Monday, January 14, 2008

Free Cash Flow

When valuing the operations of a firm using a discounted cash flow model, the operating cash flow is needed. This operating cash flow also is called the unlevered free cash flow (UFCF). The term "free cash flow" is used because this cash is free to be paid back to the suppliers of capital.

Calculating Free Cash Flow

For a particular year, the unlevered free cash flow is calculated as follows:

  1. Start with the annual sales and subtract cash costs and depreciation to calculate the earnings before interest and taxes (EBIT). The EBIT also is referred to as the operating income and represents the pre-tax earnings without regard to how the business is financed.

  2. Calculate the earnings before interest and after tax (EBIAT) by multiplying the EBIT by one minus the tax rate. Note that the EBIAT represents the after-tax earnings of the firm as if it were financed entirely with equity capital.

  3. To arrive at the UFCF, add the depreciation expense back to the EBIAT, and subtract capital expenditures (CAPEX) that were not charged against earnings and subtract any investments in net working capital (NWC).

The free cash flow calculation in equation form:

Operating Income (EBIT) = Revenues – Cash Costs – Depreciation Expense

EBIAT = EBIT – Taxes, where Taxes = (tax rate)(EBIT)

UFCF = EBIAT + Depreciation Expense – CAPEX – Increase in NWC

Capital expenditures are calculated by solving for CAPEX in the following equation:

BV of Assets at Year End=BV of assets at Beginning of Year
– Depreciation

An additional cash adjustment may be necessary for an increase in deferred taxes that would have a positive impact on cash flow.

Financial Ratios

A firm's performance can be evaluated using financial ratios. Referencing these ratios to those of other firms allows a comparison to be made. The following is a listing of some useful ratios.

Leverage : Assets / Shareholder's Equity

Gross Margin = Gross Profit / Sales.
Gross margin measures the profitability considering only variable costs and is a measure of the percentage of revenue that goes to fixed costs and profit.

Net Profit Margin = Net Income / Sales

Total Asset Turnover = defined as Sales / Total Assets

Return on Assets (ROA) = Net Income / Assets
ROA is a measure of the return on money provided by both owners and creditors, and is a measure of how efficiently all resources are managed.

Return on Equity (ROE) = defined as Net Income / Equity
where the equity value is the shareholder's equity at the end of the period in which the income was earned. ROE is a measure of the return on money provided by the firm's owners.

ROE can be calculated indirectly as:

ROE = ( Net Income / Total Assets ) ( Total Assets / Equity )

ROE also can be calculated using DuPont analysis :
ROE = (Net Income / Sales)(Sales / Total Assets)(Total Assets / Equity)

This states that ROE is determined by multiplication of three levers:

ROE = (net profit margin) (total asset turnover) (leverage)

These levers are readily viewed on the company's financial statements. While ROE's may be similar among firms, the levers may differ significantly.


The term working capital is used to describe the current items of the balance sheet. Working capital includes current assets such as cash, accounts receivable, and inventory, and current liabilities such as accounts payable and other short term liabilities. Net working capital is defined as non-cash current operating assets minus non-debt current operating liabilities. Cash, short-term debt, and current portion of long-term debt are excluded from the net working capital calculation because they are related to financing and not to operations.

Two commonly used liquidity ratios are the current ratio and the quick ratio.

Current Ratio : defined as Current Assets / Current Liabilities.
The current ratio is a measure of the firm's ability to pay off current liabilities as they become due.

Quick Ratio : defined as Quick Assets / Current Liabilities.

The quick ratio also is known as the acid test. Quick assets are defined as cash, accounts receivable, and notes receivable - essentially current assets minus inventory.

Security Analysis

Security analysis is about valuing the assets, debt, warrants, and equity of companies from the perspective of outside investors using publicly available information. The security analyst must have a thorough understanding of financial statements, which are an important source of this information. As such, the ability to value equity securities requires cross-disciplinary knowledge in both finance and financial accounting.

While there is much overlap between the analytical tools used in security analysis and those used in corporate finance, security analysis tends to take the perspective of potential investors, whereas corporate finance tends to take an inside perspective such as that of a corporate financial manager.

Equity Value and Enterprise Value

The equity value of a firm is simply its market capitalization; that is, the market price per share multiplied by the number of outstanding shares. The enterprise value, also referred to as the firm value, is the equity value plus the net liabilities. The enterprise value is the value of the productive assets of the firm, not just its equity value, based on the accounting identity:

Assets = Net Liabilities + Equity

Note that net values of the assets and liabilities are used. Any cash and cash-equivalents would be used to offset the liabilities and therefore are not included in the enterprise value.

