Arguably, the role of a corporation's management is to increase the value of the firm to its shareholders while observing applicable laws and responsibilities. Corporate finance deals with the strategic financial issues associated with achieving this goal, such as how the corporation should raise and manage its capital, what investments the firm should make, what portion of profits should be returned to shareholders in the form of dividends, and whether it makes sense to merge with or acquire another firm.

**Balance Sheet Approach to Valuation**

If the role of management is to increase the shareholder value, then managers can make better decisions if they can predict the impact of those decisions on the firm's value. By observing the difference in the firm's equity value at different points in time, one can better evaluate the effectiveness of financial decisions. A rudimentary way of valuing the equity of a company is simply to take its balance sheet and subtract liabilities from assets to arrive at the equity value. However, this book value has little resemblance to the real value of the company. First, the assets are recorded at historical costs, which may be much greater than or much less their present market values. Second, assets such as patents, trademarks, loyal customers, and talented managers do not appear on the balance sheet but may have a significant impact on the firm's ability to generate future profits. So while the balance sheet method is simple, it is not accurate; there are better ways of accomplishing the task of valuation.

**Cash vs. Profits**

Another way to value the firm is to consider the future flow of cash. Since cash today is worth more than the same amount of cash tomorrow, a valuation model based on cash flow can discount the value of cash received in future years, thus providing a more accurate picture of the true impact of financial decisions.

Decisions about finances affect operations and vice versa; a company's finances and operations are interrelated. The firm's working capital flows in a cycle, beginning with cash that may be converted into equipment and raw materials. Additional cash is used to convert the raw materials into inventory, which then is converted into accounts receivable and eventually back to cash, completing the cycle. The goal is to have more cash at the end of the cycle than at the beginning.

The change in cash is different from accounting profits. A company can report consistent profits but still become insolvent. For example, if the firm extends customers increasingly longer periods of time to settle their accounts, even though the reported earnings do not change, the cash flow will decrease. As another example, take the case of a firm that produces more product than it sells, a situation that results in the accumulation of inventory. In such a situation, the inventory will appear as an asset on the balance sheet, but does not result in profit or loss. Even though the inventory was not sold, cash nonetheless was consumed in producing it.

Note also the distinction between cash and equity. Shareholders' equity is the sum of common stock at par value, additional paid-in capital, and retained earnings. Some people have been known to picture retained earnings as money sitting in a shoe box or bank account. But shareholders' equity is on the opposite side of the balance sheet from cash. In fact, retained earnings represent shareholders' claims on the assets of the firm, and do not represent cash that can be used if the cash balance gets too low. In this regard, one can say that retained earnings represent cash that already has been spent.

Shareholder equity changes due to three things:

- net income or losses
- payment of dividends
- share issuance or repurchase.

Changes in cash are reported by the cash flow statement, which organizes the sources and uses of cash into three categories: operating activities, investing activities, and financing activities.

**Cash Cycle**

The duration of the cash cycle is the time between the date the inventory (or raw materials) is paid for and the date the cash is collected from the sale of the inventory. A company's cash cycle is important because it affects the need for financing. The cash cycle is calculated as:

days in inventory + days in receivables - days in payables

Financing requirements will increase if either of the following occurs:

Sales increase while the cash cycle remains fixed in duration. Increased sales increase the value of assets in the cycle.

Sales remain flat but the cash cycle increases in duration.

While financially it makes sense to reduce the length of the cash cycle, such a reduction should not be done without considering the impact on operations. For example, one must consider the impact on customer and supplier relations as well as the impact on order fill rates.

**Revenue, Expenses, and Inventory**

A firm's income is calculated by subtracting its expenses from its revenue. However, not all costs are considered expenses; accounting standards and tax laws prohibit the expensing of costs incurred in the production of inventory. Rather, these costs must be allocated to inventory accounts and appear as assets on the balance sheet. Once the finished goods are drawn from inventory and sold, these costs are reported on the income statement as the cost of goods sold (COGS). If one wishes to know how much product the firm actually *produced*, the cost of goods produced in an accounting period is determined by adding the change in inventory to the COGS.

