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Lecture 3: January 11, 2012




Financial Planning and Growth




                                1
Objectives

We will first learn how to use spreadsheets to develop a financial

  model that allows us to forecast future funding needs.



We will then make some simplifying assumptions to obtain useful

  formulas that allow us to get a feel for what may happen without

  doing the detailed financial modeling exercise.


                                                                 2
Variables definition: based on accounting data for year t
 ������= total assets (from balance sheet at the end of year t)
 ������ = total debt (from balance sheet at the end of year t)
 ������ = total equity (from balance sheet at the end of year t)
 ������������ = net income (from income statement for year t)

 ������ = retention ratio =                                   =1 −   ������������������������������������ ������������������������������ = 1 − ������
                       ∆ ������������������������������������������������ ������������������������������������������������
                              ������������������ ������������������������������������


 ������������������ = return on assets =
                                 ������������������ ������������������������������������
                                ������������������������������ ������������������������������������


 ������������������ = return on equity =
                                  ������������������ ������������������������������������
                                 ������������������������������ ������������������������������������

 ������ = projected sales growth rate (from year t to year t+1)

                                                                                                     3
Formal calculation of External Fund Needs (EFN)
 Increase in assets =������ ∗ ������

 Addition to ������������ = ������������ ∗ 1 + ������ ∗ ������

 ������������������ = ������������������������������������������������ ������������ ������������������������������������ − ������������������������������������������������ ������������ ������������ (∆������������ = 0)

 ������������������ = ������ ∗ ������ − ������������ ∗ 1 + ������ ∗ ������ = ������ – ������������ ∗ ������ ������ − ������������ ∗ ������

 What is the slope and what is the intercept?

 Slope: [������ – ������������ ∗ ������ ] ; Intercept: − ������������ ∗ ������

 What are their signs? Slope is + ; Intercept is -

                                                                                         4
EFN & Planned Growth Rate
 ������������������




                                                              ������


 -NI*r
 What happens when g = 0?
EFN = -Addition to RE in last year (surplus not invested in assets)
                                                                      5
The Internal Growth Rate
 Internal Growth Rate ������������: the rate of growth that can be
   supported with no external financing, i.e. EFN = 0.

 ������ − ������������ ∗ ������ ������������ − ������������ ∗ ������ = 0


                             ������������   =
                                           ������������∗������
                                        [������−������������∗������]
 Solving yields


 Divide by A & recall ������������������ =
                                             ������������
                                              ������


               ������������ =
                            ������������������∗ ������
                        (������ – ������������������ ∗ ������)
 Then
 Make sure you can derive it on your own!
                                                              6
The Internal Growth Rate
 Recall that: ������������ =
                            ������������������∗ ������
                        (������ – ������������������ ∗ ������)

 What happens with gi if the retention ratio (r) increases or
  equivalently the dividend payout ratio (d) decreases?
 Increases!

 What happens with gi if ROA increases?
 Increases!

 Suppose a firm is growing at gi each year. How is the firm’s
  debt-to-equity ratio evolving over time?
 Decreasing!

 Is this trend in the debt-to-equity ratio desirable? It depends!
                                                                     7
Towards the Sustainable Growth Rate

 The calculation of gi assumes that the firm cannot access external
  capital markets (realistic for many firms). And this drives the trend
  in the D/E of a firm growing at gi.

 Can the firm grow faster if it has access to debt markets?
 Yes! See picture.

 If the firm grows by retaining earnings and borrowing, what will
  happen to its debt-to-equity ratio over time?
 Uncertain, D/E can increase or decrease.

 If the firm cannot raise equity but can borrow, how would you
  choose a growth rate that is sustainable in the long run?
 EEFN=0!
                                                                     8
The Sustainable Growth Rate

Sustainable Growth Rate g*: the maximum growth rate a firm can
achieve without external equity financing while borrowing to
maintain a constant debt/equity ratio (given its ROE and r).

 The gap between a firm’s external financing needs and the
  portion that can be covered with new borrowing is called the
  External Equity Financing Needed (EEFN).




                                                                 9
The Sustainable Growth Rate
EEFN = EFN – New Borrowing

     = ∆+ ������������������������������������ – ������������������������������������������������ ������������ ������������ – ������������������ ������������������������������������������������������

 But recall this is true under our simplifying
  assumptions.

 Conceptually, g* is the growth rate such that EEFN = 0 !




                                                                            10
Calculating the Sustainable Growth Rate
EEFN = ������ ∗ ������ – ������������ ∗ ������ ∗ 1 + ������ – ������������ ∗ ������ ∗ ������ + ������ ∗
                                                                          ������
                                                                          ������




                            ������           ������                            ������������
What is the last term?

