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Corporate cash flows

Fundamentals of FinanceCorporate cash flows

Jukka Perttunen

University of Oulu - Department of Finance

Fall 2018

Jukka Perttunen Fundamentals of Finance


Value of assets

Assets Liabilities and owners’ equity

The value of the firm, or the value A of the assets of the firm is determined by the expected future cash flows from

assets (CFA) and the required rate of return on assets (kA).

A =∞∑t=1

CFAt

(1 + kA)t

Correspondingly, the required rate of return on assets is determined by the asset beta (βA) of the firm.

kA = r + (µm − r)βA

The value of the asset beta depends on the type of the industry, the degree of the operating leverage (i.e. the cost

structure) of the firm, and other such things which are independent of the capital structure of the firm.



Value of debt


A =∞∑t=1

CFAt

(1 + kA)t


A part of the cash flow from assets is paid to the debtors of the firm in terms of the cash flow to debtors (DFC).

?

D =∞∑t=1

CFDt

(1 + kD )t

The cash flow to debtors consists of the interest payments, the repayment of old debt, and possibly issued new debt.

In a case of a negative cash flow from assets, the deficit may be covered by a cash flow from debtors.

The value D of debt is obtained by discounting the cash flows to debtors by the required rate of return on debt (kD ).



Value of debt


A =∞∑t=1

CFAt

(1 + kA)t


?

D =∞∑t=1

CFDt

(1 + kD )t

The cash flow to debtors is strictly specified in the contracts between the firm and the debtors, and thus the riskiness

of the cash flow is relatively low when compared to that of the cash flow from assets.

The required rate of return on debt may be specified in terms of the debt beta βD :

kD = r + (µm − r)βD .

The value of the debt beta is assumed to be low, and the required rate of return on debt may be approximated by the

risk-free rate r , which corresponds to an assumption of βD = 0.



Value of equity


A =∞∑t=1

CFAt

(1 + kA)t


?

D =∞∑t=1

CFDt

(1 + kD )t

The value E of equity is what remains left of the value A of the assets after the value D of the claims of the debtors.

E = A− D-

-

(−)

At the same time it is about the present value of the cash flow to owners (CFE).

∞∑t=1

CFAt − CFDt

(1 + kE )t

(−)

?

CFEt

︷︸︸︷

The cash flow to owners consists of the dividends paid, possibly issued new equity, and repurchases of equity.

In a case of a negative cash flow from assets, the deficit may be covered by a cash flow from owners.



Value of equity


A =∞∑t=1

CFAt

(1 + kA)t


?

D =∞∑t=1

CFDt

(1 + kD )t

E = A− D-

-

(−)

∞∑t=1

CFAt − CFDt

(1 + kE )t

(−)

?

CFEt

︷︸︸︷

The discount rate kE which equalizes the present value of the cash flow to owners with the residual value E = A−D

of equity is called the required rate of return on equity.

=

We may express the required rate of return on equity it in terms of the equity beta βE .

kE = r + (µm − r)βE

The value of the equity beta βE depends on the value of the asset beta βA and the capital structure of the firm.

?D + E

EβA → βE -



Equity beta as a leveraged asset beta


A =∞∑t=1

CFAt

(1 + kA)t


?

D =∞∑t=1

CFDt

(1 + kD )t

E = A− D-

-

(−)

∞∑t=1

CFAt − CFDt

(1 + kE )t

(−)

?

CFEt

︷︸︸︷=

kE = r + (µm − r)βE

?D + E

EβA → βE -

The value of the asset beta given, the greater the relative amount of debt, the higher is the value of the equity beta.

︸︷︷︸Capital structure

The beta is leveraged by the use of debt.



Summary


To summarize:

In principle, the value of assets is determined by the expected cash flow from assets and the asset beta, which both are

purely independent of the capital structure of the firm.

A =∞∑t=1

CFAt

(1 + kA)t


The amount (and the value) of debt depends on the chosen capital structure.

D =∞∑t=1

CFDt

(1 + kD )t

The value of equity equals to the present value of the residual cash flow from assets after the claims of the debtors.

E = A− D =∞∑t=1

CFAt − CFDt

(1 + kE )t

The required rate of return on equity depends on the asset beta and the chosen capital structure.