**Assets**

Assets can be classified as current assets and long-term assets. It is useful to know the number of days of certain assets and liabilities that a firm has on hand. These numbers are easily calculated from the financial statements as follows:__Accounts Receivable (A/R)__

Number of days of A/R = ( accounts receivable / annual credit sales ) ( 365 ).

This also is known as the *collection period*.

__Inventory__

Number of days of inventory = ( inventory / annual COGS ) ( 365 ).

This also is known as the *inventory period*.

On the liabilities side:

__Payables__

Number of days of accounts payable = ( accounts payable / COGS ) ( 365 ), assuming that all accounts payable are for the production of goods. This also is known as the *payables period*.

**Financial Ratios**

A firm's performance can be evaluated using various financial ratios. Ratios are used to measure leverage, margins, turnover rates, return on assets, return on equity, and liquidity. Additional insight can be gained by comparing ratios among firms in the industry.

**Bank Loans**

Bank loans can be classified according to their durations. There are short-term loans (one year or less), long-term loans (also known as term loans), and revolving loans that allow one to borrow up to a specified credit level at any time over the duration of the loan. Some revolving loans automatically renew at maturity; these loans are said to be "evergreen."**Sources and Uses of Cash**

It can be worthwhile to know where a firm's cash is originating and how it is being used. There are two sources of cash: reducing assets or increasing liabilities or equity. Similarly, a company uses cash either by increasing assets or decreasing liabilities or equity.

**Sustainable Growth**

A company's sustainable growth rate is calculated by multiplying the ROE by the earnings retention rate.**Firm Value, Equity Value, and Debt Value**

The value of the firm is the value of its assets, or rather, the present value of the unlevered free cash flow resulting from the use of those assets. In the case of an all-equity financed firm, the equity value is equal to the firm value. When the firm has issued debt, the debt holders have a priority claim on their interest and principal, and the equity holders have a residual claim on what remains after the debt obligations are met. The sum of the value of the debt and the value of the equity then is equal to the value of the firm, ignoring the tax benefits from the interest paid on the debt. Considering taxes, the effective value of the firm will be higher since a levered firm has a tax benefit from the interest paid on the debt. If there is outstanding preferred stock, the firm value is the sum of the equity value, debt value, and preferred stock value, plus the value of the interest tax shield.

The debt holders and stock holders each have a claim on the cash flows of the firm. In a given time period, the debt holders have a claim equal to the interest payments during that period plus any principal payments that are due. The stock holders then have a claim equal to the unlevered free cash flow in that period plus the cash generated by the interest tax shield, minus the claims of the debt holders.**Capital Structure**

The proportion of a firm's capital structure supplied by debt and by equity is reported as either the debt to equity ratio (D/E) or as the debt to value ratio (D/V), the latter of which is equal to the debt divided by the sum of the debt and the equity.

One can quickly convert between the D/E ratio and the D/V ratio by using the following relationships:

**Risk Premiums**

**Business risk**is the risk associated with a firm's operations. It is the undiversifiable volatility in the operating earnings (EBIT). Business risk is affected by the firm's investment decisions. A measure for the business risk is the asset beta, also known the unlevered beta. In terms of the discount rate, the return on assets of a firm can be expressed as a function of the risk-free rate and the business risk premium (BRP):

_{A}= r

_{F}+ BRP

**Financial risk**is associated with the firm's capital structure. Financial risk magnifies the business risk of a firm. Financial risk is affected by the firm's financing decision.