       ������������ ∗ ������ ∗ 1 + ������ ∗    = Δ������������ ∗    =                                ∗ ������
                            ������           ������                             ������




                                                                         ������
Now solve for g*:

      ������ ∗   ������∗ – ������������   ∗ ������ ∗ 1 +   ������∗   – ������������ ∗ ������ ∗ 1   + ������∗   ∗    = 0
                                                                         ������


                                                                                    11
Calculating the Sustainable Growth Rate
                               ������
             ������ ∗   ������∗ –   1+               ∗ ������������ ∗ ������ ∗ (1 + ������∗ ) = 0
                               ������

                  ������                              ������
    ������ ∗ ������ – 1 +
         ∗
                                 ∗ ������������ ∗ ������– 1 +            ∗ ������������ ∗ ������ ∗ ������∗ = 0
                  ������                              ������

                ������                                          ������
        ������– 1 +                 ∗ ������������ ∗ ������ ∗    ������∗ =   1+         ∗ ������������ ∗ ������
                ������                                          ������


Note that 1 +               =           =
                    ������          ������+������       ������
                    ������            ������        ������



                                                                                     12
Calculating the Sustainable Growth Rate
Thus, 1 +        ∗ ������������ ∗ ������ =         ∗ ������������ ∗ ������ = ������ ∗ ������������������ ∗ ������
            ������                    ������
            ������                    ������



                                  ������– 1 +          ∗ ������������ ∗ ������ ∗ ������∗ = 1 +        ∗ ������������ ∗ ������
                                              ������                             ������
                                              ������                             ������
Plug this expression into

                 ������ – ������ ∗ ������������������ ∗ ������ ∗ ������∗ = ������ ∗ ������������������ ∗ ������

Divide by A to get:      1– ������������������ ∗ ������ ∗ ������∗ = ������������������ ∗ ������


                   ������∗   =
                                  ������������������∗������
                             [������ – ������������������ × ������]
Thus



                                                                                                13
EFN vs. ������, ������������, and ������∗

 EFN




   0               gi       g*   g




                                     14
Different Regions of Growth

0 < ������ < ������������ : Here RE are more than enough to finance low
 Case 1

growth, so you can also pay dividends, accumulate cash, or do
something with the money. The D/E is falling.




������������ < ������ < ������ : Here additions to RE are more than the
              ∗
 Case 2:

amount raised in debt, and thus the D/E is falling.

 Would it make sense to grow at g < g* ?
 If D/E is high, doing this for some time may be desirable

                                                              15
Different Regions of Growth
 Case 3: ������ > ������
                    ∗


 3 choices facing the firm:
    Grow without issuing equity but issuing debt: D/E
     increases because equity increases more slowly than
     debt. Is this optimal?
   Eventually you would reach bankruptcy.

    Grow issuing equity and debt. Is this sustainable in the
     long run?
   Yes, provided that D/E stays constant.

    Grow raising equity but not debt. D/E would be falling.
     Is this optimal?
   Not in the long run, but maybe in the short run.

                                                                16
Back to Sumo: Calculate EFN, gi and g*
Using the information for 2009, we see that A=6,000, NI=690,
 ROA = 11.5%, ROE = 20.3%, and r = 2/3.

Using our formulas (based on the assumptions on slide 13):


    ������������ = .115 * 2/3 / [1-.115 * 2/3] = 8.3%
   EFN (g = 20%) = 6,000 * 20% - 690 * 2/3 * 1.2 = 648


    ������∗ = .203*2/3 / [1-.203 * 2/3] = 15.6%

Note (of course) that our estimate of EFN differs from our
 estimate with more realistic assumptions in slide 10.

How far off it will be depends of how much our simplifying
 assumptions depart from what is reasonable for the firm.

                                                                17
Back to Sumo: Calculate EFN, ������������ and ������∗
Recall our simplifying assumptions:
    i) operating expenses grow 20%.
    ii) interest expenses grow 20%.
    iii) accounts payable do not change.



    If ������ = 20% then EFN = 648.
Use the spreadsheets in Lecture 3.xls to verify that:


    If ������ = ������������ then EFN = 0 (and thus balance sheet is complete)
    If ������ = ������ ∗ then EFN = 406.8. Note that in 2009 D/E = 76.5%
     and if we cover EFN with debt then in 2010 D/E = 76.5%.


                                                                 18
19
20
Caveats on Financial Planning Models
 They do not indicate which financial policies maximize firm
  value. In other words, there is no finance theory in them!

 They rely on simplifying assumptions that may not be realistic
  (e.g., not everything grows in proportion to sales).

 If you complicate them too much by adding more detail they
  may became less practical to use.

 But they are useful tools to plan investment and financing
  decisions (just be aware of the assumptions).