- -

�

βE =D + E

EβA kE = r + (µm − r)βE



Weighted average cost of capital


A =∞∑t=1

CFAt

(1 + kA)t


D =∞∑t=1

CFDt

(1 + kD )t

- -βE =D + E

EβA kE = r + (µm − r)βE

Even though the equity beta is determined by the (unobservable) asset beta, we typically use the estimated equity

beta β̂E to have an estimate β̂A of the asset beta.

β̂E =σ̂im

σ̂2m

β̂A =E

D + Eβ̂E �

It is easy to verify that the weighted average cost of capital (WACC) serves as an estimate of the required return

on assets:

WACC =D

D + EkD +

E

D + E

[r + (µm − r)βE

].





A =∞∑t=1

CFAt

(1 + kA)t

kA = r + (µm − r)βA - βE =D + E

EβA - β̂A =

E

D + Eβ̂E

Let us assume that kD = r and express the weighted average cost of capital in terms of the asset beta:

WACC =D

D + Er +

E

D + E

[r + (µm − r)β̂E

]

=D

D + Er +

E

D + Er + (µm − r)

E

D + Eβ̂E

= r + (µm − r)β̂A.



The side-effect of debt


A =∞∑t=1

CFAt

(1 + kA)tD =

∞∑t=1

CFDt

(1 + kD )t

E =∞∑t=1

CFAt − CFDt

(1 + kE )t

In a world without taxes the value A of the firm’s assets is independent of the capital structure of the firm.

-

?

I real world the interest expenses are deductible in corporate taxation and the cash-flow from assets (an after-tax cash

flow) is, ceteris paribus, higher for a firm with higher interest expenses and a lower amount of taxes.

?

Such being the case, the total value of the firm is higher in a case of a larger amount of debt.

The value of the firm consists of the unlevered intrinsic value AU of the assets and the value of the interest tax shield.

A = AU + interest tax-shield.



The case of a steady state


A =∞∑t=1

CFAt

(1 + kA)tD =

∞∑t=1

CFDt

(1 + kD )t

E =∞∑t=1

CFAt − CFDt

(1 + kE )t

In the following numerical examples we consider the case of steady state, where all cash flows are assumed the stay

at their current levels forever, and the present value V of the future cash flow CF , in the case of a discount rate k,

appears as

V =∞∑t=1

CF

(1 + k)t=

CF

k.

=CFA

kA=

CFD

kD

=CFA− CFD

kE

The results we get can be generalized to any other cases.



Cash flow from assets

Let us consider a firm with a constant level of 2000 of earnings before interest and taxes forever.

EBITEarnings before interest and taxes 2000

The firm pays a constant interest payment of 400 forever.

IInterest paid 400

With the corporate tax rate of τ = 25% and tax-deductible interest expenses, the firm pays the corporate tax of

T = τ × (EBIT − I ) = 0.25× (2000− 400) = 400.

TCorporate taxes 400

We suppose the depreciation of the fixed assets and the capital expenditures to offset each other, and the level of

the net working capital to remain constant. Such being the case, the cash flow from assets appears as

CFA = EBIT − T = 2000− 400 = 1600.

CFACash flow from assets 1600

Notice that the interest paid is a cash flow to debtors and will be paid from the cash flow from assets at a later stage.



Value of assets


IInterest paid 400



The asset beta of the firm is supposed to be βA = 0.80

βAAsset beta 0.80

The current risk-free rate is r = 3.2%, and the current market risk premium is µm − r = 4.0%.

Correspondingly, the required rate of return on assets is

kA = r + (µm − r)βA = 0.032 + 0.040× 0.80 = 6.40%.

kARequired rate of return on assets 6.40%

It is about a case of a steady state, where the cash flow is expected to stay at a constant level forever.

Such being the case, the value of assets appears as

A =CFA

kA=

1600

0.064= 25000.

AValue of assets 25000



Alternative capital structures

Let us consider the same firm, but with alternative capital structures, and thus with a varying amount of interest paid.

Capital structure alternatives 1 2 3

EBITEarnings before interest and taxes 2000 2000 2000

IInterest paid 400 200 0

The tax paid depends on the amount of tax-deductible interest expenses:

T = τ × (EBIT − I ) = 0.25× (2000− I ).

