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» Introduction » Manual of financial concepts

Mofinet is pleased to offer a manual of financial concepts to help our visitors in the resolution of some of the doubts that might arise after visiting our web site, and working with our financial simulation models.
In this manual, you will find some simple explanations, with practical examples, of some of the financial concepts which appear in our financial models.


  1. What is Future Value (FV)?
  2. What is Present Value (PV)?
  3. What is Free Cash Flow (FCF)?
  4. What is Cost of Capital?
  5. What is CAPM (Capital Asset Pricing Model)?
  6. Which are the most common methods to analyze
    the profitability of an investment?
    1. Net present Value (NPV)
    2. Internal Rate of Return (IRR)
    3. Pay Back (PB)
  7. Other financial concepts of interest
    1. Residual value of the company (RV)
    2. Yield required by the market, considering the leverage
      of the company (Ke)
    3. Debt service coverage ratio (DSCR)

  1. What is Future Value (FV)?
    It is the value that a present investment will have in the future. The formula for the calculation is:

    FV = PV (1+i)^n

    Whereas:
    PV: Present value of the investment
    n: Number of years of the investment (1,2,...,n)
    i: Annual interest rate

    FV will be higher with a higher value of i and n.

    Example of FV calculation:



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  2. What is Present Value (PV)?
    It is the present value of an investment to be received in the future.
    From the previous formula, we can calculate its value, by doing the following:

    PV = FV / (1+i)^n

    Whereas:
    FV: Future value of the investment
    n: Number of years of the investment (1,2,...,n)
    i: Annual interest rate

    PV will be higher with a lower value of i and n.

    Example of PV calculation:



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  3. What is Free Cash Flow (FCF)?
    It is the remaining amount for the shareholders, after covering debt service (interest + principal) of the company, and after investments in fixed assets and working capital needs (WCN).

    Sales
    - Cost of goods sold
    - General and administrative expense

    = Gross operating margin (EBDIT)
    - Depreciation (*)

    = Profit before interest and taxes (EBIT)
    - Income tax

    = Net profit before interest (EBI)
    + Depreciation (*)
    - Investment in fixed assets
    - Investment in WCN (**)

    = FCF


    (*): Depreciation is added back because it is a non cash item.

    (**): Working capital needs (WCN) = Cash + Receivables + Stocks - Payables.

    If we bring to present value the FCF, using as the discount rate the cost of capital of the company, we get the value of the company.

    Example of FCF calculation :



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  4. What is Cost of Capital?
    The cost of capital, or more specifically, the weighted average cost of capital (WACC), is the addition of the weighted cost of third party sources of financing plus the weighted cost of own sources of financing.

    wacc = [ Cost TF * (1-t) * (TF / (TF+OF)) ] + [ Cost OF * (OF / (TF+OF)) ]

    Whereas:
    TF: Third party sources of financing
    OF: Own sources of financing
    TF / (TF+OF): Proportion of third party financing in relation to total sources of financing
    OF / (TF+OF): Proportion of own financing in relation to total sources of financing
    Cost TF * (1-t): Cost of third party financing after taxes
    t: Income tax rate
    Cost OF: Cost of own sources of financing

    Example of wacc calculation:



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  5. What is CAPM (Capital Asset Pricing Model)?
    It is a method for the calculation of the yield to be requested to the own sources of financing

    CAPM = FY + ß (MY - FY)

    Whereas:
    FY: Yield of non risk assets (normally treasury bonds)
    MY: Yield of the stock market
    (MY-FY): Risk premium of the stock market
    ß(or beta): Coefficient of variation of the company's own sources of financing in relation to the stock market own sources of financing. With a higher value of ß, the risk of the company will be higher.
    If ß>1: The expected yield of own sources of financing of the company will be higher than the one of the market.
    If ß<1: The expected yield of own sources of financing of the company will be lower than the one of the market.
    If ß=0: The expected yield of own sources of financing of the company will be equal to the one of the market

    Example of CAPM calculation:



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  6. Which are the most common methods to analyze the profitability of an investment?

