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As Pandey, (1999) says, A shortly decision of a business firm on either to invest or to borrow based on its uneven cash inflow is difficult unless it is supported by formulae. In order to have a more certainty equivalent projected cash flow, the firm projective uneven cash flows need to adjust with future risk, inflation and sensitivity rate.
According to R Proctor, (2006), cash flows projected incorporating these future speculative resistance rates such as future risk, inflation and sensitivity rate will have a high certainty equivalent cash flow when it comes to reality. A business firm performance which is to be measured by its economic profit, Economic value added (EVA), by which it focuses on generating net cash flow is a real measuring tool so as to project the firm’s cash flow. The projection is based on risk, inflation and sensitivity rates adjusted performance rate, which is the rate, at which the current economic profit, EVA, growth from the previous years, (S Myers, 2003).
The economic value added (EVA) approach show the present and future value formulae based on risk, inflation, and sensitivity rate adjusted performance rate to match the value of the projected cash flow to that of the actual cash flow value P Chandra, (1993). The initial value of this adjusted cash flow can be any amount of cash on hand which is excess above consumption or a portion of it and the next after the first amount progress according to the growth of adjusted performance rate.
Assume that an adjustment rate ( J ) is a combined effect of risk, inflation, and sensitivity rates. Assume also again sensitivity rate ( l ) is to be an excess above the discount rate (1+i) and statistically this relationship can be interpreted as
l = J - (1+ i)
Each period’s cash flows ( ) stream for n number of period’s explained as:
From this, the present value of this uneven cash flow stream explained as:
On the other hand, the future value of uneven cash flow n cf for n periods explained as:
From this, the future value of uneven cash flow stream n (FVUC) explained as follows:
Copeland, Koller, and Murrin (1996) defined free cash flow in the following way: “Free cash flow (FCF) is a company’s true operating cash flow. It is the after-tax cash flow generated by the company and available to all providers of the company’s capital, both creditors and shareholders. It can be thought of as the after-tax cash flows that would be available to the company’s shareholders if the company had no debt.
Gary R. Evans (1998) further goes on to say that the concept of free cash flow works on a related premise that the ultimate origin of long-term corporate growth is invested capital. As Copeland, Koller, and Murrin (1996) says, generally, productive fixed assets are expected to be at the core of a company’s productive ability, which in turn is essential for the production of commodities sold by the company, which in turn is essential for sales revenues and their growth. Therefore, cash placed into invested capital (increasing net fixed assets) is a primary value driver for long-term sales growth (but not necessarily margins or other measures of profitability).
Thus in notation form free cash flow can be represented as follows:
Free Cash flow = Net Operating Cash flow - New Invested Capital (Investment)
The proforma approach involves two steps:
- Using the proforma model to generate five proforma forecast years of free cash flow then discounting each forecast year by using a discount rate, then summing them.
- After estimating a sixth year based upon average growth rates of the prior five years, obtaining a perpetuity forecast assuming constant growth using a standard constant growth formula.
The profoma model uses two or more historical years of net cash after operations to forecast the future cash flows of the firm, R Garry, (1998). From the proforma model software, the two historical years for net cash flow after operations are entered into the operations cash flow row and the data from capital expenditures are entered into the investment row Weston, (1998). This will generate two investment rates for the two separate years and these will later be averaged into one investment rate.
Next, the five forecast years for net cash after operations are entered into years 1 through 5. This will automatically generate a sixth projected year. At this point, if the actual workbook is being used, default assumptions will have produced an actual valuation.
The first override possibility is the expected long-term growth rate, which is used in the calculation of the perpetuity. The default is the average of the five forecast years. This rate represents the expected growth rate for all years following the first five.
Probably the most important rate to consider is the investment rate. The default is set to the historical investment rate determined in step 1, Fred (1998). Aside from the fact that the historical numbers might produce an unrealistic result (for example, with heavy external financing, it is possible for new capital spending (investment) to exceed operations cash flow, producing a meaningless value greater than 100%) which would have to be overridden, Garry, (1998). The analyst might conclude that investment should include more than change in net fixed assets (the proforma model defines capital expenditures as equalling, -+ Depreciation).
The present value discount rate is defaulted to be equal to the model’s first-estimate WACC (weighted average cost of capital). This model, in turn, uses a simpler estimate of WACC than some. This is meant to represent the cost of capital to the firm when some mix of equity or debt is used, (Fred 1998). The spreadsheet uses standard discounting techniques to discount for present value, and the total discounted value equals the sum of the five discounted proforma years. The formulas for each respectively are:
F: present discounted value of the five forecast years
C: proforma forecast values for operations cash flow
d: discount rate (12%)
: projected year 6 cash flow value.
r: investment rate.
g: expected long-term growth rate.
w: weighted average cost of capital.