TCorporate taxes 400 450 500

Correspondingly, the level of the cash flow from assets depends on the varying amount of taxes:

CFA = EBIT − T = EBIT − τ × (EBIT − I ) = 2000− 0.25× (2000− I ).

CFACash flow from assets 1600 1550 1500

The riskiness of the cash flow from assets does not change, and thus the asset beta is always βA = 0.80

βAAsset beta 0.80 0.80 0.80

The required rate of return on assets is the same kA = 6.40% for all three alternatives.

kARequired rate of return on assets 6.40% 6.40% 6.40%



Value of assets and interest tax-shield








The value of assets depends on the level of the cash flow from assets:

A =CFA

kA=

CFA

0.064.

AValue of assets 25000 24219 23438

The value of 23438 of the case without any interest expenses is considered as the unlevered value of the firm’s assets.

In all other cases the interest expenses provide an interest tax-shield with a present value of

τ × I

kA=

0.25× I

0.064.

Value of tax-shield 1562 781 0



Cash flow to debtors









We assume that the repayments of old debt are always covered by new debt, and thus the net cash flow to debtors

always equals to the interest paid.

CFDCash flow to debtors 400 200 0

Furthermore, we assume the debt beta to be βD = 0, which means that the required rate of return on debt equals

to the risk-free rate of r = 3.20%:

kD = r + (µm − r)βD = 0.032 + 0.040× 0.00 = 3.20%.

kDRequired rate of return on debt 3.20% 3.20% 3.20%



Value of debt











It is about a case of a steady state, where the cash flow to debtors is expected to stay at a constant level forever.

Such being the case, we are able to calculate the value of debt as

D =CFD

kD=

CFD

0.032.

DValue of debt 12500 6250 0



Cash flow to owners












The cash flow to owners is calculated as the after-debt residual of the cash flow from assets:

CFE = CFA− DFD.

CFECash flow to owners 1200 1350 1500



Value of equity













The value of equity is calculated as the after-debt residual of the value of assets:

E = A− D.

EValue of equity 12500 17969 23438



Required rate of return on equity














We are able to solve the required rate of return on equity behind the values:

E =CFE

kE⇒ kE =

CFE

E.

kERequired rate of return on equity 9.60% 7.51% 6.40%



Equity beta















Correspondingly, we are able to solve the equity betas behind the required rates of return on equity:

kE = r + (µm − r)βE ⇒ βE =kE − r

µm − r=

kE − 0.032

0.040.

βEEquity beta 1.60 1.08 0.80



Connection between the cash flows
















The cash flow the owners is the residual of the cash flow from assets after the paying of the cash flow to debtors.

-

-



Connection between the values
















The value of equity is the residual of the value of assets after the considering of the value of debt.

-

-



Connection between the betas
















The asset beta is the primary measurement of the riskiness of the assets of the firm.

�

The equity beta is determined by the asset beta, but it may be leveraged to a higher level by the use of debt.

�



Effect of financial leverage
















The equity beta of an all-equity firm is equal to it’s asset beta.

�

The greater is the amount of debt, the higher is the value of the equity beta (and the required rate of return on equity).

�

�



Capital structure ratios










D/ADebt to Assets 0.500 0.258 0.000



E/AEquity to Assets 0.500 0.742 1.000


For further purposes we calculate the Debt-to-Assets and the Equity-to-Assets.
















We are able to verify that the weighted average cost of capital equals to the required rate of return on assets:

WACC =D

AkD +

E

A

[r + (µm − r)βE

]=

D

AkD +

E

A(0.032 + 0.040× βE ) = 6.40%.

WACCWeighted average cost of capital 6.40% 6.40% 6.40%



Determinants of equity beta














The asset beta is the main determinant of the equity beta.

�

Together with the capital structure decision the asset beta defines the equity beta and the corresponding required

rate of return on equity.



Estimation of the required rate of return on assets














The equity beta and the required rate of return on debt are captured in the weighted average cost of capital.

�

The weighted average cost of capital is used to estimate the required rate of return on assets, because the asset beta

cannot be observed and the direct estimation of it is difficult.

-



Unlevered free cash flow

A common approach in firm valuation is to use the so-called unlevered free cash flow, where debt is ignored and no

interest is paid.




It means that taxes are considered to be paid without any deductions of interest payments.