    1. Net Present Value (NPV)
      It consists in bringing to present value the future cash flows of the investment project, discounted using a certain interest rate ("the discount rate"), and comparing them to the initial amount of the investment. As the discount rate, it is normally used the weighted average cost of capital (wacc) of the company which makes the investment.

      NPV = - A + [ CF1 / (1+r)^1 ] + [ CF2 / (1+r)^2 ]+...+ [CFn / (1+r)^n ]

      Whereas:
      A: Initial investment
      CF: Cash flows
      n: Number of years (1,2,...,n)
      r: Discount rate
      1/(1+r)^n: Discounting factor for an specific interest rate and number of years
      CFd.: Discounted cash flows

      If NPV> 0: the project is profitable.
      If NPV< 0: the project is not profitable.

      By the time of selecting between two projects, we will select the one with a higher NPV.
      This method is considered as the best to analyze the profitability of a project.

      Example of NPV calculation::



    2. Internal Rate of Return (IRR)
      It is the discount rate which makes the NPV equal to cero.

      NPV = - A + [ CF1 / (1+r)^1 ] + [ CF2 / (1+r)^2 ] +...+ [ CFn / (1+r)^n ] = 0

      If IRR> discount rate (r): The project is acceptable.
      If IRR< discount rate (r): The project is not acceptable.

      This method is not as reliable as the NPV method. Therefore, it is normally used in addition to the NPV.

      Example of calculation of IRR:




      If we suppose that in this example the discount rate of the company is 10 % (13%>10%) then, we can say that this project is profitable, because the IRR is higher than the discount rate of the company (normally the wacc).

    3. Pay Back (PB)
      It is the term which is necessary to recover the initial investment amount, with the cash flows generated by the project.
      The investment is recovered in the year in which the accumulated cash flows exceed the initial investment.

      It is not considered as an adequate method if it is the only method used. However, it can be used in addition to the NPV.

      Example of calculation of PB:

      Whereas:
      n: Number of years
      A: Initial investment
      CF: Annual cash flows
      CFac.: Acumulated cash flows




      In this example, the initial investment is recovered in the third year.

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  7. Other financial concepts of interest

    1. Residual value of the company (RV)
      It is the value that we consider for the company in the last year of our projections.
      We can use different methods to calculate that value. In our models we have considered a constant rate of increase in perpetual free cash flows starting in last year.

      RV = (CFn+1)/(k-g) = (CFn (1+g))/(k-g)

      Whereas:
      RV: Residual value of the company in year n
      CFn: Free cash flows generated by the company in year n
      n: Last year of our projections
      k: Discount rate
      g: Constant rate of increase in perpetual free cash flows

      Example of RV calculation:



    2. Yield required by the market, considering the leverage of the company (Ke)
      The formula for the calculation is:

      Ke = Ku + ((PTF/POF) * (1-t) * (Ku - Cost TF))

      Whereas:
      Ku: Yield required by the market without debt
      PTF: Proportion of third party financing in relation to total sources of financing
      POF: Proportion of own financing in relation to total sources of financing
      t: Income tax rate
      Cost TF: Cost of third party financing before taxes

      The yield will be higher or lower in relation to the level of debt. So, with a higher level of debt, there is more risk for the company, and a higher yield should be required by the investor.

      Example of ke calculation:



    3. Debt service coverage ratio (DSCR)
      This ratio measures the capacity of the company to repay its debt (principal plus interest).

      DSCR = CFD / DS

      Whereas:
      CFD: Cash flows available for debt service
      DS: Annual debt service = i + m
      i: Annual amount of interest
      m: Annual repayment of principal

      If DSCR > 1: The company generates enough cash flow to cover the annual debt service.
      If DSCR < 1: The company does not generate enough cash flow to cover the annual debt service.
      Therefore, with a higher value of this ratio, the company will be in a better position to cover the annual debt service.

      Example of DSCR calculation:



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