 You can use them to forecast financial needs and financial
  statements, which are the basis of cash flow projections!

                                                             21
Summary & Conclusions
With some simplifying assumptions we can develop simple
  formulas for the internal growth and sustainable growth rates.

Comparing planned growth rates with ������������ and ������∗ provides critical
  information about a firm’s future financing needs and trend in
  the debt ratio.




                                                                22

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Comm370 lecture 3 - financial planning and growth

  • 1. Lecture 3: January 11, 2012 Financial Planning and Growth 1
  • 2. Objectives We will first learn how to use spreadsheets to develop a financial model that allows us to forecast future funding needs. We will then make some simplifying assumptions to obtain useful formulas that allow us to get a feel for what may happen without doing the detailed financial modeling exercise. 2
  • 3. Variables definition: based on accounting data for year t  ������= total assets (from balance sheet at the end of year t)  ������ = total debt (from balance sheet at the end of year t)  ������ = total equity (from balance sheet at the end of year t)  ������������ = net income (from income statement for year t)  ������ = retention ratio = =1 − ������������������������������������ ������������������������������ = 1 − ������ ∆ ������������������������������������������������ ������������������������������������������������ ������������������ ������������������������������������  ������������������ = return on assets = ������������������ ������������������������������������ ������������������������������ ������������������������������������  ������������������ = return on equity = ������������������ ������������������������������������ ������������������������������ ������������������������������������  ������ = projected sales growth rate (from year t to year t+1) 3
  • 4. Formal calculation of External Fund Needs (EFN)  Increase in assets =������ ∗ ������  Addition to ������������ = ������������ ∗ 1 + ������ ∗ ������  ������������������ = ������������������������������������������������ ������������ ������������������������������������ − ������������������������������������������������ ������������ ������������ (∆������������ = 0)  ������������������ = ������ ∗ ������ − ������������ ∗ 1 + ������ ∗ ������ = ������ – ������������ ∗ ������ ������ − ������������ ∗ ������  What is the slope and what is the intercept?  Slope: [������ – ������������ ∗ ������ ] ; Intercept: − ������������ ∗ ������  What are their signs? Slope is + ; Intercept is - 4
  • 5. EFN & Planned Growth Rate ������������������ ������ -NI*r  What happens when g = 0? EFN = -Addition to RE in last year (surplus not invested in assets) 5
  • 6. The Internal Growth Rate  Internal Growth Rate ������������: the rate of growth that can be supported with no external financing, i.e. EFN = 0.  ������ − ������������ ∗ ������ ������������ − ������������ ∗ ������ = 0 ������������ = ������������∗������ [������−������������∗������]  Solving yields  Divide by A & recall ������������������ = ������������ ������ ������������ = ������������������∗ ������ (������ – ������������������ ∗ ������)  Then  Make sure you can derive it on your own! 6
  • 7. The Internal Growth Rate  Recall that: ������������ = ������������������∗ ������ (������ – ������������������ ∗ ������)  What happens with gi if the retention ratio (r) increases or equivalently the dividend payout ratio (d) decreases?  Increases!  What happens with gi if ROA increases?  Increases!  Suppose a firm is growing at gi each year. How is the firm’s debt-to-equity ratio evolving over time?  Decreasing!  Is this trend in the debt-to-equity ratio desirable? It depends! 7
  • 8. Towards the Sustainable Growth Rate  The calculation of gi assumes that the firm cannot access external capital markets (realistic for many firms). And this drives the trend in the D/E of a firm growing at gi.  Can the firm grow faster if it has access to debt markets?  Yes! See picture.  If the firm grows by retaining earnings and borrowing, what will happen to its debt-to-equity ratio over time?  Uncertain, D/E can increase or decrease.  If the firm cannot raise equity but can borrow, how would you choose a growth rate that is sustainable in the long run?  EEFN=0! 8
  • 9. The Sustainable Growth Rate Sustainable Growth Rate g*: the maximum growth rate a firm can achieve without external equity financing while borrowing to maintain a constant debt/equity ratio (given its ROE and r).  The gap between a firm’s external financing needs and the portion that can be covered with new borrowing is called the External Equity Financing Needed (EEFN). 9
