CORPORATE VALUATION
Separation of Financing from Investment
The Separation Theorem allows for the evaluation of an investment without regard to how
it is financed as long as the required rate of return reflects the financing via the use of the Average
Cost of Capital.
Assume the following:
Cost of Debt =
10%
Tax Rate =
40%
After-tax Cost of Debt = 6%
Cost of Equity =
14%
Percent Debt Financing = 50%
Percent Equity Financing = 50%
Average Cost of Capital = Cost of Debt * (Percent Debt Financing) +
Cost of Equity * (Percent Equity Financing)
= 10% * (1-.4) * (.5) + 14% * (.5)
= 6% * (.5) + 14% * (.5)
= 10%
A)
Project Cash Flows
Year 0
Investment Cost
Revenues
Costs
Year 2
Year 3
3,000
(800)
3,000
(800)
4,792
(1,000)
2,200
(880)
2,200
(880)
3,792
(1,517)
1,320
1,320
2,275
(4,000)
Taxable Inc.
Taxes (40%)
Net Cash Flows
Year 1
(4,000)
NPV @ 10% = 0
A NPV of zero indicates that both lenders and stockholders are earning their respective
required rates of return as well as getting their investment back (with no surplus). Consider the
financing explicitly with the payment of interest and a repayment of principal as follows:
B)
Equity Cash Flows
Year 0
Year 1
Year 2
3,000
(800)
3,000
(800)
4,792
(1,000)
Operating Inc.
Interest Expense
2,200
(200)
2,200
(154)
3,792
(103)
Taxable Income
Taxes (40%)
2,000
(800)
2,046
(818)
3,689
(1,475)
2,000
1,200
(460)
1,228
(506)
2,213
(1,034)
(2,000)
740
722
1,179
Investment Cost
Revenues
Costs
Net Income
Debt Payment
Equity Cash Flow
IRR =
Year 3
(4,000)
14%
Return of Principal Calculations:
Year 1 Cash Flow
Interest on Debt
Shareholder Rate of Return
Taxes
2,200
(200) (10% * 2,000)
(280) (14% * 2,000)
(800)
Return of Principal
920
Return of Principal to Lenders =
Return of Principal to Stockholders =
Beg. Debt Balance - Yr. 1:
Debt Repayment
Ending Debt Balance - Yr. 1:
460 (50%)
460 (50%)
2,000
(460)
Beg. Equity Balance - Yr. 1
Equity Repayment
1,540
End. Equity Balance - Yr. 1
Year 2 Cash Flow
Interest on Debt
Shareholder Rate of Return
Taxes
2,200
(154) (10% * 1,540)
(216) (14% * 1,540)
(818)
Return of Principal
1,012
Return of Principal to Lenders =
Return of Principal to Stockholders =
506 (50%)
506 (50%)
2,000
(460)
1,540
Beg. Debt Balance - Yr. 2:
Debt Repayment
1,540
(506)
Beg. Equity Balance - Yr. 2
Equity Repayment
1,540
(506)
Ending Debt Balance - Yr. 2
1,034
End. Equity Balance - Yr. 2
1,034
Year 3 Cash Flow
Interest on Debt
Shareholder Rate of Return
Taxes
3,792
(103) (10% * 1,034)
(145) (14% * 1,034)
(1,475)
Return of Principal
2,068
Return of Principal to Lenders =
Return of Principal to Stockholders =
Beg. Debt Balance - Yr. 3:
Debt Repayment
1,034 (50%)
1,034 (50%)
1,034
(1,034)
Ending Debt Balance - Yr. 3:
Cash Flows To Lenders
Beg. Equity Balance - Yr. 3
Equity Repayment
0
End. Equity Balance - Yr. 3
Year 0
1,034
(1,034)
0
Year 1
Year 2
Year 3
200
460
154
506
103
1,034
Loan
Interest
Principal
(2,000)
Net Cash Flows
(2,000)
660
660
1,138
Year 0
Year 1
Year 2
Year 3
280
460
216
506
145
1,034
740
722
1,179
IRR = 10%
Cash Flows To Stockholders
Investment
Dividends
Principal
(2,000)
Net Cash Flow
(2,000)
IRR = 14%
Since the result is the same whether utilizing Project Cash Flows and the average cost of
capital, or Equity Cash Flows and the cost of equity, the investment decision can be made at the
divisional level and the financing decision can be made at the corporate level.
Project Valuation
Capital budgeting, as in the previous example, usually assumes that a project “ends” after
a number of years. In general, however, investments are made with the expectation that, if
successful, the activities will continue indefinitely. The best way to evaluate any sort of investment
is to create two scenarios: a base-case which projects the cash flows if a company just continues
business as usual, and an expansion (or NewCo, etc.) scenario which reflects the anticipated
cash flows should a project be undertaken. The relevant cash flows are just the difference
between the two scenarios. Rather than shutting the project down at the end of the planning
horizon, however, the free cash flow can be capitalized using the WACC.
