Chapter 12, Problem 24QP

Adjusted Cash Flow from Assets. Ward Corp. is expected to have an EBIT of $1.9 million next year. Depreciation, the increase in net working capital, and capital spending are expected to be $165,000, $85,000, and $115,000, respectively. All are expected to grow at 18 percent per year for four years. The company currently has $13 million in debt and 800,000 shares outstanding. After Year 5, the adjusted cash flow from assets is expected to grow at 3 percent indefinitely. The company’s WACC is 8.5 percent and the tax rate is 35 percent. What is the price per share of the company’s stock?

Summary Introduction

To determine: The price per equity share.

Introduction:

Adjusted cash flow from assets refers to the cash flow from assets that excludes the tax benefit obtained from debt financing. It calculates the taxes on the earnings before interest and taxes.

Answer to Problem 24QP

The price per share is $28.20 percent.

Explanation of Solution

Given information:

The EBIT (Earnings before interest and taxes) of Company W is $1,900,000 for the first year. It will have depreciation amounting to $165,000, change in net working capital amounting to $85,000, and capital spending amounting to $115,000. All the estimates will grow at 18 percent for the next four years.

The debt value of the company is $13,000,000, and it has 800,000 shares outstanding. The adjusted cash flow from assets in Year 5 will grow for an indefinite period at 3 percent. The weighted average cost of capital of the company is 8.5 percent, and the tax rate is 35 percent.

The formula to calculate the EBIT from Year 2 to Year 5:

$\text{EBIT for the current year}=\text{EBIT for the previous year}+\left(\begin{array}{l}\text{EBIT for the previous year}\times \\ \text{Growth percentage}\end{array}\right)$

The formula to calculate the depreciation from Year 2 to Year 5:

$\begin{array}{l}\text{Depreciation for}\\ \text{the current year}\end{array}\}=\left(\begin{array}{l}\text{Depreciation for}\\ \text{the previous year}\end{array}\right)+\left(\begin{array}{l}\text{Depreciation for the previous year}\times \\ \text{Growth percentage}\end{array}\right)$

The formula to calculate the “Taxes*”:

$\text{Taxes*}=\text{EBIT×}{T}_C$

“EBIT” refers to the earnings before interest and taxes

“T_C” refers to the corporate tax rate

The formula to calculate the change in net working capital from Year 2 to Year 5:

$\begin{array}{l}\text{Change in net}\\ \text{working capital}\\ \text{for the current year}\end{array}\}=\left(\begin{array}{l}\text{Change in net}\\ \text{working capital}\\ \text{for the previous year}\end{array}\right)+\left(\begin{array}{l}\left(\begin{array}{l}\text{Change in net working capital}\\ \text{for the previous year}\end{array}\right)\times \\ \text{Growth percentage}\end{array}\right)$

The formula to calculate the capital spending from Year 2 to Year 5:

$\begin{array}{l}\text{Capital spending}\\ \text{for the current year}\end{array}\}=\left(\begin{array}{l}\text{Capital spending for}\\ \text{the previous year}\end{array}\right)+\left(\begin{array}{l}\text{Capital spending for the previous year}\times \\ \text{Growth percentage}\end{array}\right)$

The formula to calculate the “CFA*”:

$\text{CFA*}=\text{EBIT}+\text{Depreciation}-\text{Taxes*}-\left(\begin{array}{l}\text{Changes in net}\\ \text{working capital}\end{array}\right)-\text{Capital spending}$

Where,

“CFA*” refers to the adjusted cash flow from assets

“EBIT” refers to the earnings before interest and taxes

“Taxes*” refer to the tax on EBIT

The formula to calculate the terminal value or the value of the company at period “t”:

$V_t=\frac{{\text{CFA*}}_{t+1}\left(1+g\right)}{WACC-g}$

Where,

“V_t” refers to the terminal value

“CFA*_t+1” refers to the adjusted cash flow from assets at the end of period “t+1”

“WACC” refers to the weighted average cost of capital

“g” refers to the growth rate at which the cash flow will grow indefinitely

The formula to calculate the value of the company:

$V_0=\frac{{\text{CFA*}}_1}{1+WACC}+\frac{{\text{CFA*}}_2}{{\left(1+WACC\right)}^2}+\frac{{\text{CFA*}}_3}{{\left(1+WACC\right)}^3}+\mathrm{...}+\frac{{\text{CFA*}}_t+V_t}{{\left(1+WACC\right)}^t}$

Where,

“V₀” refers to the value of the company at present

“CFA*₁ to CFA*_t” refer to the adjusted cash flow from assets from period 1 to period t

“V_t” refers to the terminal value or the value of the company at period “t”

“WACC” refers to the weighted average cost of capital

The formula to calculate the total value of equity:

$\text{Total value of equity}=\text{Value of the company}-\text{Total value of debt}$

The formula to calculate the price per share of the company’s stock:

$\text{Price per share}=\frac{\text{Total value of equity}}{\text{Number of shares}}$

Compute the EBIT for Year 2:

The EBIT for Year 1 is $1,900,000. The growth rate is 18 percent.