The actual cash flow is now replaced with the corresponding unlevered free cash flow.

UFCFAUnlevered free cash flow from assets 1500 1500 1500



After-tax weighted average cost of capital










We bring the capital structure ratios, the required rate of return on debt and the equity beta from the previous

analysis of the actual cash flow from assets.

To value the unlevered free cash flow we need to calculate the after-tax weighted average cost of capital, where

the required rate of return on debt is adjusted by the corporate tax rate τ :

WACC∗ =D

A(1− τ)kD +

E

A

[r + (µm − r)βE

]=

D

A(1− 0.25)kD +

E

A(0.032 + 0.040× βE ).

WACC∗After-tax weighted average cost of capital 6.0000% 6.1935% 6.4000%



Value of the unlevered free cash flow










WACC∗After-tax weighted average cost of capital 6.0000% 6.1935% 6.4000%

Let us calculate the value A∗ of the unlevered free cash flow by the after-tax weighted average cost of capital:

A∗ =UFCFA

WACC∗.

A∗Value of unlevered free cash flow 25000 24219 23438

The value is equal to the value we get by the actual cash flow and the pre-tax weighted average cost of capital.




Tax-adjustment in the weighted average cost of capital








With the actual cash flow from assets we need to use the pre-tax weighted average cost of capital:

WACC =D

AkD +

E

A

[r + (µm − r)βE

].

WACCPre-tax weighted average cost of capital 6.4000% 6.4000% 6.4000% �

With the unlevered free cash flow we need to use the after-tax weighted average cost of capital:

WACC∗ =D

A(1− τ)kD +

E

A

[r + (µm − r)βE

].

WACC∗After-tax weighted average cost of capital 6.0000% 6.1935% 6.4000% �



Unlevered beta



AUUnlevered value of assets ? ? 23438



By the unlevered cash flow we are able to calculate the unlevered value AU of the firm’s assets.

Suppose that we know the capital structure and the equity beta of a firm and want to know the unlevered value of

the firm’s assets, in this case the value of 23438 of the third capital structure alternative.

For instance, we may want to have such a valuation of the firm’s assets, which is independent of the future capital

structure decisions of the firm’s owners.

We may calculate the unlevered beta of the firm:

βU =E

AβE .

βUUnlevered beta 0.80 0.80 0.80

The unlevered beta equals to the asset beta of the firm.



Unlevered value of assets



AUUnlevered value of assets ? ? 23438




By the unlevered beta we are able to calculate the required rate of return on unlevered assets:

kU = r + (µm − r)βU = 0.032 + 0.040× 0.80 = 6.40%.

kURequired rate of return on assets 6.40% 6.40% 6.40%

The value of the unlevered assets is the present value of the expected unlevered free cash flow from assets:

AU =UFCFA

kU=

1500

0.064.

AUUnlevered value of assets 23438 23438 23438



Example of firm valuation

Let us consider a firm for which we expect a constant level of 4000 of earnings before interest and taxes forever.


With the current capital structure the firm is expected to pay a constant interest payment of 400 forever.

IInterest paid 400

With the corporate tax rate of τ = 25% and tax-deductible interest expenses, the firm pays the corporate tax of

T = τ × (EBIT − I ) = 0.25× (4000− 400) = 900.


We suppose the depreciation of the fixed assets and the capital expenditures to offset each other, and the level of

the net working capital to remain constant. Such being the case, the cash flow from assets appears as

CFA = EBIT − T = 4000− 900 = 3100.




Example of firm valuation


IInterest paid 400



We do not know the asset beta of the firm, and thus we are not able to calculate the value of the firm’s assets.

βAAsset beta ?

kARequired rate of return on assets ?

AValue of assets ?

We have got at least a crude estimate of the value of debt of the firm, the book value of debt, if nothing else.

DValue of debt 12500

As we do not know the value of assets, we are not able to calculate the value of equity.

EValue of equity ?

Neither we know the equity beta of the firm.

βEEquity beta ?



Benchmark firms


IInterest paid 400



βAAsset beta ?


AValue of assets ?


EValue of equity ?

βEEquity beta ?

Suppose that there are three listed firms which can be considered to be comparable with our target firm with respect

to the riskiness of their cash flows from assets.