As an example, consider the following company which is considering opening an office in
another city to expand its territory. For simplicity, we’ll use the percentage-of-sales method for
forecasting the balance sheet.
Base-case:
Income Statements
Year 0
Revs
COGS
Year 1
Year 2
Year 3
1,000,000 1,040,000 1,081,600 1,124,864
600,000
624,000
648,960
674,918
4% Growth
60% of Sales
Gross Profit
400,000
416,000
432,640
449,946
Salaries
Utilities
Depreciation
150,000
16,000
12,500
153,000
16,320
13,000
156,060
16,646
13,520
159,181
16,979
14,061
2% Inflation
2% Inflation
5% of Net FA
EBIT
Interest
221,500
15,600
233,680
15,600
246,414
15,600
259,724
15,600
8% of Debt
Tax. Inc.
Taxes (40%)
205,900
82,360
218,080
87,232
230,814
92,325
244,124
97,650
Net Income
123,540
130,848
138,488
146,475
Balance Sheets
Year 0
Year 1
Year 2
Year 3
25,000
150,000
26,000
156,000
27,040
162,240
28,122
168,730
175,000
182,000
189,280
196,851
Net Fixed Assets
250,000
260,000
270,400
281,216
Total Assets
425,000
442,000
459,680
478,067
A/P
Bank Note
60,000
15,000
62,400
15,000
64,896
15,000
67,492
15,000
Total CL
75,000
77,400
79,896
82,492
L-T Debt
C/S
Retained Earnings
180,000
10,000
160,000
180,000
10,000
174,600
180,000
10,000
189,784
180,000
10,000
205,575
Total Liabs. & Eq.
425,000
442,000
459,680
478,067
0
0
0
0
Cash
A/R
Total CA
Assets - Liab. & Eq.
Pct of Sales
Pct of Sales
Pct of Sales
Pct of COS
Constant
Constant
Constant
Plug Figure
Statement of Cash Flows
From Operations:
Year 1
Year 2
Year 3
Net Income
Depreciation
130,848
13,000
138,488
13,520
146,475
14,061
Oper. CF
143,848
152,008
160,535
Working Capital
A/R
A/P
(6,000)
2,400
(6,240)
2,496
(6,490)
2,596
Total W/C
(3,600)
(3,744)
(3,894)
Total From Operations
140,248
148,264
156,642
From Investing Activities
Net Fixed Assets
(23,000)
(23,920)
(24,877)
(23,000)
(23,920)
(24,877)
0
0
0
(116,248)
0
0
0
(123,304)
0
0
0
(130,683)
(116,248)
(123,304)
(130,683)
Total Cash Flows
Plus: Beg. Cash
Ending Cash
1,000
25,000
26,000
1,040
26,000
27,040
1,082
27,040
28,122
Cash from B/S
26,000
27,040
28,122
Total from Investing
From Financing Activities
Bank Note
L-T Debt
Common Stock
Dividends
Total from Financing
Of course, the actual financing may vary either by borrowing more money to finance the asset
expansion or by paying down the debt due to a debt schedule for the loans. It really doesn’t
matter with respect to the valuation since we are assuming that either (1) the actual long-term
financing target is reflected in the WACC or (2) the average cost of capital is independent of
capital structure. In any event, the cash flows we will be analyzing will not include any financing
cash flows since the financing is reflected in the WACC.
Now consider the expansion case where we anticipate the following:


Sales will increase by $200,000 in Year 1 over current projections and then grow at 4%
annually.
Salaries will increase by $40,000 in Year 1 over current projections and then grow at 2%



per year.
Utilities will increase by $5,000 over current projections and grow by 2% per year.
$150,000 of additional Fixed Assets will be required
Additional L-T debt of $75,000 will be required to cover much of the asset expansion
Expansion:
Income Statements
Revs
COGS
Gross Profit
Salaries
Utilities
Depreciation
EBIT
Interest
Tax. Inc.
