The Borrowing Mix

05/15/08Ch. 8

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What is the Borrowing Mix?

The Borrowing Mix The funds used to finance the operations and

the sources of the funds Debt

Bank Loans Bonds

Hybrid Stock – Preferred Stock Equity

Shares Owner’s Money

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Objective of the Firm

The objective of the firm Maximize Shareholder/Owner Wealth Wealth is the future cash flow of the firm

discounted back to today at the appropriate weight

Debt holders paid first Debt is leverage and can increase the wealth

of the owner Objective is to find the borrowing mix that

maximizes the value of the firm

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Value of the Firm

Value of the company “claimed” by owners Think of company as a project Value is NPV = -Inv + Σ Cash Flowi / (1+ r)I

And r is the cost of capital, hurdle rate, or WACC

CDE TRV

DR

V

E 1Capital ofCost

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If Cash Flow is fixed…

Lowest cost of capital maximizes the value of the firm

Find borrowing mix that results in the lowest cost of capital

This is the optimal capital structure of the firm Ways to find optimal capital structure

Operating Income Approach Cost of Capital Approach Adjusted Present Value Approach

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Operating Income Approach

What operating income is the firm capable of producing (distribution)

What different levels of debt will the firm be able to make payments on debt (probability of default)

Select an acceptable probability of default Compare probability of default at different borrowing

amounts… If you can handle more debt, add debt If you can not handle more debt, reduce debt

Difficult part of the task…distribution of operating income

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Operating Income Approach

Personal Example…How big a house can you buy? You estimate your annual income Cash you have on hand (down payment) Percent of your income you want to commit to

the house payment (P&I, Insurance, PMI, Taxes)

Rule of thumb is 35% of income Same concept for a corporation, how much

debt can it handle?

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Operating Income Approach

Average Income and standard deviation of income (normal distribution assumption)

Estimate the cash outflow per year for the debt (principal (sinking fund) and interest) Adjust cost of debt as you borrow more

Find probability of default (find the t-statistic and look up the probability)

Compare probability of default to Company’s acceptable level

Borrow until you hit the acceptable level…

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Example from the book…

Disney’s average income $2,713 Disney’s standard deviation on income

19.54% Disney’s acceptable level of default, 5% Break-even debt level

($2,713 – X) / (0.1954 x $2,713) = 1.645

1.645 is the t-statistic where you have 5% probability of default

X = $1,841 million

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Cost of Capital Approach

Want to find the lowest WACC Lowest WACC is the combination of borrowing

that produces the highest firm value As you add debt

Cost of equity rises

CDE TRV

DR

V

E 1Capital ofCost

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Calculating WACC

Cost of Equity Security Market Line

Cost of Debt YTM on an outstanding bond Multiply by 1 minus the tax rate

Market value of Equity and Debt Equity + Debt = Value of the Firm

Adjusting from current D/E to Optimal D/E

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Increasing Leverage – Impact on WACC

Beta increases as more debt is added and thus equity holders require higher return BetaLEV = BetaUNLEV x (1+ [1-tax rate] x [D/e])

Cost of debt (Yield) increases with more debt… Bond ratings fall as you increase debt Bond ratings correlated with yields

How to estimate bond rating from interest coverage ration

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Interest Coverage Ratio

Measure of how many times over the current (or projected) EBIT can cover the interest expense of the debt Interest Coverage Ratio = EBIT / Interest

Expense Table 8.3 for Bond Rating (page 351) Table 8.4 for yield by Bond Rating (page 352) Market interest rate is a function of current risk

free rate and the default spread This is RD

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Table of Cost of Capital

With the levered beta and the current risk free rate and market premium… Find the cost of equity at different D/E Your increasing beta as you increase D/E

Calculate Interest Coverage Ratio as you add more debt (Interest Expense increases and EBIT is constant) Find bond rating at the Interest Coverage

Ratio Find the yield based on spread and risk free

rate

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Table Cost of Capital

Find the Market Value of Equity Find the Market Value of Debt Find WACC at the different D/E ratios… Look for the lowest WACC This is the optimal D/E ratio

Adjustment to tax rate at higher levels of debt The (1 – tax rate) in WACC assumes you can

use all of the tax shield from debt Benefit only up to the EBIT of the company

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Application of Lowest WACC

Once you find the optimal debt structure of the firm You can estimate the value of the firm Dividend growth model

gWACC /g1Firm) toflow(Cash FirmValue

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What is Cash Flow to the Firm

EBIT (Earnings before interest and taxes)

+ Depreciation (non cash flow expense)- Taxes - Capital Spending (funds used to buy PPE)- Change in Net Working Capital

= Free Cash Flow to Owners

With Market Value of Equity (outstanding shares x price) and Market Value of Debt (bonds outstanding x price of bonds)

Find the growth rate in the company…

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Finding a growth rate

First, from the “dividend growth” model we are looking at the growth rate of the cash flow to the firm…

One way to find the growth rate is too find the historical cash flows to the firm and calculate either an arithmetic or geometric growth rate

A second way…example in the book is to assume you have current cash flow, current firm value and WACC then back into growth rate…conservative approach is to use the risk-free rate

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Moving to Optimal D/E

Once we know the WACC at the optimal D/E Once we find the Cash Flow to Firm Once we find growth rate We can use the “Dividend Growth Model” to

find the new firm value at the optimal D/E Increase in firm value goes to the owners

Recall debt is a fixed claim Calculate new stock price

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Disney Example – page 357

Cash Flow to Firm = $1,722 Market Value of Equity = $55,101 Market Value of Debt = $14,668 Growth Rate = 5.98% Lowest WACC = 8.50% Firm Value = $72,420 at optimal D/E Increase in Firm Value = $2,651 Increase in price of stock = $1.29 per share

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Adjustments to Cost of Capital Approach Growth rate...what is a sustainable growth

rate? Is 5.98% too high…should it match risk free rate?

Is the firm willing to accept low bond ratings? If not the highest D/E may not be the optimal D/E

Is Cash Flow to the Firm at the appropriate level…was this a good year or a bad year

Was capital spending high or low for the year?

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Adjusted Present Value Approach

Start with an all equity firm… Find its value

Find the marginal benefit of the tax shield Find the marginal cost of bankruptcy

(distress) Add debt to the firm as long as the marginal

benefit of the tax shield is greater than the marginal cost of bankruptcy (distress)

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Marginal Benefits of Debt

The interest payment on debt is an expense and reduces the taxes of the firm as long as the interest expense is equal to or less than the EBIT (there are carry forwards…but skip that for now)

Value of Tax Shield Marginal Tax Rate times Amount of Debt This is the present value of the Tax Shield

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Marginal Cost of Bankruptcy

This is very difficult to estimate but it is the cost if you fall into default and those indirect costs that you incur to stay out of default

Assess the probability of default (again, not easy to do…book suggests a probit regression of past sinners)

Cost to firm is probability of default times the present value of the cost of bankruptcy

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Value of the Firm APV

Find Current Value Discounted Cash Flows, “Dividend growth

model” etc. Starting point for value then start adding debt

Add in the present value of the tax shield Subtract the present value of bankruptcy Does Firm Value Increase?

Yes, add more debt No, subtract debt

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Tuesday Homework

Problem #1 Problem #2 a and b only Problem #3 a, b, c and d only Problem #7 Problem #10 Problem #13 Problem #21 a and b only