As an analogy, imagine purchasing a house with a market value of $100,000, for which the owner has $50,000 in equity and a $50,000 assumable mortgage. To purchase the house, the new owner would pay $50,000 in cash and assume the $50,000 mortgage, for a total capital structure of $100,000. If $20,000 of that market value were due to $20,000 in cash locked in a safe in the basement, and the owner pledged to leave the money in the house, the cash could be used to pay down the $50,000 mortgage and the net assets would become $80,000 and the net liabilities would become $30,000. The "enterprise value" of the house therefore would be $80,000.

Valuation Methods

Two types of approaches to valuation are discounted cash flow methods and financial ratio methods.

Two discounted cash flow approaches to valuation are:

  1. value the cash flow to equity, and
  2. value the cash flow to the enterprise.

The "cash flow to equity" approach to valuation directly discounts the firm's cash flow to the equity owners. This cash flow takes the form of dividends or share buybacks. While intuitively straightforward, this technique suffers from numerous drawbacks. First, it is not very useful in identifying areas of value creation. Second, changes in the dividend payout ratio result in a change in the calculated value of the company even though the operating performance might not change. This effect must be compensated by adjusting the discount rate to be consistent with the new payout ratio. Despite its drawbacks, the equity approach often is more appropriate when valuing financial institutions because it treats the firm's liabilities as a part of operations. Since banks have significant liabilities that are owed to the retail depositors, they indeed have significant liabilities that are part of operations.

The "cash flow to the enterprise" approach values the equity of the firm as the value of the operations less the value of the debt. The value of the operations is the present value of the future free cash flows expected to be generated. The free cash flow is calculated by taking the operating earnings (earnings excluding interest expenses), subtracting items that required cash but that did not reduce reported earnings, and adding non-cash items that did reduce reported earnings but that did not result in cash expenditures. Interest and dividend payments are not subtracted since we are calculating the free cash flow available to all capital providers, both equity and debt, before financing. The result is the cash generated by operations. The free cash flow basically is the cash that would be available to shareholders if the firm had no debt - the cash produced by the business regardless of the way it is financed. The expected future cash flow then is discounted by the weighted average cost of capital to determine the enterprise value. The value of the equity then is the enterprise value less the value of the debt.

When valuing cash flows, pro forma projections are made a certain number of years into the future, then a terminal value is calculated for years thereafter and discounted back to the present.

Free Cash Flow Calculation

The free cash flow (FCF) is calculated by starting with the profits after taxes, then adding back depreciation that reduced earnings even though it was not a cash outflow, then adding back after-tax interest (since we are interested in the cash flow from operations), and adding back any non-cash decrease in net working capital (NWC). For example, if accounts receivable decreased, this decrease had a positive effect on cash flow.

If the accounting earnings are negative and the free cash flow is positive, the carry-forward tax benefit is in effect realized in the current year and must be added to the FCF calculation.


In 1958, economists and now Nobel laureates Franco Modigliani and Merton H. Miller proposed that the capital structure of a firm did not affect its value, assuming no taxes, no bankruptcy costs, no transaction costs, that the firm's investment decisions are independent of capital structure, and that managers, shareholders, and bondholders have the same information. The mix of debt and equity simply reallocates the cash flow between stockholders and bondholders, but the total amount of the cash flow is independent of the capital structure. According to Modigliani and Miller's first proposition, the value of the firm if levered equals the value if unlevered:


However, the assumptions behind Proposition I do not all hold. One of the more unrealistic assumptions is that of no taxes. Since the firm benefits from the tax deduction associated with interest paid on the debt, the value of the levered firm becomes:

VL = VU + tcD

where tc = marginal corporate tax rate.

When considering the effect of taxes on firm value, it is worthwhile to consider taxes from a potential investors point of view. For equity investors, the firm first must pay taxes at the corporate tax rate, tc, then the investor must pay taxes at the individual equity holder tax rate, te. Then for debt holders,

After-tax income = ( debt income )( 1 – td )

For equity holders,

After-tax income = ( equity income )( 1 – tc )( 1 – te )

The relative advantage (if any) of equity to debt can be expressed as:

Relative Advantage (RA) = ( 1 – tc )( 1 – te ) / ( 1 – td )

RA > 1 signifies a relative advantage for equity financing.
RA <>

One can define T as the net advantage of debt :

T = 1 – RA

For T positive, there is a net advantage from using debt; for T negative there is a net disadvantage.