$\begin{array}{c}\text{EBIT for Year 2}=\text{EBIT for Year 1}+\left(\text{EBIT for Year 1}\times \text{Growth percentage}\right)\\ =\$1,900,000+\left(\$1,900,000\times 0.18\right)\\ =\$2,242,000\end{array}$

Hence, the EBIT for Year 2 is $2,242,000.

Compute the EBIT for Year 3:

The EBIT for Year 2 is $2,242,000. The growth rate is 18 percent.

$\begin{array}{c}\text{EBIT for Year 3}=\text{EBIT for Year 2}+\left(\text{EBIT for Year 2}\times \text{Growth percentage}\right)\\ =\$2,242,000+\left(\$2,242,000\times 0.18\right)\\ =\$2,645,560\end{array}$

Hence, the EBIT for Year 3 is $2,645,560.

Compute the EBIT for Year 4:

The EBIT for Year 3 is $2,645,560. The growth rate is 18 percent.

$\begin{array}{c}\text{EBIT for Year 4}=\text{EBIT for Year 3}+\left(\text{EBIT for Year 3}\times \text{Growth percentage}\right)\\ =\$2,645,560+\left(\$2,645,560\times 0.18\right)\\ =\$3,121,761\end{array}$

Hence, the EBIT for Year 4 is $3,121,761.

Compute the EBIT for Year 5:

The EBIT for Year 4 is $3,121,761. The growth rate is 18 percent.

$\begin{array}{c}\text{EBIT for Year 5}=\text{EBIT for Year 4}+\left(\text{EBIT for Year 4}\times \text{Growth percentage}\right)\\ =\$3,121,761+\left(\$3,121,761\times 0.18\right)\\ =\$3,683,678\end{array}$

Hence, the EBIT for Year 5 is $3,683,678.

Compute the depreciation for Year 2:

The depreciation for Year 1 is $165,000. The growth rate is 18 percent.

$\begin{array}{c}\begin{array}{l}\text{Depreciation}\\ \text{for Year 2}\end{array}\}=\left(\begin{array}{l}\text{Depreciation}\\ \text{for Year 1}\end{array}\right)+\left(\begin{array}{l}\text{Depreciation for Year 1}\times \\ \text{Growth percentage}\end{array}\right)\\ =\$165,000+\left(\$165,000\times 0.18\right)\\ =\$194,700\end{array}$

Hence, the depreciation for Year 2 is $194,700.

Compute the depreciation for Year 3:

The depreciation for Year 2 is $194,700. The growth rate is 18 percent.

$\begin{array}{c}\begin{array}{l}\text{Depreciation}\\ \text{for Year 3}\end{array}\}=\left(\begin{array}{l}\text{Depreciation}\\ \text{for Year 2}\end{array}\right)+\left(\begin{array}{l}\text{Depreciation for Year 2}\times \\ \text{Growth percentage}\end{array}\right)\\ =\$194,700+\left(\$194,700\times 0.18\right)\\ =\$229,746\end{array}$

Hence, the depreciation for Year 3 is $229,746.

Compute the depreciation for Year 4:

The depreciation for Year 3 is $229,746. The growth rate is 18 percent.

$\begin{array}{c}\begin{array}{l}\text{Depreciation}\\ \text{for Year 4}\end{array}\}=\left(\begin{array}{l}\text{Depreciation}\\ \text{for Year 3}\end{array}\right)+\left(\begin{array}{l}\text{Depreciation for Year 3}\times \\ \text{Growth percentage}\end{array}\right)\\ =\$229,746+\left(\$229,746\times 0.18\right)\\ =\$271,100\end{array}$

Hence, the depreciation for Year 4 is $271,100.

Compute the depreciation for Year 5:

The depreciation for Year 4 is $271,100. The growth rate is 18 percent.

$\begin{array}{c}\begin{array}{l}\text{Depreciation}\\ \text{for Year 5}\end{array}\}=\left(\begin{array}{l}\text{Depreciation}\\ \text{for Year 4}\end{array}\right)+\left(\begin{array}{l}\text{Depreciation for Year 4}\times \\ \text{Growth percentage}\end{array}\right)\\ =\$271,100+\left(\$271,100\times 0.18\right)\\ =\$319,898\end{array}$

Hence, the depreciation for Year 5 is $319,898.