Target firm

Benchmark firms

27000 4800 12250

73650 3720 16340

0.82 1.42 1.12

The three benchmark firms belong to the same industry as the target firm, they have a pretty similar business ideas,

they operate with quite identical levels of operating leverage, i.e. they have comparable costs structures etc..

The benchmark firms have different capital structures and thus their equity betas differ from each other, although the

underlying asset betas are supposedly quite near to each other.



Benchmarking the beta

Target firm

Benchmark firms


IInterest paid 400



βAAsset beta ?


AValue of assets ?


EValue of equity ?

βEEquity beta ?

27000 4800 12250

73650 3720 16340

0.82 1.42 1.12

We are able to estimate the unlevered betas of the benchmark firms:

βU =E

AβE =

E

D + EβE .


The average of the estimated betas may be used as a proxy of the unlevered beta of the target firm.

︸︷︷︸β̄U = 0.62

�0.62



Unlevered cost of capital

Target firm

Benchmark firms


IInterest paid 400



βAAsset beta ?


AValue of assets ?


EValue of equity ?

βEEquity beta ?

27000 4800 12250

73650 3720 16340

0.82 1.42 1.12

βUUnlevered beta 0.60 0.62 0.64︸︷︷︸β̄U = 0.62

�0.62

Now we are able to calculate the required rate of return on assets of the target firm:

kU = r + (µm − r)βU = 0.032 + 0.040× 0.62 = 5.68%.

kURequired rate of return on assets 5.68%




Target firm

Benchmark firms


IInterest paid 400



βAAsset beta ?


AValue of assets ?


EValue of equity ?

βEEquity beta ?

27000 4800 12250

73650 3720 16340

0.82 1.42 1.12


�0.62


The valuation of the firm’s assets requires us to calculate the unlevered free cash flow from assets:

UFCFA = (1− τ)× EBIT = (1− 0.25)× 4000 = 3000.

UFCFAUnlevered free cash flow from assets 3000



Unlevered value of assets

Target firm

Benchmark firms


IInterest paid 400



βAAsset beta ?


AValue of assets ?


EValue of equity ?

βEEquity beta ?

27000 4800 12250

73650 3720 16340

0.82 1.42 1.12


�0.62



Under our assumption of a steady state the unlevered value of the firm’s assets is

AU =UFCFA

kU=

3000

0.0568= 52817.

AUUnlevered value of assets 52817



Value of equity

Target firm

Benchmark firms


IInterest paid 400



βAAsset beta ?


AValue of assets ?


EValue of equity ?

βEEquity beta ?

27000 4800 12250

73650 3720 16340

0.82 1.42 1.12


�0.62



AUUnlevered value of assets 52817

The value of equity of the firm can be considered to be

E = AU − D = 52817− 12500 = 40317.




Current assets

Cash

Accounts receivable

Inventory

Fixed assets

Equipment

Current liabilities

Accounts payable

Long-term liabilities

Long-term debt

Owners’ equity

Common stock

Retained earnings

120

185

250

690

210

310

300

425

140

200

260

720

220

225

310

565

Net sales 1500

Cost of goods sold 935

Depreciation 40

EBIT 525

Interest paid 25

Taxes 125

Net income 375

We start the calculation of the cash flow from assets from the earnings before interest and taxes (EBIT).

EBIT 525

Depreciation is returned back to EBIT due to its accrual basis.

Depreciation 40+

We subtract the change in the net working capital: (140 + 200 + 260− 220)− (120 + 185 + 250− 210) = 35.

Change in net working capital 35−

We subtract the capital expenditures: (720 + 40)− 690 = 70.

Capital expenditures 70−

We subtract the taxes paid.

Taxes 125−

Cash flow from assets 335



Cash flow to debtors and owners

Current assets

Cash

Accounts receivable

Inventory

Fixed assets

Equipment

Current liabilities

Accounts payable


Long-term debt

Owners’ equity

Common stock

Retained earnings

120

185

250

690

210

310

300

425

140

200

260

720

220

225

310

565

Net sales 1500


Depreciation 40

EBIT 525

Interest paid 25

Taxes 125

Net income 375

EBIT 525

Depreciation 40+

Change in net working capital 35−Capital expenditures 70−Taxes 125−


We subtract the change in the long-term debt: 310− 225 = 85.