Empirical evidence suggests that T is small; in equilibrium T = 0. This is known as Miller's equilibrium and implies that the capital structure does not affect enterprise value (though it can affect equity value, even if T=0).

Calculating the Cost of Capital

Note that the return on assets, ra, sometimes is referred to as ru, the unlevered return.

Gordon Dividend Model:

P0 = Div1 / ( re – g )


P0 = current stock price,
Div1 = dividend paid out one year from now,
re = return of equity
g = dividend growth rate


re = ( Div1 / P0 ) + g

Capital Asset Pricing Model:

The security market line is used to calculate the expected return on equity:

re = rf + βe ( rm – rf )


rf = risk-free rate,
rm = market return
βe = equity beta

However, this model ignores the effect of corporate income taxes.

Considering corporate income taxes:

re = rf ( 1 – tc ) + βe [ rm – rf ( 1 – tc ) ]

where tc = corporate tax rate.

Once the expected return on equity and on debt are known, the weighted average cost of capital can be calculated using Modigliani and Miller's second proposition:

WACC = re E / ( E + D ) + rd D / ( E + D )

Taking into account the tax shield:

WACC = re E / ( E + D ) + rd ( 1 – tc ) D / ( E + D )

For T = 0 (no tax advantage for debt), the WACC is equivalent to the return on assets, ra.

rd is calculated using the CAPM:

rd = rf + βd [ rm – rf ( 1 – tc ) ]

For a levered firm in an environment in which there are both corporate and personal income taxes and in which there is no tax advantage to debt (T=0), WACC is equal to ra, and the above WACC equation can be rearranged to solve for re:

re = ra + (D/E)[ ra – rd(1 – tc) ]

From this equation it is evident that if a firm with a constant future free cash flow increases its debt-to-equity ratio, for example by issuing debt and repurchasing some of its shares, its cost of equity will increase.

ra also can be calculated directly by first obtaining a value for the asset beta, βa, and then applying the CAPM. The asset beta is:

βa = βe ( E / V ) + βd ( D / V )( 1 – tc )

Then return on assets is calculated as:

ra = rf ( 1 – tc ) + βa [ rm – rf ( 1 – tc ) ]

In summary, for the case in which there is personal taxation and in which Miller's Equilibrium holds ( T = 0 ), the following equations describe the expected returns on equity, debt, and assets:

re = rf ( 1 – tc ) + βe [ rm – rf ( 1 – tc ) ]

ra = rf ( 1 – tc ) + βa [ rm – rf ( 1 – tc ) ]

rd = rf + βd [ rm – rf ( 1 – tc ) ]

The cost of capital also can be calculated using historical averages. The arithmetic mean generally is used for this calculation, though some argue that the geometric mean should be used.

Finally, the cost of equity can be determined from financial ratios. For example, the cost of unleveraged equity is:

re,U = [ re, L + rf,debt ( 1 – tc ) D/E ] / ( 1 + D/E )

re,L = b(1+g) / (P/E) + g

where b = dividend payout ratio

g = ( 1 – b ) (ROE)

where (1 – b) = plowback ratio.

The payout ratio can be calculated using dividend and earnings ratios:

b = ( Dividend / Price ) ( Price / Earnings)

Share Buy-Back

Take a firm that is 100% equity financed in an environment in which T is not equal to zero; i.e., there is a net tax advantage to debt. If the firm decides to issue debt and buyback shares, the levered value of the firm then is:

VL = VU + T (debt)

The number of shares that could be repurchased then is:

n = (debt) / ( price per share after relevering)

where the price per share after relevering is:

VL / (original number of outstanding shares)

The buyback will lower the firm's WACC.

Project Valuation

The NPV of a capital investment made by a firm, assuming that the investment results in an annual free cash flow P received at the end of each year beginning with the first year, and assuming that the asset is financed using current debt/equity ratios, is equal to:

NPV = – P0 + P / WACC

Warrant Valuation

Warrants are call options issued by the firm and that would require new shares to be issued if exercised. Any outstanding warrants must be considered when valuing the equity of the firm. The Black-Scholes option pricing formula can be used to value the firm's warrants.

Valuation Calculation

Once the free cash flow and WACC are known, the valuation calculation can be made. If the free cash flow is equally distributed across the year, an adjustment is necessary to shift the year-end cash flows to mid-year. This adjustment is performed by shifting the cash flow by one-half of a year by multiplying the valuation by ( 1 + WACC )1/2.

