- If a firm continues to earn negative free cash flow to the firm (FCFF), it means its cash from operations is insufficient to meet investing needs and it will require external financing like debt or equity issuance.
- The FCFF and free cash flow to equity (FCFE) models will only lead to the same firm value if the firm has no debt. With debt, the models are unlikely to yield the same value.
- Using market values for debt and equity avoids problems of circularity that can arise when using book values in the weighted average cost of capital (WACC) calculation under the FCFF approach. Differences between the models can also arise if the firm's debt-to-equity ratio is changing
Value Proposition canvas- Customer needs and pains
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Tutorial 6 Solutions.docx
1. EVA TUTORIAL SOLUTIONS
TUTORIAL 6: FREE CASH FLOWS
DISCUSSION QUESTION
Q1 If a firm continues to earn negative FCFF then it means that cash flows from operations is
not sufficient to meet its investing needs and therefore requires external financing in the form
of increased borrowings and/ or raising capital from shareholders by share issue whilst reducing
cash distributions to existing shareholders, such as dividends or share buy-backs. Although a
firm can make up the shortfall in the short run there is a limit to how often a firm can do this as
the market becomes aware of its inability to generate enough cash flows from its own
operations. Therefore there is an expectation that a firm will attempt to improve its profitability
(ROC) by improving in operating efficiency and reducing costs or to sell off non- performing
assets.
Q2 Will the FCFF and FCFE models lead to the identical value for a firm?
(I have already been derived in the lectures so there is no need to do this in class but you can use
it to highlight the possible differences). For simplicity assume cash flows in perpetuity
๐ฝ๐ฌ(๐ญ๐ช๐ญ๐ญ) =
๐ญ๐ช๐ญ๐ฌ + ๐ฐ๐๐๐๐๐๐๐(๐ โ ๐ป) โ ๐ต๐๐ ๐ฉ๐๐๐๐๐๐๐๐
๐พ๐จ๐ช๐ช
โ ๐ฝ๐ซ
And
๐๐ธ (๐น๐ถ๐น๐ธ) =
๐น๐ถ๐น๐ธ
๐๐
Then VE (FCFF) - VE (FCFE)
๐ญ๐ช๐ญ๐ฌ + ๐ฐ๐๐๐๐๐๐๐(๐ โ ๐ป) โ ๐ต๐๐ ๐ฉ๐๐๐๐๐๐๐๐
๐พ๐จ๐ช๐ช
โ ๐ฝ๐ซ โ
๐ญ๐ช๐ญ๐ฌ
๐๐
= ๐
Re-arranging
๐ญ๐ช๐ญ๐ฌ (
๐
๐พ๐จ๐ช๐ช
โ
๐
๐๐
) +
๐ฐ๐๐๐๐๐๐๐(๐ โ ๐ป) โ ๐ต๐๐ ๐ฉ๐๐๐๐๐๐๐๐
๐พ๐จ๐ช๐ช
โ ๐ฝ๐ซ
2. If Debt = $0, both models will lead to the same value since WACC will collapse to r thereby
discounting the same cash flows by the same discount rate. However when Debt โ $0; the
condition is unlikely to hold. For companies that invest in a lot of human capital, like CSL, it is
likely that the WACC will be understated if equity is based on book value leading to a higher
valuation using the FCFF methodology. This difference can be mitigated by substituting it with
market capitalisation.
PROBLEMS
Q1. Calculate FCFF employing the Net Income method.
CSR Free Cash Flows 2015
From Q2 Tute 5 Total FCFE 114.3
Add Int(1-T) 15.7
Less Net borrowing 34.4
Total FCFF 164.4
Workings (see cash flow statement and below)
Interest (1-T) = 20.7 (1 โ .24) = $15.7๐
(see answer to Q4 Tute 2 for tax rate)
Cross checking using cash distributed to shareholders = FCFF
๐ท๐๐ ๐ก๐๐๐๐ข๐ก๐๐๐ ๐ก๐ ๐ โ๐๐๐โ๐๐๐๐๐๐ ๐๐๐ ๐๐๐๐กโ๐๐๐๐๐๐
= (๐ต + ๐ท)๐กโ1 + ๐ธ๐ก + ๐ผ๐๐ก๐๐๐๐ ๐ก(1 โ ๐)๐ก โ (๐ต + ๐ท)๐ก
= (825.2 + 34.4) + 125.5 + 15.7 โ (836.4 + 0) = $164.4
Interpretation of cash flows. CSR earns enough cash from operations to meet investments
however it is noted that CSR was disinvesting and reducing borrowings to zero.