Change in long-term debt 85−

We subtract the interest paid.

Interest paid 25−

We add the change in the common stock: 310− 300 = 10.

Common stock issued 10+

We subtract the dividends paid: 375− (565− 425) = 235.

Dividends paid 235−

0




Current assets

Cash

Accounts receivable

Inventory

Fixed assets

Equipment

Current liabilities

Accounts payable


Long-term debt

Owners’ equity

Common stock

Retained earnings

120

185

250

690

210

310

300

425

140

200

260

720

220

225

310

565

Net sales 1500


Depreciation 40

EBIT 525

Interest paid 25

Taxes 125

Net income 375

EBIT 525

Depreciation 40+



Change in long-term debt 85−Interest paid 25−Common stock issued 10+


0

The cash flow from assets is 335 euros.

The cash flow to debtors is 85 + 25 = 110 euros.

The cash flow to owners is 235− 10 = 225 euros.




Current assets

Cash

Accounts receivable

Inventory

Fixed assets

Equipment

Current liabilities

Accounts payable


Long-term debt

Owners’ equity

Common stock

Retained earnings

120

185

250

690

210

310

300

425

140

200

260

720

220

225

310

565

Net sales 1500


Depreciation 40

EBIT 525

Interest paid 25

Taxes 125

Net income 375

EBIT 525

Depreciation 40+





In the unlevered free cash flow the corporate tax-rate is applied to the

earnings before interest and taxes, and any interest expenses are ignored.

Here we assume the corporate tax-rate of τ = 25%.

(1 - τ)× EBIT 394

All other adjustments are as before.

Depreciation 40+

Change in net working capital 35−Capital expenditures 70−

Unlevered free cash flow 329



Cash flow from sales

Current assets

Cash

Accounts receivable

Inventory

Fixed assets

Equipment

Current liabilities

Accounts payable


Long-term debt

Owners’ equity

Common stock

Retained earnings

120

185

250

690

210

310

300

425

140

200

260

720

220

225

310

565

Net sales 1500


Depreciation 40

EBIT 525

Interest paid 25

Taxes 125

Net income 375

We start the calculation of the cash flow from assets from the earnings before interest and taxes (EBIT).

EBIT 525

Depreciation is returned back to EBIT due to its accrual basis.

Depreciation 40+

The resulting 525 + 40 = 565 equals to the difference 1500− 935 = 565 of the net sales and the cost of goods sold.



Adjustment of cash account

Current assets

Cash

Accounts receivable

Inventory

Fixed assets

Equipment

Current liabilities

Accounts payable


Long-term debt

Owners’ equity

Common stock

Retained earnings

120

185

250

690

210

310

300

425

140

200

260

720

220

225

310

565

Net sales 1500


Depreciation 40

EBIT 525

Interest paid 25

Taxes 125

Net income 375

EBIT 525

Depreciation 40+

In the course of the fiscal period an amount of 140− 120 = 20 euros of

the incoming cash flow is used to increase the level of the cash account.

-

�

Cash (t − 1) 120+

Cash (t) 140+

It is not available for the debtors and the owners of the firm, in terms of

the cash flow from assets, and will be removed from the cash flow a few

steps later.



Adjustement of receivables

Cash (t − 1) 120+

Cash (t) 140+

Current assets

Cash

Accounts receivable

Inventory

Fixed assets

Equipment

Current liabilities

Accounts payable


Long-term debt

Owners’ equity

Common stock

Retained earnings

120

185

250

690

210

310

300

425

140

200

260

720

220

225

310

565

Net sales 1500


Depreciation 40

EBIT 525

Interest paid 25

Taxes 125

Net income 375

EBIT 525

Depreciation 40+

An amount of 200 euros of the fiscal period’s net sales has not yet been

received, whereas 185 euros from the previous period is now collected.

-

�

Accounts receivable (t − 1) 185+

Accounts receivable (t) 200+

In other words, an amount of 200− 185 = 15 euros of sales has not been

realized in terms of cash, and will be removed from the cash flow a few

steps later.