The enterprise value includes the value of any outstanding warrants. The value of the warrants must be subtracted from the enterprise value to calculate the equity value. This result is divided by the current number of outstanding shares to yield the per share equity value.

PEG Ratio

As a rule of thumb, the P/E ratio of a stock should be equal to the earnings growth rate. Mathematically, this can be shown as follows:

P = D / re + PVGO


P = price

D = annual dividend

re = return on equity

PVGO = present value of growth opportunities.

For high growth firms, PVGO usually dominates D / re. PVGO is equal to the earnings divided by the earnings growth rate.

Treatment of Goodwill

Prior to 2002, amortization of goodwill was an expense on the income statement, but unlike depreciation of fixed assets, amortization of goodwill is not tax deductible.

In 2002, FASB Statement No. 142 discontinued the depreciation of goodwill and specified that it be kept on the books as a non-depreciating asset and written off only when its value is determined to have declined.


APV: Adjusted Present Value

CAPM: Capital Asset Pricing Model

EBIT: Earnings Before Interest and Taxes

EBITDA: Earnings Before Interest, Taxes, Depreciation, and Amortization

Enterprise Value: Market value of a firm's equity plus the net market value of its debt.

  • Enterprise value = market cap + LTD - net cash & investments

FCF: Free Cash Flow

LTD: Long-Term Debt

MRP: Market risk premium, defined as rm – rf , unless it specifically is referred to as tax-adjusted market risk premium, in which case there would be a factor to adjust rf for taxes.

NOPLAT: Net Operating Profits Less Adjusted Taxes

OLS: Ordinary Least Squares (method of regression)

PEG: The ratio of P/E to growth rate in earnings.

RADR: Risk Adjusted Discount Rate

RAYTM: Rating-Adjusted Yield-To-Maturity

ROE: Return On Equity; equivalent to the expected return on retained earnings

YTM: Yield To Maturity

Recommended Reading

McKinsey & Company, Inc., Thomas E. Copeland, et al., Valuation: Measuring and Managing the Value of Companies

Valuation is a practitioner's guide to valuation. It begins by making the case for valuation as a performance metric and then introduces valuation frameworks focusing on discounted cash flow, concluding with applications to real-world environments. Required reading for many MBA security analysis courses.

Corporate Finance

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 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.


Number of days of inventory = ( inventory / annual COGS ) ( 365 ).
This also is known as the inventory period.

On the liabilities side:


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:

D / V = ( D / E ) / ( 1 + D / E )

D / E = ( D / V ) / ( 1 - D / V )

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):

rA = rF + 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:

rE = rF + 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:

rD = rF + 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:

rD = rF + betadebt ( rM - rF )

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

rA = rF + betaunlevered ( rM - rF )

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

rE = rF + betalevered ( rM - rF )

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

rE = rA + (1-τ)(rA - rD)(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 = rE (E / VL) + rD (1-τ)(D / VL)

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

WACC = rA [ 1 - τ(D / VL)]

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 = rA - τ rD (D / VL)(1+rA) / (1+rD)

Under the same assumptions, the cost of equity capital can be calculated from rA and rD using the following relationship from Miles and Ezzell:

rE = rA + [ 1 - τ rD / (1+rD)] [ rA - rD ] D/E

For low values of rD, [ 1 - τ rD / (1+rD)] 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:

betalevered = betaunlevered­ [ 1 + (1 - τ) D/E ] - betadebt(1- τ) D/E

betaunlevered = [ betalevered + betadebt(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,


where VL = value if levered
VU = 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, rD.

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, VL = 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.


Compounding and Discounting

Compound annual growth rate (CAGR): ( FV/C )1/T - 1

Continuous compounding: FVt = C er 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:

  • Press the yellow button then "EXIT" to reset the calculator.
  • Press button under "FIN"
  • Pess button under "CFLO"
  • Press yellow button then INPUT to clear list
  • Press button under "YES"
  • Enter the initial cash inflow (negative number for outflow). Press "INPUT".
  • For "FLOW(1)", enter the cash flow value for the end of year 1, then press "INPUT".
  • Enter the number of periods for that value, then press "INPUT".
  • For "FLOW(2)", enter the next cash flow value, then press "INPUT".
  • The number of times will default to the previous number. Press "INPUT" to keep, or enter a new value.
  • When the cash flow entries are complete, press the button under "CALC".
  • Press the button under "IRR%" to calculate the IRR of the cash flow.
  • SAP for Fresh MBA, Finance Graduates

    Sorry to jump in at this point- I personally feel for Deepti (in this case) technical is not the right choice. The reasons are- Having coming from MBA background, i would presume she must be a novice on tech front (programming/any tech), if she has to start NOW, its a long long way to go..factors TIME, EFFORT & COMPETITION.