BORAL. Calculate FCFF employing the Net Income method using the data from Tute 5.
BORAL Free Cash Flows 2015
From tute 5 Q3 Total FCFE $170.5
Add Int(1-T) 64.5
Less Net borrowing -221.1
3. Total FCFF $13.9
Interest (1-T) = 76.5 (1- 45.1/ 288.5) = 64.5
๐ท๐๐ ๐ก๐๐๐๐ข๐ก๐๐๐ ๐ก๐ ๐ โ๐๐๐โ๐๐๐๐๐๐ ๐๐๐ ๐๐๐๐กโ๐๐๐๐๐๐
= (๐ต + ๐ท)๐กโ1 + ๐ธ๐ก + ๐ผ๐๐ก๐๐๐๐ ๐ก(1 โ ๐)๐ก โ (๐ต + ๐ท)๐ก =
= (3,194+ 215.4 + 886.1) + 257 + 64.5 โ (3,280.5 + 1.8 + 1,320.8)
= $13.9๐
Interpretation of cash flows. Boral does earn enough cash from its operations to meet
investment needs, which is not a good sign and therefore needs to borrow money for this
purpose plus for distribution to shareholders.
Q2 Under the FCFF approach.
๐๐ด๐ถ๐ถ = 13.87% (600
1,000
โ ) + 7% (1 โ .4)(400
1,000
โ ) = 10%
๐๐น๐๐๐ =
๐น๐ถ๐น๐น
๐๐ด๐ถ๐ถ
=
100
0.1
= $1,000๐
๐๐ธ๐๐ข๐๐ก๐ฆ = ๐๐๐๐๐ โ ๐๐๐๐๐ก = 1,000๐ โ 400๐ = $600๐
Under the FCFE approach.
๐๐ธ๐๐ข๐๐ก๐ฆ =
๐น๐ถ๐น๐ธ
๐๐
=
๐น๐ถ๐น๐น โ ๐ผ๐๐ก๐๐๐๐ ๐ก(1 โ ๐) + ๐๐๐ก ๐ต๐๐๐
๐๐
=
100 โ 7%(400)(1 โ .4)
0.1387
=
83.202
0.1387
= $600๐
Interest = rd*Debt
Note the cost of equity is equal to
๐๐ = 10% + 4
6
โ [10% โ 7%(1 โ .4)] = 13.87%
What is important to note here is that the market weights of debt and equity are based on their
true market values which avoids the problem of circularity in the FCFF methodology (equity is
both a required input in the WACC calculation and required solution). Using proxies, such as
book values, will introduce errors.
4. There is a further problem if a firm has not reached a stable D/E ratio, which is to be expected
in the short to medium term. Under these conditions the value of debt may differ to that under
a target D/E ratio, which will in turn affect the WACC calculation.
Q3. Using FCFE = $114.30 FCFF $164.40 T = 24% Interest = 20.7 Debt = $0m
Interest rate on new debt = 20.7 /400 = 5.2% re = 12%
Net Borrowings = -$34.4
a) FCFF methodology
No debt for 2015 WACC = re
๐๐ธ = ๐๐น โ ๐๐ท =
164.4
. 12
โ 0 = $1,370
๐๐โ๐๐๐ =
1,370
504
= $2.72 ๐๐
FCFE methodology
Revised FCFE = 114.3 + 34.4 + 20.7 (0.76) = $164.4m since there is no debt and the target debt
level is $0 then there can be no borrowings or interest expense.
๐๐ธ (๐น๐ถ๐น๐ธ) =
๐น๐ถ๐น๐ธ
๐๐
=
164.4
. 12
= $1,370๐
Conclusion: The answer under both methodologies is the same for the situation of no debt and
recognising that net borrowings is not projected indefinitely, which makes sense given that the
target level of debt has been reached. Also given that debt = 0, there should be no interest
costs.
