19.2 Impact of Risk

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Problem. What impact does the firm's risk have upon the firm's Debt and Equity valuation? Specifically,

if you increased Firm Asset Standard Deviation, then what would happen to the firm’s Equity Value and

Risky Debt Value?

Solution Strategy. Create a Data Table of Equity Value and Risky Debt Value for different input values

for the Firm's Asset Standard Deviation. Then graph the results and interpret it.

FIGURE 19.2 Spreadsheet of the Sensitivity of Equity Value and Risky Debt Value.

How To Build This Spreadsheet Model.

1. Start with the Debt and Equity Valuation - Two Methods Spreadsheet and Change the

Inputs. Open the spreadsheet that you created for Debt and Equity Valuation – Two Methods and

immediately save the spreadsheet under a new name using the File | Save As command.

2. Create A List of Input Values and Add Two More Output Formulas. Create a list of input

values for the Firm Asset Standard Deviation (30.0%, 40.0%, 50.0%, etc.) in the range C35:G35.

Add two more output formulas. One that references the firm’s Equity Value (E) by entering the

formula =C27 in cell B36. Another that references the firm’s Risky Debt Value (D) by entering

the formula =C29 in cell B37.

3. Data Table. Select the range B35:G37 for the Data Table. This range includes both the list of

input values at the top of the data table and the two output formulas on the side of the data table.

Then choose Data | Table from the main menu and a Table dialog box pops up. Enter the Firm

Asset Standard Deviation cell B5 in the Row Input Cell and click on OK.

4. Graph the Sensitivity Analysis. Highlight the range C36:G37 and then choose Insert | Chart

from the main menu. Select an XY(Scatter) chart type and make other selections to complete

the Chart Wizard.

Looking at the chart, we see that increasing the firm's asset standard deviation causes a wealth transfer

from debtholders to equityholders. This may seem surprising, but this is a direct consequence equity

being a call option and debt being V minus a call option. We know that increasing the standard deviation

makes a call more valuable, so equivalently increases the firm's asset standard deviation makes the firm's

Equity Value more valuable and reduces the Risky Debt Value by the same amount.

The intuitive rational for this is that an increase in standard deviation allows equityholders to benefit from

more frequent and bigger increases in V, while not being hurt by more frequent and bigger decreases in

V. In the later case, the equityholders are going to declare bankruptcy anyway so they don’t care how

much V drops. Debtholders are the mirror image. They do not benefit from more frequent and bigger

increases in V since repayment is capped at B, but they are hurt by more frequent and bigger decreases in

V. In the latter case, the size of the repayment default (B – V) increases as V drops more.

The possibility of transferring wealth from debtholders to equityholders (or visa versa) illustrates the

potential for conflict between equityholders and debtholders. Equityholders would like the firm to take on

riskier projects, but debtholders would like the firm to focus on safer projects. Whether the firm

ultimately decides to take on risky or safe projects will determine how wealth is divided between the two

groups.