Chapter 17, Problem 3MC

One year from now, how much value creation is expected from the expansion? How much value is expected for stockholders? Bondholders?

Summary Introduction

To determine: The Expected Value creation from expansion one year from now and the Expected Value for Stockholders and Bondholders.

Introduction:

The cost of equity is the yield than an investor anticipates from the security as returns for the risk they accept by spend in the specific security. Additionally it is the return an investor needs before they prefer for an alternative investment which pays higher than the correct. The cost of debt is the effective interest rate of cost which a business earns on their current debts. Debt involves in the formation of capital structure. As the debt is considered as deduction expenditure, the cost of debt is usually determined as after-tax cost in order to formulate similar to the cost of equity.

Answer to Problem 3MC

Solution:

The Expected Value creation from expansion one year from now for With Expansion is $8,900,000 and Without Expansion is $3,600,000 and the Expected Value for Stockholders is $5,300,000 and Bondholders is $600,000.

Explanation of Solution

Determine the Expected Value of Equity Without Expansion

The company’s equity with low economic growth is 0 for both the plans as the value of the company is lower than its face value of debt. Hence the values of equity with normal or high growth are subtracted with the face value of debt of $25,000,000.

$\begin{array}{c}ExpectedValu{e}_{WithoutExpansion}=\left[\begin{array}{l}\left(\mathrm{Pr}obabilit{y}_{Low}\times Valu{e}_{Low}\right)+\\ \left(\mathrm{Pr}obabilit{y}_{Normal}\times Valu{e}_{Normal}\right)+\\ \left(\mathrm{Pr}obabilit{y}_{High}\times Valu{e}_{High}\right)\end{array}\right]\\ =\left[\begin{array}{l}\left(0.30\times 0\right)+\left(0.50\times \left(\$25,000,000-\$25,000,000\right)\right)+\\ \left(0.20\times \left(\$43,000,000-\$25,000,000\right)\right)\end{array}\right]\\ =\left[\$0+\$0+\$3,600,000\right]\\ =\$3,600,000\end{array}$

Therefore the Expected Value of Equity Without Expansion is $3,600,000.

Determine the Expected Value of Equity With Expansion

$\begin{array}{c}ExpectedValu{e}_{WithExpansion}=\left[\begin{array}{l}\left(\mathrm{Pr}obabilit{y}_{Low}\times Valu{e}_{Low}\right)+\\ \left(\mathrm{Pr}obabilit{y}_{Normal}\times Valu{e}_{Normal}\right)+\\ \left(\mathrm{Pr}obabilit{y}_{High}\times Valu{e}_{High}\right)\end{array}\right]\\ =\left[\begin{array}{l}\left(0.30\times 0\right)+\left(0.50\times \left(\$32,000,000-\$25,000,000\right)\right)+\\ \left(0.20\times \left(\$52,000,000-\$25,000,000\right)\right)\end{array}\right]\\ =\left[\$0+\$3,500,000+\$5,400,000\right]\\ =\$8,900,000\end{array}$

Therefore the Expected Value of Equity With Expansion is $8,900,000.

Determine the Stockholders Profit

$\begin{array}{c}Stockholders\mathrm{Pr}ofit=\left[ExpectedValu{e}_{WithExpansion}-ExpectedValu{e}_{WithoutExpansion}\right]\\ =\left[\$8,900,000-\$3,600,000\right]\\ =\$\text{5,300,000}\end{array}$

Therefore the Stockholders Profit is $5,300,000.

Determine the Expected Value of Stockholders

$\begin{array}{c}ExpectedValu{e}_{Stockholders}=\left[-CostofEquity+Stockholders\mathrm{Pr}ofit\right]\\ =\left[-\$5,700,000+\$5,300,000\right]\\ =-\$400,000\end{array}$

Therefore the Expected Value of Stockholders is -$400,000.

Determine the Expected Value of Bondholders

$\begin{array}{c}ExpectedValu{e}_{Bondholders}=\left[\begin{array}{l}ExpectedValueofDeb{t}_{WithExpansion}-\\ ExpectedValueofDeb{t}_{WithoutExpansion}\end{array}\right]\\ =\left[\$24,100,000-\$23,500,000\right]\\ =\$600,000\end{array}$

Therefore the Expected Value of Bondholders is $600,000.