Limitations of profoma models:
- This forecasting technique is dependent upon the correct use of a reliable proforma forecasting model and is therefore extremely sensitive to even small variations in some of the key variables, such as the growth rate in after-cash tax flows or the marginal profitability rate.
- Also another problem arises when the analyst tries to evaluate weaker companies with poor or negative cash flow or companies that, because of restructuring or similar reasons, are going through a spurt of negative cash flow in recent years on the path to recovery.
According to T Lucey (2008), Money cash flows are the actual amounts of money changing hands and real cash flows are the purchasing power equivalents of the actual cash flows. The general treatment of inflation in investment appraisal in a dollarized environment is concerned with distinguishing between the real and nominal value of money and is dealt with by either single or double discounting thus a money discount factor or real discount factor respectively, (Khan, 2004)
Kaplan,& Atkinson, (2007), defined time value of money as the concept stating that amounts of money received at different periods of time must be converted into their value on a common date to be compared. The cost of money is the lost opportunity to invest the money in another investment alternative. Money has a time-dated value, as comparisons can and should be made for like items it should be adjusted to be at a particular date, (Panday, 2004). The time value of money applies even if there is zero inflation as inflation is not the basis of the concept though it increases the discrepancy in value (T Lucey, 2008). Discounting and compounding methods allow for the time value of money but in investment appraisal discounting methods are often used.
Sound estimates of the cost of capital are crucial for the evaluation of investments and for corporate valuation. In a dollarized economy the estimation is the same as any other period of economic since all the factors will be adjusted to the risk inherent in that particular market, T Laurens (2010). The following are the various ways of estimating the cost of equity.
The weighted average cost of capital (WACC) of a firm simply refers to how much, on average, it costs the firm to raise money Miller, (1997) That is, it is the average rate that the firm must pay on any new capital that it raises and thus the importance of the WACC is in its relation to the evaluation of projects Hail, (2003). For a scale-enhancing project, the WACC is the appropriate discount rate at which to evaluate the project.
According to T Laurens (2010), the WACC is recognized as one of the most critical parameters in strategic decision-making. It is relevant for business valuation, capital budgeting, feasibility studies and corporate finance decisions. When estimating the WACC for a company, there is a clear trade-off between theoretical purity and actual circumstances faced by a company Werner, (1994).The decision in this context should reflect the actual environment in which a company operates Dawn, (1994).The WACC cannot be observed and so must be estimated Rafael, (1996). The standard estimation method is to take a weighted average of the estimated expected returns on debt and equity:
The estimation of the WACC is based on several key assumptions:
- It is market driven. It is the expected rate of return that the market requires to commit capital to an investment.
- It is a function of the investment, not the investor.
- It is forward looking, based on expected returns.
- The base against which the WACC is measured is market value, not book value.
- It is usually measured in nominal terms, which includes expected inflation.
- It is the link, called a discount rate, which equates expected future returns for the life of the investment with the present value of the investment at a given
According to, Kothari (2001), the first step in developing an estimate of the WACC is to determine the capital structure for the company or project that is being valued, that is the proportion of debt and equity that is being invested in the project. This provides the market value weights for the WACC formula. Best market practice is to define a target capital structure and this is for several reasons.
Firstly, the current capital structure may not reflect the capital structure that is expected to prevail over the life of the business or the capital project being undertaken. The second reason for using a target capital structure is that it solves the potential problem of circularity involved in estimating the WACC, which arises when calculating the WACC for private companies. Since the WACC for the project is dependent upon the inputs, therefore the proper and accurate estimation of the inputs that is, the cost of debt and cost of equity is what is important.
The most common way of estimating the cost of debt is to use the promised yield on newly issued debt of the firm Erthard, (1994). However, Bernard and Thomas (1996), say this is not correct. They go to say, the expected return on debt should allow for the probability of default whereas the promised yield does not. If the promised yield is used for the cost of debt then the WACC will be too high. In extreme cases, use of the promised yield as the cost of debt could lead to the nonsensical result that the cost of debt exceeds the cost of equity. As (Kaplan and Stein, 1990) say, Because of default risk expected returns on corporate debt are undoubtedly lower than promised returns.