    On functional side- Its easy for her to leverage on the experience and education, and build from there.. I agree its difficult to get in to a live proj. but its not impossible. If I were to suggest, since you have a quite a bit of end-user experience leverage it to your product expertise. Couple with your domain knowledge, try to understand the various business processes and the corresponding solution of SAP. Put your thinking cap on, and try MAP the requirements to SAP module, and identify the GAPs. This process will make, you identifying/suggesting the potential solutions for customizations as well. However it takes time as well, but you dont need to get off-track into tech.

    Sunday, January 13, 2008

    MBA - Finance

    (Term 3 & 4: April - September)

    The aim of the MBA Finance programme is to develop a broad but critical understanding of the major areas of finance and enable the student to apply this theoretical understanding to the practical management of the financial affairs of a business, both domestically and internationally.

    Term 3

    Financial Risk Strategy:
    The module will focus on the application of various financial tools and techniques, such as futures and options, used to man-age financial risks within an organisation. Hence students will cover all the main treasure tools, learn how to apply and evaluate them and devise strategies for dealing with risk.

    Corporate Financial Management:
    This module aims to provide students with a critical understanding of the strategic relationship and interaction between a firm’s investment, financing and dividend policy decisions within the context of Shareholder Value Analysis. It also considers the agency problems that can arise in these key corporate financial decisions of the firm and how they can be minimised.

    International Finance:
    This module aims to provide students with an understanding of the development and growth of Multinational Corporations (MNC’s), the issues involved in international finance and investment decisions, and the use of global financial markets. It also considers international cash management and risks in international business operations.

    Term 4

    Pathway Dissertation:
    The dissertation is a major piece of work which demonstrates the student’s ability to qualify for the award of MBA. The study must have a business focus and be appropriate to the student’s pathway. No lectures take place during Term 4, however, you will maintain individual contact with your dissertation supervisor.

    MBA Career Enhancement & Planning:
    The aim of Career Enhancement & Planning activity is to provide support in relation to addressing the students’ concerns regarding issues relating to the question of What next?, for example: future prospects, career aspirations and further study opportunities.

    MBA Finance Ranking

    The term MBA finance ranking refers to the measurement of aid that a student will have in order to finance his studies. We recommend referring to the following channels in the order given in order to maximize financial ability from outward sources in combination with the wish to return loans given during the post-study period. It is surmised that toward the end of studies, one's financial position is more advantageous and loans will be easier to repay.

    Certain financial aid packages may be given in the form of grants that do not have to be repaid and may cover some or all costs of studies. These usually come with stipulations, such as the supposition that the student will return to his own country on completion of MBA studies. In cases where the loan does need to be repaid, there will probably be some sort of benefit, such as a long repayment period.

    Three options for MBA finance ranking:

    1. Support from the School of Business: Scholarships and Bursaries are offered at a number of schools. These are usually offered on a competitive basis. The student applies for MBA Finance Ranking and if he meets the criteria, he will be offered funds. Schools wishing to attract students from particular countries, professions, ethnic groups will offer aid under a number of different variants. They may offer jobs as research assistants to help with fees, for instance. Prospective students would be wise to check for MBA Finance Ranking in the Prospectus, Website, etc. or ask for them.
    2. Support from governments, charities by grants/scholarships and bursaries.
    3. Support from financial institutions

    MBA Edge

    A masters programme viz MBA is professional preparation for a management career. It provides a starting platform for understanding the structure of the business that you are entering. An MBA holder has better decision-making abilities, has structural thinking, is focused and can do better business. One gets a taste of how theory is applied in practice. It provides knowledge of many aspects of business - not enough for one to claim mastery over it, but enough to know the issue that need to be looked at, the possibilities and options available, the ramification etc. The same knowledge can certainly be acquired without MBA also but it would come through trial and error, through making most mistakes during one's working life. MBA programme helps in fast forwarding the learning process, vicariously based on other peoples' experiences. The kind of skill-sets that an employer look for are most commonly found in MBA's. The kind of skills that you learn while doing MBA, find better use at a later stage, when you are in the middle or senior management level.