Note: if we donโt adjust for net borrowings our valuation under FCFE would be as follows which
is completely different
๐๐ธ =
114.3
. 12
= $952.5๐
Difference= 1,370 โ 952.5 = $417.5m
b) Debt $400m and assume the correction to net borrowings and interest
FCFF methodology
Revise WACC
๐๐ด๐ถ๐ถ = 12% (
836.4
836.4 + 400
) + 5.2% (1 โ .24)(
400
836.4 + 400
)
= 12% (0.6765) + 3.952%(0.3235) = 8.12% + 1.28% = 9.4%
๐๐น =
164.4
0.094
= $1,749๐
5. ๐๐ธ = ๐๐น โ ๐๐ท = 1,749 โ 400 = $1,349
FCFE methodology
Revise
Interest expense is unchanged 20.7 (.76) = $15.7
Revise FCFE = 114.3 + 34.4 = $148.7m
๐๐ธ =
148.7
. 12
= $1,239๐
Difference= 1,349 - 1,239โ= $110m
Reconcile Difference
= 148.7 (
1
0.094
โ
1
0.12
) +
15.7 + 0
0.094
โ 400 = 343 + 167 โ 400 = $110
Conclusion: Even though net borrowings has been removed there is still a difference between
the two methodologies. This suggests that the problem is with the WACC.
c) Consider using market value of equity 504m x $4.21 = $2,121.8 to determine WACC
FCFF methodology
Consider using
๐๐ด๐ถ๐ถ = 12% (
2,121.8
2,121.8 + 400
) + 5.2% (1 โ .24)(
400
2,121.8 + 400
)
= 12% (0.842)+ 3.95%(0.158) = 10.1% + 0.6% = 10.7%
๐๐น =
164.4
0.107
= $1,536๐
๐๐ธ = 1,536 โ 400 = $๐,๐๐๐๐
FCFE methodology
As with part c)
๐๐ธ =
148.7
. 12
= $1,239๐
Difference= 1,136 โ 1,239 = $103m (slightly better)
Reconcile
= 148.7 (
1
0.107
โ
1
0.12
) +
15.7 + 0
0.107
โ 400 = 151 + 147 โ 400 = $103๐
6. Conclusion: Adjusting WACC for market values has not solved the inconsistency between the
two models.
d) Using ๐๐ธ =
๐น๐ถ๐น๐น
๐๐ด๐ถ๐ถ
โ ๐ท
And recognising the Equity can be replace by VE
Removing denominator
๐๐ธ. ๐๐ด๐ถ๐ถ = ๐น๐ถ๐น๐น โ ๐ท. ๐๐ด๐ถ๐ถ
Rearranging
๐๐ธ. ๐๐ด๐ถ๐ถ + ๐ท. ๐๐ด๐ถ๐ถ = ๐น๐ถ๐น๐น
Since E+D = V and substitute
๐. ๐๐ด๐ถ๐ถ = ๐น๐ถ๐น๐น
Expanding WACC
๐ [๐๐
๐๐ธ
๐
+ ๐๐(1โ ๐)
๐ท
๐
] = ๐น๐ถ๐น๐น
Simplifies to
๐๐. ๐๐ธ + ๐๐(1โ ๐)๐ท = ๐น๐ถ๐น๐น
Therefore
๐๐ธ =
๐น๐ถ๐น๐น โ ๐๐(1โ ๐)๐ท
๐๐
Using Debt $400m
๐๐ธ =
164.4 โ 5.2% (1 โ .24) (400)
0.12
=
148.7
0.12
= $1,239๐
Revise WACC (FCFF methodology)
๐๐ด๐ถ๐ถ = 12% (
1,239
1,239 + 400
) + 5.2% (1 โ .24) (
400
1,239 + 400
)
= 12% (0.756)+ 3.952%(0.244) = 9.07% + 0.964% = 10.034%
๐๐น =
164.4
0.10034
= $1,638๐
๐๐ธ = 1,638 โ 400 = $1,239๐
FCFE methodology
As with part c)
๐๐ธ =
148.7
. 12
= $๐,๐๐๐๐
Comment:
Therefore except for a rounding error both models yield the same result. However, this
outcome is easily achieved if the relationship between debt and equity is maintained for period
7. t+1 onwards. This becomes far more complicated if we consider changes to this relationship
over time ie donโt assume in perpetuity.