1+8\%\right)}^4}\right]\\ =\$9,789.67\end{array}$

f.

Summary Introduction

To calculate: Company FS post-merger value of levered operations and value of equity. Also compute the minimum stock price.

Explanation of Solution

Calculation of value of levered operations:

$\begin{array}{c}\text{Value}\text{of}\text{levered}\text{operations}=\text{Unlevered}\text{opertaions}+\text{Value of tax shield}\\ =\$63,170.16+\$9,789.67\\ =\$72,959.83\end{array}$

Hence, value of levered operations is $72,959.83.

Calculation of value of equity:

$\begin{array}{c}\text{Value of Equity}=\left(\text{Value of levered operations}-\text{Value of pre-merger debt proportion}\right)\\ =\$72,959.83-\$7,700\\ =\$65,259.83\end{array}$

Hence, value of equity is $65,259.83.

Calculation of stock price:

$\begin{array}{c}\text{Stock}\text{price}=\frac{\text{Value}\text{of}\text{equity}}{\text{Outstanding}\text{Shares}}\\ =\frac{\$65,259.83}{800\text{Shares}}\\ =\$81.57\end{array}$

Hence, maximum stock price is $81.57 per share.

g.

Summary Introduction

To calculate: The percentage of Company FS pre-merger and post-merger capital structure at year 4 consisted of debt. Also, the increase in value to Company CR due to improved free cash flow.

Explanation of Solution

Calculation of pre-merger capital structure consisted of debt:

$\begin{array}{c}\text{Pre-merger}\text{at}\text{horizon}=\left(\frac{\text{Debt}\text{at}\text{horizon}}{\text{Horizon}\text{Value}\text{unlevered}+\text{Horizon}\text{value}\text{tax}\text{shield}}\right)\\ =\left(\frac{\$8,300}{\$70,000+\$4,357.5}\right)\\ =11.2\%\end{array}$

Hence, Company FS consisted of 11.2% of debt in its overall capital structure.

Calculation of post-merger capital structure consisted of debt:

$\begin{array}{c}\text{Pre-merger}\text{at}\text{horizon}=\left(\frac{\text{Debt}\text{at}\text{horizon}}{\text{Horizon}\text{Value}\text{unlevered}+\text{Horizon}\text{value}\text{tax}\text{shield}}\right)\\ =\left(\frac{\$22,500}{\$77,000+\$11,812.5}\right)\\ =25.3\%\end{array}$

Hence, Company FS consisted of 25.3% of debt in its overall capital structure.

Calculation of increase in the value due to free cash flows:

$\begin{array}{c}\text{Increase}\text{in}\text{value}=\left(\text{Post-merger value of operations}-\text{Pre-merger value of operations}\right)\\ =\$63,170.16-\$57,455.12\\ =\$5,715.04\end{array}$

Hence, increase in value due to free cash flows is $5,715.04.

Calculation of increase in value due to change in capital structure:

$\begin{array}{c}\text{Increase}\text{in}\text{value}=\left(\text{Post-merger value of tax shield}-\text{Pre-merger value of tac shield}\right)\\ =\$9,789.67-\$3,605.93\\ =\$6,183.74\end{array}$

Hence, increase due to change in capital structure is $6,183.74.