Compute the “Taxes*”:

Taxes*
	Year 1	Year 2	Year 3	Year 4	Year 5
EBIT(A)	$1,900,000	$2,242,000	$2,645,560	$3,121,761	$3,683,678
Tax rate(B)	35%	35%	35%	35%	35%
Taxes*(A)×(B)	$665,000	$784,700	$925,946	$1,092,616	$1,289,287

Compute the change in net working capital of Year 2:

The change in net working capital for Year 1 is $85,000. The growth rate is 18 percent.

$\begin{array}{c}\begin{array}{l}\text{Change in net}\\ \text{working capital}\\ \text{for Year 2}\end{array}\}=\left(\begin{array}{l}\text{Change in net}\\ \text{working capital}\\ \text{for Year 1}\end{array}\right)+\left(\begin{array}{l}\left(\begin{array}{l}\text{Change in net working capital}\\ \text{for Year 1}\end{array}\right)\times \\ \text{Growth percentage}\end{array}\right)\\ =\$85,000+\left(\$85,000\times 0.18\right)\\ =\$100,300\end{array}$

Hence, the change in net working capital for Year 2 is $100,300.

Compute the change in net working capital of Year 3:

The change in net working capital for Year 2 is $100,300. The growth rate is 18 percent.

$\begin{array}{c}\begin{array}{l}\text{Change in net}\\ \text{working capital}\\ \text{for Year 3}\end{array}\}=\left(\begin{array}{l}\text{Change in net}\\ \text{working capital}\\ \text{for Year 2}\end{array}\right)+\left(\begin{array}{l}\left(\begin{array}{l}\text{Change in net working capital}\\ \text{for Year 2}\end{array}\right)\times \\ \text{Growth percentage}\end{array}\right)\\ =\$100,300+\left(\$100,300\times 0.18\right)\\ =\$118,354\end{array}$

Hence, the change in net working capital for Year 3 is $118,354.

Compute the change in net working capital of Year 4:

The change in net working capital for Year 3 is $118,354. The growth rate is 18 percent.

$\begin{array}{c}\begin{array}{l}\text{Change in net}\\ \text{working capital}\\ \text{for Year 4}\end{array}\}=\left(\begin{array}{l}\text{Change in net}\\ \text{working capital}\\ \text{for Year 3}\end{array}\right)+\left(\begin{array}{l}\left(\begin{array}{l}\text{Change in net working capital}\\ \text{for Year 3}\end{array}\right)\times \\ \text{Growth percentage}\end{array}\right)\\ =\$118,354+\left(\$118,354\times 0.18\right)\\ =\$139,658\end{array}$

Hence, the change in net working capital for Year 4 is $139,658.

Compute the change in net working capital of Year 5:

The change in net working capital for Year 4 is $139,658. The growth rate is 18 percent.

$\begin{array}{c}\begin{array}{l}\text{Change in net}\\ \text{working capital}\\ \text{for Year 5}\end{array}\}=\left(\begin{array}{l}\text{Change in net}\\ \text{working capital}\\ \text{for Year 4}\end{array}\right)+\left(\begin{array}{l}\left(\begin{array}{l}\text{Change in net working capital}\\ \text{for Year 4}\end{array}\right)\times \\ \text{Growth percentage}\end{array}\right)\\ =\$139,658+\left(\$139,658\times 0.18\right)\\ =\$164,796\end{array}$

Hence, the change in net working capital for Year 5 is $164,796.

Compute the capital spending for Year 2:

The capital spending for Year 1 is $115,000. The growth rate is 18 percent.

$\begin{array}{c}\begin{array}{l}\text{Capital spending}\\ \text{for Year 2}\end{array}\}=\left(\begin{array}{l}\text{Capital spending for}\\ \text{Year 1}\end{array}\right)+\left(\begin{array}{l}\text{Capital spending for Year 1}\times \\ \text{Growth percentage}\end{array}\right)\\ =\$115,000+\left(\$115,000\times 0.18\right)\\ =\$137,500\end{array}$

Hence, the capital spending for Year 2 is $137,500.

Compute the capital spending for Year 3:

The capital spending for Year 2 is $137,500. The growth rate is 18 percent.

$\begin{array}{c}\begin{array}{l}\text{Capital spending}\\ \text{for Year 3}\end{array}\}=\left(\begin{array}{l}\text{Capital spending for}\\ \text{Year 2}\end{array}\right)+\left(\begin{array}{l}\text{Capital spending for Year 2}\times \\ \text{Growth percentage}\end{array}\right)\\ =\$137,500+\left(\$137,500\times 0.18\right)\\ =\$160,126\end{array}$

Hence, the capital spending for Year 3 is $160,126.

