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.
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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)
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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 -
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5. EFN & Planned Growth Rate
������������������
������
-NI*r
What happens when g = 0?
EFN = -Addition to RE in last year (surplus not invested in assets)
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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!
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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!
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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!
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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).
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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 !
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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
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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.
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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.
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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%.
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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!
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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.
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