    The MBA and PGDF Program will give you the opportunity to develop a range of highly valued professional skills and a competitive edge in your Finance career.

    Career Progression : In most professional organizations, the senior managers are usually trained in management areas. There are more opportunities for management trained personnel than for almost any other functional qualification. Our Programs will provide a quantum jump in career progression.

    The MBA/PGDF Program with its general management focus, and the blend of Indian and International perspective will be your key competitive advantage as you enter the fiercely competitive business environment. It will help you move ahead of the pack and allow you accelerated access to senior management positions.

    Personal Growth : The MBA Program will impart you with a perspective which enables you to relate to the entire business environment within which you may operate. You will be able to understand the impact of various decisions and play a significant role in them. The MBA Program will also help you understand business sufficiently to plan your own career and entrepreneurial moves successfully. And, of course, a more rewarding life, a better set of peers and recognition by society are sources of additional satisfaction.

    Continuous Learning : The MBA Program is a tremendous learning opportunity. It will allow you to update your knowledge and skills significantly. The knowledge you acquire needs constant upgradation. And the learning methodology in the MBA Program provides you with a mechanism to seek, comprehend and internalize knowledge on a continuing basis.


    Minimum Qualification : Should be a Graduate in any discipline
    Special Features :
    No Age Limit;
    No Entrance Test;
    Through Distance Learning;
    No Cadre Stipulations Course
    Structure -
    A. Core Courses -11 (Compulsory courses);
    B. Specialisation Course in Banking - Any 5 out of 7 courses;
    C. Integrative Courses - 2 compulsory courses and 1 Project Course;
    D. Electives - 1 out of 3 courses
    Credit transfers are available
    Procedure for enrolment : Enrolment is done for each semester. Student Handbook and Prospectus are available from IGNOU Regional Offices;
    Course Fee is Rs.600/- per course.
    The Prospectus can be obtained from any of the IGNOU Regional Centres or Director (SR&E), Maidan Garhi, New Delhi - 110 068, on payment of Rs.300/- in cash or Rs.350/- through Demand Draft for sending by post and submit application form at Regional Centre.
    Candidate should be a Life Member of Indian Institute of Banking & Finance and should have passed the CAIIB examination. He should be a Graduate working in the Banking or Financial Services sector for at least two years. An electronic version of the Prospectus is also available at IGNOU website as under.

    Finance and Accounting Careers

    Accounting or financial managers are the people responsible for overseeing and maintaining the financial strategy and history of a company. The accounting manager is focused more on financial reporting, while the financial manager is focused on strategy and money management. Finance has been one of the more popular choices for MBA focus or concentration.

    A finance MBA can offer numerous possibilities and can be an effective tool to help with promotions in the professions discussed below. Most prospective jobs for finance MBAs fall within investment banks, corporations, and securities firms. Many finance MBA graduates also follow careers in the consulting industry .

    Financial Managers or Financial Analysts

    Financial analysts and managers use historical (accounting) data in their decision making, however the number one role of the financial manager is to oversee the production of financial analysis and reports to help the company with decision making, business development, strategic planning, and alliance management. Through the use of these reports, the financial analyst helps to shape the company�s investment and business growth. Cash management strategies developed and implemented by the financial analyst help the company to grow efficiently and allow for maximum profitability in its investments.

    Financial analysts and mangers play an important part in mergers and global financing and expansion. Highly specialized knowledge in these areas is an important asset to the financial manager and his or her employer to maximize potential profit and reduce risk. Many companies utilize globally active consulting firms exclusively for these purposes.

    Accounting Managers

    Accounting managers working in a corporate setting perform responsibilities relating to tax reporting and management, and creating income statements inside of controller and audit groups. This career path may bring one to the positions of corporate treasurer, corporate controller, or CFO (chief finance officer). Professional accountants working for a public accounting company will perform functions similar to those performed by independent audit or tax consultants. An educational history or background based in accounting, either as a Masters degree or as a finance MBA, will give you some of the coursework you need to have in order to take the CPA (Certified Public Accountant) exam.

    Corporate Controllers

    A controller is someone who is in charge of preparing a company�s financial reports to forecast and sum-up the company�s financial situation. The statements a controller would get together consist of balance sheets, income statements, earnings analyses, and expense analyses. Regulatory agencies may also require special reports from companies. Controllers prepare these reports. In addition, a controller will frequently be over the budget, auditing, and accounting departments of a company.

