Appendix: Mathematics of the Mean–Variance Model
I. A.5.4.2 Debt can be attractive
There are a number of circumstances when increasing the proportion of debt financing will either improve the expected cash flow or reduce the cost of capital, thereby increasing the value of the business.
I.A.5.4.2.1 Differential treatment of payments to debt-holders and shareholders
Classical taxation systems, such as that currently operating in the USA, treat payments of interest to debt-holders more favourably than payments to shareholders. Payment of interest is deductible, whereas payment of dividends is not. Consequently, financing with debt offers an advantage that financing with equity does not. The total cash outflow to the tax authorities will be lower, the greater the debt employed. This is, in fact, a powerful incentive to use debt as the value of the firm will rise as the funding mix is changed from all equity to more and more debt.
Illustration
The value of the health insurance business in the last section was $1,250,000, valued as follows:
V = OFCF / WACC
= 150,000 / 0.12
= $1,250,000.
If corporate tax is now introduced at 30% (tc) the value will fall because less earnings are available for distribution. Or put another way, the government has taken a portion of the value of the firm to meets broader society goals. In this case the relevant operating free cash flow will be
Copyright© 2004 S. Bishop and the Professional Risk Managers’ International Association 15
after tax and becomes OFCF(1 – tc) or 150,000 × 0.7 = $105,000. The value of the business becomes:
V = OFCF (1 – tc) / WACC
= 105,000 / 0.12
= $875,000.
What happens if the business is financed in part by debt? Suppose $500,000 of debt is raised at 8%. Here the business gets relief on its tax bill because of the interest payment. Tax will be
$12,000 lower each year:
Tax relief p.a. = Interest × tax rate
= Debt × interest rate × tax rate = 500,000 × 0.08 × 0.3
= 12,000.
Since this will be received each year, and its risk is a function of the risk of the debt, the present value (PV) of this benefit in perpetuity will be
PV of tax relief = (Debt × interest rate × tax rate) / interest rate
= 12,000 / 0.08
= $150,000,
and the value of the business will be higher by this amount, that is,
V = value before plus PV of tax relief
= 875,000 + 150,000
= $1,025,000.
The implication of this analysis is that the greater the debt employed, the bigger the tax shield and the higher the value of the business!
In this illustration, all the benefit flowing from the lower tax payment has been treated as an increase in the operating free cash flow after tax, relative to the all-equity case. The benefit of lower tax could also have been calculated by keeping the after tax operating free cash flow at
$105,000 and reflecting the benefit as a lower WACC.
The tax benefit associated with debt arises because interest payments to debt-holders are tax-deductible but dividend payments to shareholders are not. Imputation tax systems, such as that Copyright© 2004 S. Bishop and the Professional Risk Managers’ International Association 16
operating in Australia, work to reduce this bias. The bias is not fully removed, however, as overseas investors do not receive the tax rebate on tax paid on dividends which is available to Australian residents. Consequently, debt is less attractive from this perspective in Australia than in the USA.
I.A.5.4.2.2 Greater Flexibility
Retaining earnings, rather than paying dividends, is the lowest transaction cost method of raising equity. In rapidly growing businesses, however, the funds available from this source are often inadequate. Further, investment opportunities generally do not offer themselves concurrently with the availability of cash earnings. Raising new equity, on the other hand, is quite expensive and time-consuming.
Debt can often be raised relatively quickly and when needed with little notice – for example, stand-by facilities provide funds with little time delay.
Debt finance gives greater flexibility so that value-creating opportunities can be exploited.
Undue reliance on equity finance might mean that value-creating opportunities are passed over, causing a relative loss in shareholder value.
I.A.5.4.2.3 Monitoring ‘improves’ performance and reduces the negative aspect of information asymmetry
An interesting empirical finding noted earlier is that the value of a firm rises when it announces bank-issued debt. One explanation for this is that banks are good at watching the value of their debt. They require frequent reporting from the firm so that they can carefully monitor its prospects, the quality of its strategy and the performance of management. The banks therefore serve to reduce the negative impact of information asymmetry between investors and management; investors have greater confidence that their interests are partially protected as the bank protects its interests. Consequently, one positive impact of debt is the increased monitoring of the prospects of the firm by interested parties, which can lead to an increase in shareholder value.
I.A.5.4.2.4 Debt enforces a discipline of paying out operating earnings
Another potential benefit of having debt financing is that it reduces the opportunity for management to invest earnings in bad investments (negative net present value (NPV) investments). By being committed to meet interest payments, management has less unused funds to divert to poor decisions. With high interest payments relative to income, there is less uncommitted cash to invest. Consequently, with high debt payouts, if management wants to undertake a substantive investment opportunity it has to go to the market to request the capital.
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The investment opportunity is subjected to much more careful scrutiny than if funded through retained earnings.
This has greatest importance for mature businesses that generate large amounts of cash and have few positive NPV investment opportunities. Here we might expect to see a higher proportion of debt financing in mature industries where management face the temptation of investing for size rather than value!
It is also argued that the high level of debt and consequent interest payments sharpen management’s attention in leveraged buyouts and management buyouts. These transactions are typified by a substantial proportion of debt financing providing a challenge for management to turn the business around and pay down the debt to a level sustainable in the longer term.
I.A.5.4.2.5 Debt financing avoids negative signals about management’s view of the value of equity
It was noted earlier that there is well-documented evidence that, on average, the value of equity falls when a firm issues new shares. This is attributed to management having more knowledge about the firm’s prospects than do investors. Managers tend to issue equity when they perceive it to be over-valued and the market responds accordingly with a downgrade of share price. Use of debt rather than equity minimises this impact. Myers and Majluf (1984) argue that a firm should use internal sources of funds first, then debt, then hybrid, and finally equity for this reason.