**Total corporate risk**is the sum of the business and financial risks and is measured by the equity beta, also known as the levered beta. The business risk premium (BRP) and financial risk premium (FRP) are reflected in the levered (equity) beta, and the return on levered equity can be written as:

_{E}= r

_{F}+ BRP + FRP

Debt beta is a measure of the risk of a firm's defaulting on its debt. The return on debt can be written as:

_{D}= r

_{F}+ default risk premium

**Cost of Capital**

The cost of capital is the rate of return that must be realized in order to satisfy investors. The cost of debt capital is the return demanded by investors in the firm's debt; this return largely is related to the interest the firm pays on its debt. In the past some managers believed that equity capital had no cost if no dividends were paid; however, equity investors incur an opportunity cost in owning the equity of the firm and they therefore demand a rate of return comparable to what they could earn by investing in securities of comparable risk.

The return required by debt holders is found by applying the CAPM:

r_{D} = r_{F} + beta_{debt} ( r_{M} - r_{F} )

The required rate of return on assets (that is, on unlevered equity) can be found using the CAPM:

r_{A} = r_{F} + beta_{unlevered} ( r_{M} - r_{F} )

Using the CAPM, a firm's required return on equity is calculated as:

r_{E} = r_{F} + beta_{levered} ( r_{M} - r_{F} )

Under the Modigliani-Miller assumptions of constant cash flows and constant debt level, the required return on equity is:

r_{E} = r_{A} + (1-τ)(r_{A} - r_{D})(D / E)

where τ is the corporate tax rate.

The overall cost of capital is a weighted-average of the cost of its equity capital and the after-tax cost of its debt capital. The weighted average cost of capital (WACC) then is given by:

WACC = r_{E} (E / V_{L}) + r_{D} (1-τ)(D / V_{L})

Assuming perpetuities for the cash flows, the weighted average cost of capital can be calculated as:

WACC = r_{A} [ 1 - τ(D / V_{L})]

Neglecting taxes, the WACC would be equal to the expected return on assets because the WACC is the return on a portfolio of all the firm's equity and all of its debt, and such a portfolio essentially has claim to all of the firm's assets.

For arbitrary cash flows, and under the assumption that the debt to value ratio is held constant, the following relationship derived by James A. Miles and John R. Ezzell is applicable:

WACC = r_{A} - τ r_{D} (D / V_{L})(1+r_{A}) / (1+r_{D})

Under the same assumptions, the cost of equity capital can be calculated from r_{A} and r_{D} using the following relationship from Miles and Ezzell:

r_{E} = r_{A} + [ 1 - τ r_{D} / (1+r_{D})] [ r_{A} - r_{D} ] D/E

For low values of r_{D}, [ 1 - τ r_{D} / (1+r_{D})] is approximately equal to one, and the expression can be simplified if high precision is not required.

If one cannot assume a constant debt to value ratio, then the APV method should be used.

#### Estimating Beta

In order to use the CAPM to calculate the return on assets or the return on equity, one needs to estimate the asset (unlevered) beta or the equity (levered) beta of the firm. The beta that often is reported for a stock is the levered beta for the firm. When estimating a beta for a particular line of business, it is better to use the beta of an existing firm in that exact line of business (a pure play) rather than an average beta of several firms in similar lines of business that are not exactly the same.

Expressing the levered beta, unlevered beta, and debt beta in terms of the covariance of their corresponding returns with that of the market, one can derive an expression relating the three betas. This relationship between the betas is:

beta_{levered} = beta_{unlevered} [ 1 + (1 - τ) D/E ] - beta_{debt}(1- τ) D/E

beta_{unlevered} = [ beta_{levered} + beta_{debt}(1- τ) D/E ] / [ 1 + (1 - τ) D/E ]

The debt beta can be estimated using CAPM given the risk-free rate, bond yield, and market risk premium.

**Unlevered Free Cash Flows**

To value the operations of the firm using a discounted cash flow model, the unlevered free cash flow is used. The unlevered free cash flow represents the cash generated by the firm's operations and is the cash that is free to be paid to stock and bond holders after all other operating cash outlays have been performed.

**Terminal Value**

The value of the firm at the end of the last year for which unique cash flows are projected is known as the terminal value. The terminal value is important because it can represent 50% or more of the total value of the firm.