    Chief Financial Officers

    The top financial executive of an organization is the CFO. The CFO supervises all accounting and financial operations, as well as administering the company�s general financial policies and strategies. While the CFO in a small company will often be responsible for all of the financial management duties, a CFO in a large company may delegate some or all of the responsibilities to other managers or vice presidents within the company.

    Treasurers and Finance Officers

    Finance officers other than the CFO and treasurers oversee and guide a company�s financial objectives and budgets. The financial officer may formulate and implement strategies to raise capital, oversee cash management, or manage the company�s capital investment activity. Financial officers also play a significant role in a company�s merger and/or acquisition activities. The treasurer, while he or she may share some of the financial officer�s duties, will usually have some banking experience.

    Cash Managers

    The Cash Manager is responsible for overseeing and controlling cash flow, both accounts receivable and accounts payable. He or she is also responsible for ensuring that the cash position of the company is sufficient to meet current and forecasted needs, or whether adjustments in investment quantity and type are necessary.
    Risk and Insurance Managers

    Business operation and transactions involve a certain amount of risk. Risk managers and insurance managers work to minimize the amount of loss a company incurs and the amount of risk it is exposed to.

    Management Consultants

    Management consultants work to help companies with a wide variety of problems and issues. Everything from profitability improvement to corporate restructuring to financial strategy. The MBA going into this field should have either an expert understanding of a wide base of knowledge, or be highly skilled in two or more sub groups. The management consultant will also help companies with cash management and emerging market analysis.

    Investment Bankers

    An investment banker will work together with corporations needing capital to grow and institutions or investors who have money available to invest. An MBA is an enormous asset in this field as the investment banker will be giving investment advice to his or her clients regarding raising capital. Most investment banks have a corporate finance division that assists clients in structuring financial instruments such as stocks or bonds to raise capital.

    Investment Banking Associates

    People graduating with an MBA in finance often begin their career as an associate with an investment bank firm or investment firm. This is usually at least one level above the entry-level position as an analyst typically obtained by persons with only an undergraduate degree. Most analysts end up pursuing an MBA degree after a couple of years in the industry in order to obtain promotions. Many people in the corporate finance side of investment banking will obtain a CFA (Chartered Financial Analyst) designation as a supplement to their MBA. The Association for Investment Management Research (AIMR) is the governing body for the CFA exam and designation.

    The mergers and acquisitions departments of investment banks provide consulting services to companies in the process of merging or acquiring other companies or organizations. Organizations wishing to acquire, dispose of, or invest in real estate will deal with the real estate division of an investment bank. Equities research and consulting for private clients are also frequently chosen as career paths for MBAs with focus in investment banking.

    Investment Sales Associates and Traders

    While MBA skills and knowledge are not explicitly required in this field, they do come in as very valuable in enabling a person to understand the economic principles that drive the financial markets. Investment traders and sales associates assist corporate or institutional investors in the purchase and sale of securities such as stocks and bonds. The sales associate makes recommendations and helps with the analysis, while the trader actually executes the orders for the client.

    Credit Managers nd Specialysts

    The Credit manager is in charge of managing the credit a company may issue to its clients or others. Credit managers formulate criteria for rating risk and credit, determine the maximum amount of credit to offer, and supervise past-due account collections.

    Saturday, January 12, 2008

    Financing your MBA

    Resigning from a secure job, moving country, even leaving behind family and friends; potential MBAs seem to take such obstacles in their stride. But with programmes at top-flight school now costing as much as US $75,000, one question seems to occupy business school applicants more than any other: just how can I find the money to pay for my education?

    Every year, TopMBA surveys nearly 4000 aspiring MBAs around the world to establish whether finance is likely to prove a barrier to study. The latest survey found that most had already looked seriously into how they would fund business school. A wide variety of methods were cited, from scholarships to personal loans. Worldwide, 74% of respondents favoured scholarships. Next came a student’s own savings at 68% followed by some form of external loan at 61%. Overall, only 28% expected to get financial help from their employer.

    Favoured funding methods vary considerably from area to area. Help from family and friends appears to be most common in the Asia-Pacific region, where it was cited by 48% of those questioned, contrasting with 43% in the USA and Western Europe. Personal loans were the preferred source for over 81% of US students, but for fewer than 57% of those from Latin America. Company sponsorship was expected by 36% of respondents in the Middle East and Africa, but by only 21% of those in Latin America. Own savings were the favoured method for 80% of Western European candidates, but for only 62% of those from the Middle East and Africa.