  • 10. The Sustainable Growth Rate EEFN = EFN – New Borrowing = ∆+ ������������������������������������ – ������������������������������������������������ ������������ ������������ – ������������������ ������������������������������������������������������  But recall this is true under our simplifying assumptions.  Conceptually, g* is the growth rate such that EEFN = 0 ! 10
  • 11. Calculating the Sustainable Growth Rate EEFN = ������ ∗ ������ – ������������ ∗ ������ ∗ 1 + ������ – ������������ ∗ ������ ∗ ������ + ������ ∗ ������ ������ ������ ������ Δ������������ What is the last term? ������������ ∗ ������ ∗ 1 + ������ ∗ = Δ������������ ∗ = ∗ ������ ������ ������ ������ ������ Now solve for g*: ������ ∗ ������∗ – ������������ ∗ ������ ∗ 1 + ������∗ – ������������ ∗ ������ ∗ 1 + ������∗ ∗ = 0 ������ 11
  • 12. Calculating the Sustainable Growth Rate ������ ������ ∗ ������∗ – 1+ ∗ ������������ ∗ ������ ∗ (1 + ������∗ ) = 0 ������ ������ ������ ������ ∗ ������ – 1 + ∗ ∗ ������������ ∗ ������– 1 + ∗ ������������ ∗ ������ ∗ ������∗ = 0 ������ ������ ������ ������ ������– 1 + ∗ ������������ ∗ ������ ∗ ������∗ = 1+ ∗ ������������ ∗ ������ ������ ������ Note that 1 + = = ������ ������+������ ������ ������ ������ ������ 12
  • 13. Calculating the Sustainable Growth Rate Thus, 1 + ∗ ������������ ∗ ������ = ∗ ������������ ∗ ������ = ������ ∗ ������������������ ∗ ������ ������ ������ ������ ������ ������– 1 + ∗ ������������ ∗ ������ ∗ ������∗ = 1 + ∗ ������������ ∗ ������ ������ ������ ������ ������ Plug this expression into ������ – ������ ∗ ������������������ ∗ ������ ∗ ������∗ = ������ ∗ ������������������ ∗ ������ Divide by A to get: 1– ������������������ ∗ ������ ∗ ������∗ = ������������������ ∗ ������ ������∗ = ������������������∗������ [������ – ������������������ × ������] Thus 13
  • 14. EFN vs. ������, ������������, and ������∗ EFN 0 gi g* g 14
  • 15. Different Regions of Growth 0 < ������ < ������������ : Here RE are more than enough to finance low  Case 1 growth, so you can also pay dividends, accumulate cash, or do something with the money. The D/E is falling. ������������ < ������ < ������ : Here additions to RE are more than the ∗  Case 2: amount raised in debt, and thus the D/E is falling.  Would it make sense to grow at g < g* ?  If D/E is high, doing this for some time may be desirable 15
  • 16. Different Regions of Growth  Case 3: ������ > ������ ∗  3 choices facing the firm:  Grow without issuing equity but issuing debt: D/E increases because equity increases more slowly than debt. Is this optimal? Eventually you would reach bankruptcy.  Grow issuing equity and debt. Is this sustainable in the long run? Yes, provided that D/E stays constant.  Grow raising equity but not debt. D/E would be falling. Is this optimal? Not in the long run, but maybe in the short run. 16
  • 17. Back to Sumo: Calculate EFN, gi and g* Using the information for 2009, we see that A=6,000, NI=690, ROA = 11.5%, ROE = 20.3%, and r = 2/3. Using our formulas (based on the assumptions on slide 13):  ������������ = .115 * 2/3 / [1-.115 * 2/3] = 8.3%  EFN (g = 20%) = 6,000 * 20% - 690 * 2/3 * 1.2 = 648  ������∗ = .203*2/3 / [1-.203 * 2/3] = 15.6% Note (of course) that our estimate of EFN differs from our estimate with more realistic assumptions in slide 10. How far off it will be depends of how much our simplifying assumptions depart from what is reasonable for the firm. 17
  • 18. Back to Sumo: Calculate EFN, ������������ and ������∗ Recall our simplifying assumptions:  i) operating expenses grow 20%.  ii) interest expenses grow 20%.  iii) accounts payable do not change.  If ������ = 20% then EFN = 648. Use the spreadsheets in Lecture 3.xls to verify that:  If ������ = ������������ then EFN = 0 (and thus balance sheet is complete)  If ������ = ������ ∗ then EFN = 406.8. Note that in 2009 D/E = 76.5% and if we cover EFN with debt then in 2010 D/E = 76.5%. 18
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  • 21. Caveats on Financial Planning Models  They do not indicate which financial policies maximize firm value. In other words, there is no finance theory in them!  They rely on simplifying assumptions that may not be realistic (e.g., not everything grows in proportion to sales).  If you complicate them too much by adding more detail they may became less practical to use.  But they are useful tools to plan investment and financing decisions (just be aware of the assumptions).  You can use them to forecast financial needs and financial statements, which are the basis of cash flow projections! 21
  • 22. Summary & Conclusions With some simplifying assumptions we can develop simple formulas for the internal growth and sustainable growth rates. Comparing planned growth rates with ������������ and ������∗ provides critical information about a firm’s future financing needs and trend in the debt ratio. 22