Compute the capital spending for Year 4:

The capital spending for Year 3 is $160,126. The growth rate is 18 percent.

$\begin{array}{c}\begin{array}{l}\text{Capital spending}\\ \text{for Year 4}\end{array}\}=\left(\begin{array}{l}\text{Capital spending for}\\ \text{Year 3}\end{array}\right)+\left(\begin{array}{l}\text{Capital spending for Year 3}\times \\ \text{Growth percentage}\end{array}\right)\\ =\$160,126+\left(\$160,126\times 0.18\right)\\ =\$188,949\end{array}$

Hence, the capital spending for Year 4 is $188,949.

Compute the capital spending for Year 5:

The capital spending for Year 4 is $188,949. The growth rate is 18 percent.

$\begin{array}{c}\begin{array}{l}\text{Capital spending}\\ \text{for Year 5}\end{array}\}=\left(\begin{array}{l}\text{Capital spending for}\\ \text{Year 4}\end{array}\right)+\left(\begin{array}{l}\text{Capital spending for Year 4}\times \\ \text{Growth percentage}\end{array}\right)\\ =\$188,949+\left(\$188,949\times 0.18\right)\\ =\$222,959\end{array}$

Hence, the capital spending for Year 5 is $222,959.

Compute the adjusted cash flow from assets “CFA*”:

Adjusted cash flow from assets "CFA*"
	Year 1	Year 2	Year 3	Year 4	Year 5
EBIT	$1,900,000	$2,242,000	$2,645,560	$3,121,761	$3,683,678
Add:
Depreciation	$165,000	$194,700	$229,746	$271,100	$319,898
	$2,065,000	$2,436,700	$2,875,306	$3,392,861	$4,003,576
Less:
Taxes*	$665,000	$784,700	$925,946	$1,092,616	$1,289,287
Capital spending	$115,000	$135,700	$160,126	$188,949	$222,959
Change in Net working capital	$85,000	$100,300	$118,354	$139,658	$164,796
CFA*	$1,200,000	$1,416,000	$1,670,880	$1,971,638	$2,326,533

Compute the terminal value or the value of the company at period “t”:

The adjusted cash flow from assets in year 5 is $2,326,533. The weighted average cost of capital is 8.5 percent. The adjusted cash flow from assets will grow at 3 percent for an indefinite period.

$\begin{array}{c}{V}_t=\frac{{\text{CFA*}}_{t+1}\left(1+g\right)}{WACC-g}\\ =\frac{\$2,326,533\left(1+0.03\right)}{0.085-0.03}\\ =\$43,569,618\end{array}$

Hence, the terminal value at Year 5 is $43,569,618.

Compute the value of the company:

The adjusted cash flow from assets for Year 1, Year 2, Year 3, Year 4, and Year 5 are $1,200,000, $1,416,000, $1,670,880, $1,971,638, and $2,326,533. The terminal value is $43,569,618. The weighted average cost of capital is 8.5 percent.

$\begin{array}{c}{V}_0=\frac{{\text{CFA*}}_1}{1+WACC}+\frac{{\text{CFA*}}_2}{{\left(1+WACC\right)}^2}+\frac{{\text{CFA*}}_3}{{\left(1+WACC\right)}^3}+\frac{{\text{CFA*}}_4}{{\left(1+WACC\right)}^4}+\frac{{\text{CFA*}}_5+V_5}{{\left(1+WACC\right)}^5}\\ =\left(\begin{array}{l}\frac{\$1,200,000}{1+0.085}+\frac{\$1,416,000}{{\left(1+0.085\right)}^2}+\frac{\$1,670,880}{{\left(1+0.085\right)}^3}+\\ \frac{\$1,971,638}{{\left(1+0.085\right)}^4}+\frac{\$2,326,533+\$43,569,618}{{\left(1+0.085\right)}^5}\end{array}\right)\\ =\$1,105,990.78+\$1,202,828.69+\$1,308,145.48+\$1,422,683.29+\$30,523,025.18\\ =\$35,562,673.40\end{array}$

Hence, the value of the company is $35,562,673.40.

Compute the total value of equity:

$\begin{array}{c}\text{Total value of equity}=\text{Value of the company}-\text{Total value of debt}\\ =\$35,562,673.40-\$13,000,000\\ =\$22,562,673.40\end{array}$

Hence, the total value of equity is $22,562,673.40.

Compute the price per share of the company’s stock:

$\begin{array}{c}\text{Price per share}=\frac{\text{Total value of equity}}{\text{Number of shares}}\\ =\frac{\$22,562,673.40}{800,000\text{ shares}}\\ =\$28.20\end{array}$

Hence, the price per share is $28.20.