    However, whatever a student’s initial preference, in practice, the most common source of finance is now the education or career loan. We look at some of the sources of such loans across the globe.

    Selected sources of MBA Finance around the world

    UK citizens can borrow up to two thirds of their pre-study salary in any twelve-month period from NatWest to fund an MBA. Applicants need to contribute at least 20% of the course fees from their own resources and repayment periods range from 7 years for sums under £20,000 to 10 years for sums over £20,000. Interest is currently 6.9% APR. HSBC offers loans to students of a number of British based schools, including Cranfield, London Business School and Manchester Business School. Unlike many other schemes, this facility is open to students from anywhere in the world. Interest is charged at 2% over HSBC’s base rate for the duration of the loan. There are no upfront commissions or early repayment charges.


    There are several sources of aid for US students studying at home or abroad and for overseas candidates looking to study in the USA. These include:

    Citibank has a very well developed student loan division, which provides standard loans and also partners with individual schools to provide tailored packages. The Wharton School at the University of Pennsylvania, for example, offers funding through Citibank, which guarantees most accepted students a prime plus 0.5% interest rate, with a 15-year payback period, and no co-signers or credit check required.

    IEFC – Students interested in studying at one of nearly 400 institutions around the world may be eligible for loans of up to US $45,000 from the IEFC (International Education Finance Corporation). The IEFC has three loan programs: the Stafford for US citizens or permanent residents, Can HELP for Canadians and ISLP for foreign students. To be eligible for ISLP you must be able to provide a guarantor, who is a US citizen or permanent resident.

    GATE Universal is a student loan program managed by First Marblehead Corporation and Bank of America.

    MBA LOANS is a private loan program run by Sallie Mae and targeted specifically at US citizens.


    CA-Post-Graduate, Creditanstalt offers some loans.


    French residents of any nationality who have worked in the country can apply to FONGECIF (Fonds de Gestion du Congé Individuel de Formation) for up to 90% funding of tuition fees plus a part of their current salary.

    MBA in India

    It’s the proverbial debate. Is an Indian MBA degree at par with global standards, or does one still have to look abroad for quality education? Here we are outlining a direct account of the advantages of pursuing an MBA at a premier institute in India.

    As far as higher education is concerned, the educational scenario has changed dramatically in India in the last decade. In the debate of an MBA in India versus abroad, a student currently pursuing MBA in India believes that an Indian MBA scores over an international MBA on several counts.

    The main advantage is the cost. An MBA from any good B-school in the US or UK cost anywhere between Rs 25 to 50 lakhs, whereas Indian MBA schools charge ten percent of the same amount. Secondly, when living abroad, a student has to spend far more than he would in India, and as a result need to work there for at least a few years to recover the amount. This severely hampers his prospect of returning to India after the completion of the degree.

    On the other hand, a student from a reputed Indian B-School always has the option to work at either place, since all premier B-Schools have a significant amount of foreign placements taking place each year. Also, Indian is a vibrant economy today and corporate companies the world over value the pool of talent that exists here. In fact, people opt for position in India to be apart of the growing economy. Lately there has been an increase in the number of NRIs coming back to India. In this thriving scenario, it makes sense to get ones degree from an Indian B-School.

    There has also been steady increase in the number of the tie-ups between Indian and foreign universities. Some of them include the SP Jain Institute of Management and Research with Virginia Tech, the Indian School of business with the Wharton School Kellogg School of Management, the management Development institute with Cambridge College, Great Lake & Yale, Wellingkar College with Temple University the institute of Management and technology with Fairleigh Dickinson University, Great Lakes and Yale University. Thus, with more and more premium international education its way to Indian shores one can experience the benefits a international education and a lesser cost.

    Also, Indian MBA courses have been expanding and growing significantly in recent years. MBA graduates from Indian B-Schools have proved their mettle in the global working environment and are offered top positions in several organizations. Considering the purchasing power parity, initial expenditure (cost of the program), initial placements, and growth in salary as inputs in decision, MNCs do not have to think twice before coming to India in search of middle and senior management talent.

    In every Indian B-school participants with two to five years of IT industry experience always fill a certain percentage of the batch. These students often have international exposure. Their multicultural experience adds value to the entire batch and program as a whole. And to a certain extent, it compensates for the rich diverse cultural experience that is associated with a US or UK MBA. Finally, Indian B-Schools are more open to non-experienced candidates than international B-schools, and thus prove to be an advantage to most people. Hence, keeping in mind today’s scenario we believe that an Indian MBA is the way to go. —