The Merton model is the simplest equilibrium model of the relationship between corporate interest rates and the inputs to the WACC. It assumes that the value of the firm's assets follows a geometric Brownian motion:
The Merton model further assumes that the firm has a single class of zero coupon risky debt of maturity. Other assumptions include a constant interest rate and a simple bankruptcy procedure; namely, if at maturity the value of the assets is lower than the liability, the assets are handed over to the bondholders without costs or violation of priority rules. The simplicity of the model has led to difficulties in using it to explain the relationship between the absolute levels of debt spreads capital structure and asset volatility.
2.6.2 Estimation of the cost of equity used in WACC
18.104.22.168 Gordon Dividend Growth Model:
The Gordon Dividend Growth Model is based upon the price of a stock being the discounted value of all the future dividends:
If we know all of the future dividends then we can solve for the discount rate in the above equation. This rate (the IRR of the stock) would be analogous to the yield on a bond. This rate would be the “yield” of the stock. In other words, it the expected return that is required in order to make the present value of the future dividends equal to the current price. Another way of saying the same thing is that new investors require this return to induce them to invest in the firm’s shares.
The rate that one solves for in the above equation is the cost of equity (rs) in the Gordon Model. The question is, how does one estimate this rate given that one cannot know all future dividends?
Consider the case where dividends are constant forever:
Thus, given constant dividends, the cost of equity is simply the current dividend yield on the stock (the cost of preferred equity can thus be seen as an application of this approach). However, the following should make clear that perpetually constant dividends imply that all profits of the firm are paid out as dividends (which are not a very common real world phenomenon).
Let Et be the earnings per share in year t (total firm profit divided by the number of shares). Most firms will pay some of Et out as dividends, but will retain some for re-investment in the firm. Assume that the firm retains a constant percentage of Et each period, b. This number, b, is the retention ratio. The idea is that the firm retains some earnings and re-invests them in the company so that future earnings are higher. Let R be the return generated on the re-invested earnings.
Thus, the earnings per share are a perpetually increasing series that is growing at the rate bR each period.
Let g=bR be the growth rate.
Since the fraction b of earnings per share is retained each period, (1-b) of earnings must be paid out as dividends. Thus:
Therefore, it can be seen that g represents the growth rate in earnings per share and in dividends. G is determined by how much the firm re-invests in itself and the rate of return on those investments. Now, set the present value of future dividends equal to the current stock price and solve for rs:
This is the cost of equity capital by the Gordon Dividend Growth Model.
22.214.171.124 Capital Asset Pricing Model (CAPM)
To calculate the cost of capital based on the Capital Asset Pricing Model (CAPM), the project’s cost of capital is the rate investors require to undertake the investment, and we should discount all future cash flows at this rate, Lee (1998). The cost of capital in the CAPM equals the risk free rate plus a risk premium. The CAPM asserts that the only relevant risk measure for a project is its beta, Robert, (1995). The beta factor, times the excess return of the market over the risk free rate determines the risk premium of the investment, (Litner, 1964). The cost of capital can be determined using the following CAPM formulae.
The CAPM is based on the following assumptions:
- This model applies in markets with perfect information where all investors are utility maximisers
- All investors have similar expectations about the mean and standard deviation of the return of every risky asset.
- An asset with zero yields a risk-free rate at which every investor can borrow or lend.
- Also, in this world, there is a portfolio where every asset in the economy is included, proportional to its market value, and by definition, its beta is 1.0.
According to the CAPM, the cost of capital of a project can be predicted from knowledge of the beta of the project and the market risk premium, Jensen (1968). The required rate of return determined by CAPM provides a market-based measure of the return required by shareholders for investing in the firm. This method is consistent with Gunasekarage (2004). This is the cost of equity capital of the firm that can be used as the benchmark rate for evaluating performance of investment proposals. The return on equity (ROE) can be compared with the CAPM-based required return on equity to determine whether company managers have worked for the best interest of shareholders by investing in value creating investment projects, (Lee, 1998).
Ray Aggarwal, (1993), accepts that all capital budgeting is done under uncertainty, but argues that traditional capital budgeting procedures often ignore or postpone consideration of the uncertainty inherent in future estimates.
Therefore uncertainty stems from various sources such as the cost accounting systems that often use approximations of overhead allocation. The unique nature of each application, thus capital equipment may not work exactly as estimated resulting in variations in labor, material, inventory, or other costs. The uncertainties in the estimation of future benefits and cost, in inflation and interest rates, capital market imperfections and changing tax rates make the estimation of an appropriate discount rate difficult and subject to error (Ray Aggarwal 1993).
Agency costs and information asymmetry also influence the efficiency of the capital budgeting process. Agency costs due to differences in the goals, objectives and utility functions amongst owners, managers and other stakeholders introduce inefficiencies in each stage of capital budgeting process, and the selection and management of new investments may not be economically optimal.