Explanation of two alternative timing assumptions for corporate financial planning
Alternative Timing Assumption 1: Sales Driven by End-of-Year Assets
The timing assumption used in the paper “Spreadsheet Exercises for Linking Financial
Statements, Valuation and Capital Budgeting is that assets in place at the end of one year drive
sales, profits and other flows in the following year. The rationale for this assumption is that
assets are needed first to support the coming year’s sales. An alternative assumption is that
end-of-year assets drive sales and other flows in a given year. To construct a spreadsheet based
on the latter assumption, start with the same Year 0 balance sheet information in Column E, as
shown in the accompanying worksheet labeled “Supp 1.” . Unlike, text Exhibits 2 and 3,
however, construct the first income statement for Year 0, rather than Year 1. Year 0 sales equal
the asset turnover ratio times Year 0 total assets. Year 0 depreciation is equal to the ratio of
depreciation to fixed assets times Year 0 fixed assets. Year 0 interest expense is equal to the
interest rate times Year 0 debt. For Year 1 and beyond, copy formulas to the right.
One difference between the model in Section I of the text and this one is the sustainable
growth rate. As shown in Ross, Westerfield and Jordan (1998, Chapter 4), the sustainable growth
rate under this alternative timing assumption is
g = ROEb/(1-ROEb)
(A.1)
It is verified in Rows 25 and 26 of the worksheet “Supp 1” that the actual growth rate in sales
under this timing assumption is equal to the rate in Equation (A.1).
Alternative Timing Assumption 2: Sales Driven by the Average of Beginning- and
End-of-Year Assets
Another possible timing assumption is that sales and other flows in a given year are
driven by the average of beginning- and end-of-year assets. This is a relatively natural
assumption if one calculates flow-to-stock financial ratios in this way, as is often done in finance
textbooks. Using this assumption does lead to a different sustainable growth rate, however, and
also complicates the set-up of the spreadsheet somewhat.
To derive the sustainable growth rate expression, note that in any year t+1 a company’s
assets grow by the amount gAt over assets at the end of year t, where g is the sustainable growth
rate. An amount gAt(D/A) of this asset growth can be financed by new debt, where D/A is the
specified debt/assets ratio. Retained earnings during Year t+1 (equal to the retention ratio times
ROE times the average of beginning- and end-of-year equity) are also available to finance asset
growth. Since no new equity can be issued, however, asset growth must be financed entirely
from these two sources. Thus:
gAt = gAt(D/A) – ROEb(Et+Et+1)/2
Since Et+1 = (1+g)Et, we can write
(A.2)
gAt(1 - D/A) = gAt(E/A)= ROEbEt(1+g/2)
(A.3)
Dividing both sides by At and noting that the equity/assets ratio is constant, this implies
g = ROEb(1+g/2)
(A.4)
Solving for g then gives
g = ROEb/(1-ROEb/2)
(A.5)
To set up a spreadsheet reflecting this timing assumption, start with the initial balance
sheet. Sales in Year 1 will then be equal to total asset turnover times the average of Year 0 and
Year 1 total assets. The other income statement items for Year 1 can be calculated as in any
previous spreadsheets, except that depreciation and interest expense are based on the average of
Year 0 and Year 1 fixed assets and debt, respectively. If we knew Year 1 total assets, we could
calculate the values of all individual balance sheet items based on the fact that each item always
bears the same relationship to total assets plus the assumption that Year 1 equity equals Year 0
equity plus Year 1 retained earnings. All Year 1 (Column F) cells except for total assets in the
accompanying worksheet “Supp 2” contain formulas analogous to those illustrated for Year 4.
Next, we note that total assets must grow at the sustainable growth rate. Add spreadsheet
lines for the sustainable growth rate (Row 25), the fractional growth in assets (Row 26) and the
difference between the sustainable and the actual asset growth rate (Row 27). Finally, to find
Year 1 total assets, bring down Solver from the tools menu, and instruct it to set Cell F27 “Equal
to Value of 0 By Changing Cells: F6.” This gives us the value (approximately $107.695 million)
of Year 1 total assets that is simultaneously consistent with both the sustainable growth rate and
all other known income statement and balance sheet relationships. For Year 2, set total assets
equal to the sum of accounts payable, debt and equity and copy all other Year 1 cells to the right.
For all subsequent years, copy all of the balance sheet and income statement cells to the right.
Text Timing Assumption: Sales Driven by Beginning-of-Year Assets,
and ROE = rE
A property of the timing assumption used in Section I is that when the company’s return
on equity is exactly equal to the cost of capital, the market value of equity is equal to the book
value in each year. To see this, rewrite the constant growth DDM as
EMt= Divt+1/(rE – ROEb) = (1-b)(net incomet+1)/(rE – ROEb)
(A.6)
When ROE = rE, (A.6) reduces to:
EMt = net incomet+1/rE = ROE(EBt)/rE = rE(EBt)/rE = EBt
(A.7)