**Three Discounted Cash Flow Methods for Valuing Levered Assets**

__APV (Adjusted Present Value) Method__

The APV approach first performs the valuation under an unlevered all-equity assumption, then adjusts this value for the effect of the interest tax shield. Using this approach,

_{L}= V

_{U}+ PVITS

where V

_{L}= value if levered

V

_{U}= value if financed 100% with equity

PVITS = present value of interest tax shield

The unlevered value is found by discounting the unlevered free cash flow at the required return on assets. The present value of the interest tax shield is found by discounting the interest tax shield savings at the required return on debt, r

_{D}.

The APV method is useful for valuing firms with a changing capital structure since the return on assets is independent of capital structure. For example, in a leveraged buyout, the debt to equity ratio gradually declines, so the required return on equity and the weighted average cost of capital change as the lenders are repaid. However, when calculating the terminal value it may be appropriate to assume a stable capital structure, so in calculating the terminal value in a leveraged buyout situation the WACC method may be a better approach.

__Flows to Equity Method__

The flows to equity method sums the NPV of the cash flows to equity and to debt.

Then, V

_{L}= E + D

__WACC Method__

The WACC method discounts the unlevered free cash flow at the weighted average cost of capital to arrive at the levered value of the firm.

**Cash Flows to Debt and Equity**

When calculating the amount of cash flowing to debt and equity holders, it is not appropriate to use the unlevered free cash flows because these cash flows do not reflect the tax savings from the interest paid. Starting with the UFCF, add back the taxes saved to obtain the total amount of cash available to suppliers of capital.**Hurdle Price**

At times a firm may wish to know at what price it would have to sell its product for a particular investment to have a positive net present value. A procedure for determining this price is as follows:

- Express the operating cash flow in terms of price. There may be multiple phases such as a short start-up period, a long operating period, and a final year in which the terminal value is calculated.

- Write out the expression for the NPV using the appropriate discount rate. For the longer operating period, one can calculate an annuity factor to multiply by the operating cash flow expression. Solve the expression for the cash flow that would result in an NPV of zero.

- Since the operating cash flow was written in terms of price, the price now can be found.

**Debt Valuation**

While debt may be issued at a particular face value and coupon rate, the debt value changes as market interest rates change. The debt can be valued by determining the present value of the cash flows, discounting the coupon payments at the market rate of interest for debt of the same duration and rating. The final period's cash flow will include the final coupon payment and the face value of the bond.

**Investment Decision**

If the unlevered NPV of a project is negative, aside from potential strategic benefits, the project is destroying value, even if the levered NPV is positive. The firm always could benefit from the tax shield of debt by borrowing money and putting it to other uses such as stock buybacks.**Optimal Capital Structure**

The total value of a firm is the sum of the value of its equity and the value of its debt. The optimal capital structure is the amount of debt and equity that maximizes the value of the firm.**Share Buyback**

If a firm has extra cash on hand it may choose to buy back some of its outstanding shares. One interesting aspect of such transactions is that they can be based on information that the firm has that the market does not have. Therefore, a share buyback could serve as a signal that the share price has potential to rise at above average rates.**Mergers and Acquisitions**

Companies may combine for direct financial reasons or for non-financial ones such as expanding a product line. The target firm usually is acquired at a premium to its market value, with the hope that synergies from the merger will exceed the price premium. Mergers and acquisitions do not always achieve their goals, as promised syngeries may fail to materialize.

Appendix

**Compounding and Discounting**

Compound annual growth rate (CAGR): ( FV/C )

^{1/T}- 1

Continuous compounding: FV

_{t}= C e

^{r t}

Perpetuity: PV = C / r

Growing perpetuity: PV = C / ( r - g )

T-year annuity (T equally spaced payments): PV = ( C / r ) [ 1 - 1/(1+r)

^{T}]

T-year growing annuity: PV = [C / (r - g)] { 1 - [(1+g) / (1+r)]

^{T}}

**HP 19BII Calculator Tip**

IRR Calculation:

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