Taxes (40%)
Net Income
Year 0
Year 1
Year 2
Year 3
1,000,000 1,240,000 1,289,600 1,341,184
600,000
744,000
773,760
804,710
400,000
496,000
515,840
536,474
150,000
16,000
12,500
221,500
15,600
205,900
82,360
123,540
193,000
21,320
20,500
261,180
21,600
239,580
95,832
143,748
196,860
21,746
21,320
275,914
21,600
254,314
101,725
152,588
200,797
22,181
22,173
291,322
21,600
269,722
107,889
161,833
4% Growth
60% of Sales
2% Inflation
2% Inflation
5% of Net FA
8% of Debt
Balance Sheets
Cash
A/R
Total CA
Year 0
25,000
150,000
175,000
Year 1
31,000
186,000
217,000
Year 2
32,240
193,440
225,680
Year 3
33,530
201,178
234,707
Pct of Sales
Pct of Sales
Net Fixed Assets
250,000
410,000
426,400
443,456
Pct of Sales
Total Assets
425,000
627,000
652,080
678,163
60,000
15,000
75,000
74,400
15,000
89,400
77,376
15,000
92,376
80,471
15,000
95,471
Pct of COS
Constant
L-T Debt
C/S
Retained Earnings
180,000
10,000
160,000
255,000
10,000
272,600
255,000
10,000
294,704
255,000
10,000
317,692
Constant
Constant
Plug Figure
Total Liabs. & Eq.
425,000
627,000
652,080
678,163
0
0
0
0
A/P
Bank Note
Total CL
Assets - Liab. & Eq.
Statements of CF
Year 2
152,588
21,320
173,908
Year 3
161,833
22,173
184,006
From Operations:
Net Income
Depreciation
Oper. CF
Year 1
143,748
20,500
164,248
Working Capital
A/R
A/P
Total W/C
(36,000)
14,400
(21,600)
Total From Operations
142,648
169,444
179,364
From Investing Activities
Net Fixed Assets
Total from Investing
(180,500)
(180,500)
(37,720)
(37,720)
(39,229)
(39,229)
From Financing Activities
Bank Note
L-T Debt
Common Stock
Dividends
Total from Financing
0
75,000
0
(31,148)
43,852
0
0
0
(130,484)
(130,484)
0
0
0
(138,845)
(138,845)
Total Cash Flows
Plus: Beg. Cash
Ending Cash
6,000
25,000
31,000
1,240
31,000
32,240
1,290
32,240
33,530
Cash from B/S
31,000
32,240
33,530
(7,440)
2,976
(4,464)
(7,738)
3,095
(4,643)
The incremental cash flows can be calculated by simply subtracting the cash flows in the BaseCase from the cash flows in the Expansion Case. Note that the financing cash flows have been
ignored with the exception that a line has been included to add back the after-tax additional
interest expense that occurred in the Expansion case due to the additional loan of $75,000.
Incremental Cash Flows
From Operations:
Net Income
Depreciation
Oper. CF
Year 1
12,900
7,500
20,400
Working Capital
A/R
A/P
Total W/C
(30,000)
12,000
(18,000)
(1,200)
480
(720)
(1,248)
499
(749)
2,400
21,180
22,722
(13,800)
(13,800)
(14,352)
(14,352)
3,600
3,600
3,600
3,600
10,980
31,000
41,980
11,970
32,240
44,210
Total From Operations
From Investing Activities
Net Fixed Assets
Total from Investing
From Financing Activities
Bank Note
L-T Debt
Common Stock
Add-back After-tax Interest
Total from Financing
Total Cash Flows
Plus: Beg. Cash
Ending Cash
(157,500)
(157,500)
3,600
3,600
(151,500)
25,000
(126,500)
Year 2
14,100
7,800
21,900
Year 3
15,359
8,112
23,471
The Free Cash Flows (FCF) are readily available from these figures. It is customary to
accelerate the outflows, in this case the investment in Fixed Assets and Working Capital, to the
beginning of each year. Thus, we’ll have to add in an adjustment for the now-missing 3rd year.
We also need to calculate a Terminal (or Residual) Value to capture the cash flows beyond our
three-year planning horizon.
Free Cash Flows and Valuation
Year 0
Net Income
Plus: After-tax Interest
Plus: Depreciation
Working Capital
Capital Investment
Free Cash Flows
Terminal Value
Total Cash Flows
(18,000)
(157,500)
(175,500)
(175,500)
Terminal Value Calculation:
Increase Year 3 FCF by 4%
WACC = 10%
Growth = 4%
Terminal Value = 147,659/(0.10 - 0.04) =
Year 1
12,900
3,600
7,500
(720)
(13,800)
9,480
9,480
Year 2
14,100
3,600
7,800
(749)
(14,352)
10,399
10,399
Year 3
15,359
3,600
8,112
(779) Increase by 4%
(14,926) Increase by 4%
11,366
197,010
208,376
11,821
197,010
NPV @ 10% = $(1,574)
Since the NPV is negative, the expansion is not desirable. Of course, it is very close to be
acceptable. One could argue that there are strategic reasons for going ahead with the expansion.
That, however, assumes that there are benefits that have not been captured in the cash flow
projections.