Discounted cash flow (DCF) is the present value of an estimated future flow of money into a business, financial instrument or project. Multiples refer to ratio multipliers where the results of financial ratios are multiplied and then compared to the same multiplier for competing businesses.

Both discounted cash flow and multiples are valuation tools, where the former technique weighs present value of future cash flow against an asking price, and the latter compares operational aspects of business performance. This article will discuss advantages and disadvantage to each valuation method in addition to illustrating how each is calculated.

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**Advantages and disadvantages of discounted cash flows **

The discounted cash flow equation allows one to estimate how much a future stream of payments are worth at present value. This can be useful in determining bond, and annuity values given an assumed future cash flow of specified amounts. In other words, the discounted cash flow is a mathematical method to determine actual rather than estimated present value of cash flow. In the case of large transactions or financial agreements involving considerable and predictable payment streams, this calculation can be invaluable.

A problem with the discounted cash flow equation is that the equation does not take into account several other factors such as 1) investment risk associated with opportunity cost. 2) unforeseen variations in future cash flow and 3) In other words, investments that could return greater cash flow yields would add an unrealized element of risk to the DCF. Additionally, economic factors such as interest rates and inflation are not incorporated into the equation.

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**Multiples: Advantages and disadvantages **

Multiples can be a good way to get a general sense of business performance across a range of metrics such as asset and debt management, liquidity, profitability etc. If the ratios perform lower than industry averages or competitors, the company may not be a good strategic investment, acquisition or franchise opportunity depending on the circumstances surrounding the calculation.

With multiples, ratios are compared between similar companies. For example, company A produces serrated metal pipes for pluming and has a market capitalization of $250 million making it a small cap. Company B also manufacturers serrated metal pipes but is vertically integrated meaning it also distributes and installs the pipes. This element alone makes the ratio multiple somewhat invalid in the sense it is not an exact comparison.

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**How to calculate discounted cash flows and multiples**

• Discounted cash flow: Financial calculator method

A simple way to calculate discounted cash flow is using a financial calculator. Using a financial calculator allows the step of incorporating mathematical steps to be bypassed and in the case of a present value of an annuity only three variable inputs are required 1) interest rate 2) time as expressed by a number integer and 3) cash flow as either a single or multiple set of payments at either the same or different amounts.

To do this all one need do is input number of payments by pressing (N) on the calculator followed by the number, then interest, by pressing (I) then interest, then (PMT) for payments with a negative payment amount and (FV) with 0 then computer (PV). This will yield the present value of a future flow of cash payments and assist in determining value of that cash flow. For varying cash flows, the series of uneven cash flows will have to be entered into the calculator using the (CF) cash flow function.

• Discounted cash flow: Mathematical method

There are several different methods for calculating discounted cash flow, each making use of different variables such future capital investments, weighted average costs, and cash flow streams. Determining which method(s) are most suitable for a valuation may require an additional understanding into the entity in question and is in and of itself an appraisal method decision. Calculating discounted cash flow manually involves calculating net present value (NPV). The following is one such method and makes use of the weighted average cost of capital (WACC).

Step 1: Calculate WACC: For each percentage portion of 100% of capital invested calculate the percentage interest then average. Incorporating For example, 45% of 100% of capital invested costs 6% annually whereas the other 55% costs 5%. 45% of 6%=2.7 and 55% of 5%=2.75%. 2.7%+2.75%=5.45% =WACC This is a simple method for calculating WACC that does not incorporate taxation and does not differ between types of investment capital, but rather percentage costs of investment.

A equation for incorporating tax costs into weighted average cost is as follows: (Debt)*(1-Tax rate percent)*(Percent cost or Interest on debt)+(Equity Investment capital)*(percent cost of equity investment) (www.wikepdia.com)

Step 2:

NPV=Cash flow(s)/1+r to the exponent of the numerical order of the cash flow payment, where r=WACC (www.investopedia.com) For example, for 3 cash flows of $100.00 the equation using weighted average percentage cost of capital would be as follows. $100.00/(1+5.45%)exp 1+ $100.00/(1+5.45)exp 2 + $100.00/(1+5.45)exp 3=$64.73+$41.89+$27.11=$133.73

In addition to the above two methods of calculating discounted cash flow, are other methods such as via statistical programs and online financial calculators. Instructions for these calculations can be found using software tutorials and/or online financial calculators.

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**Calculating multiples**

Calculating multiples simply involves determining the result of financial ratios such as the price earnings (P/E) ratio or Days sales outstanding (DSO) and comparing them across an industry average. For example, if company A has a price per share of $25.00 and annual earnings per share of $1.25, the P/E ratio is 20. If the industry average has a P/E of 30, it means competing companies have higher expected earnings as reflected through share prices making company A's ratio multiple below industry average.

How to incorporate discounted cash flow and multiples in investment decisions:

To make the best investment decisions will always be an art or at best a quasi-scientific estimate due to the elements of risk, probability, varied market conditions, inflation, leveraging etc. For this reason, making use of equations and tools such as the discounted cash flow and multiples can be of quantitative assistance in determine more accurate estimates of worth and/or valuation of a potential investment.

To illustrate the above, Mr. Jones wants to buy an annuity through Company I, the annuity agreement involves a monthly payment of $500.00 for 10 years at interest rate of 5%, with annuity payments beginning on the 11th year for $625.00/month. Using the financial calculator method above, this amounts to a present value of just $9701.89 when the actual payments amount to $60,000.00. What's more reversing the scenario and calculating future value for the same payments at 5% interest the value becomes $176,791.854 after compounding interest. In other words, the annuity would have to pay back approximately 22.66 payments or more to meet the 10 year future value level.

In summary, the discounted cash flow calculation can be useful in numerically determining actual value of a future cash flow stream as opposed to estimated value. The discounted cash flow equation is thus more useful in determining present value of future cash flows rather than business operational factors as measured by multiples. The former DCF, may be more beneficial in the valuation of financial instruments such as bonds, and annuities than in business acquisitions and equity positions. Nevertheless, both equations can be used in valuation in both scenarios however each is more suited to particular financial conditions.

Online sources:

1. http://www.investopedia.com/terms/d/dcf.asp

2. http://www.investopedia.com/terms/m/multiplesapproach.asp

3. http://en.wikipedia.org/wiki/Weighted_average_cost_of_capital

4. http://en.wikipedia.org/wiki/Discounted_cash_flow

Text references:

1.Howard Bryan Bonham CPA, The complete Investment and Finance Dictionary. Avon Media Corporation, 2001.p.62

2.Eugene F. Brigham, and Joel F. Houston. Fundamentals of Financial Management 9th Ed. South-Western, 1999.p.107.

3.Howard Bryan Bonham CPA, The complete Investment and Finance Dictionary. Avon Media Corporation, 2001.p.62

4.Zvi Bodei, Alex Kane and Alan J.Marcus. 'Investments' Mcraw-Hill Irwin. New York, 2002. P. 265-271

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