Adjustement of inventory

Cash (t − 1) 120+


Cash (t) 140+


Current assets

Cash

Accounts receivable

Inventory

Fixed assets

Equipment

Current liabilities

Accounts payable


Long-term debt

Owners’ equity

Common stock

Retained earnings

120

185

250

690

210

310

300

425

140

200

260

720

220

225

310

565

Net sales 1500


Depreciation 40

EBIT 525

Interest paid 25

Taxes 125

Net income 375

EBIT 525

Depreciation 40+

An amount of 260− 250 = 10 euros of the incoming cash flow is used to

increase the level of inventory.

-

�

Inventory (t − 1) 250+

Inventory (t) 260+

It is not available for the debtors and the owners of the firm, in terms of

the cash flow from assets, and will be removed from the cash flow a few

steps later.



Adjustment of payables

Cash (t − 1) 120+



Cash (t) 140+


Inventory (t) 260+

Current assets

Cash

Accounts receivable

Inventory

Fixed assets

Equipment

Current liabilities

Accounts payable


Long-term debt

Owners’ equity

Common stock

Retained earnings

120

185

250

690

210

310

300

425

140

200

260

720

220

225

310

565

Net sales 1500


Depreciation 40

EBIT 525

Interest paid 25

Taxes 125

Net income 375

EBIT 525

Depreciation 40+

An amount of 220 euros of the fiscal period’s cost of goods sold has not

yet been paid, whereas 210 euros from the previous period is now paid.

-

�

Accounts payable (t − 1) 210−

Accounts payable (t) 220−In other words, an amount of 220− 210 = 10 euros less is paid in cash,

than what appears in the cost of goods sold, and will be returned to the

cash flow in the next step.



Net working capital

Current assets

Cash

Accounts receivable

Inventory

Fixed assets

Equipment

Current liabilities

Accounts payable


Long-term debt

Owners’ equity

Common stock

Retained earnings

120

185

250

690

210

310

300

425

140

200

260

720

220

225

310

565

Net sales 1500


Depreciation 40

EBIT 525

Interest paid 25

Taxes 125

Net income 375

EBIT 525

Depreciation 40+

The net effect of the above adjustments can be expressed in terms of the

change in the net working capital.

�

Cash (t − 1) 120+



Accounts payable (t − 1) 210−

Net working capital (t − 1) 345

Cash (t) 140+


Inventory (t) 260+

Accounts payable (t) 220−

Net working capital (t) 380

An amount of 380− 345 = 35 euros of the 535 + 40 = 565 euros of the

cash flow statement is either not available in terms of the cash flow from

assets, or it is not yet received/paid in cash.




Adjustment of depreciation

Current assets

Cash

Accounts receivable

Inventory

Fixed assets

Equipment

Current liabilities

Accounts payable


Long-term debt

Owners’ equity

Common stock

Retained earnings

120

185

250

690

210

310

300

425

140

200

260

720

220

225

310

565

Net sales 1500


Depreciation 40

EBIT 525

Interest paid 25

Taxes 125

Net income 375

EBIT 525

Depreciation 40+


A part of the cash flow is used to capital investments.

The amount of fixed assets is increased by 720− 690 = 30 euros.

-

�Fixed assets (t) 720+

Fixed assets (t − 1) 690−However, the value of the fixed assets has been decreased by a non-cash

depreciation of 40 euros which has to be returned back to it.

�

Depreciation 40+



Capital expenditures

Current assets

Cash

Accounts receivable

Inventory

Fixed assets

Equipment

Current liabilities

Accounts payable


Long-term debt

Owners’ equity

Common stock

Retained earnings

120

185

250

690

210

310

300

425

140

200

260

720

220

225

310

565

Net sales 1500


Depreciation 40

EBIT 525

Interest paid 25

Taxes 125

Net income 375

EBIT 525

Depreciation 40+


Fixed assets (t) 720+

Depreciation 40+

Fixed assets (t − 1) 690−

Capital expenditures 70

Capital expenditures represents the cash-spending to the investments

in fixed assets, and is subtracted from the cash flow available to the

debtors and the owners of the firm.



Taxes

Current assets

Cash

Accounts receivable

Inventory

Fixed assets

Equipment

Current liabilities

Accounts payable


Long-term debt

Owners’ equity

Common stock

Retained earnings

120

185

250

690

210

310

300

425

140

200

260

720

220

225

310

565

Net sales 1500


Depreciation 40

EBIT 525

Interest paid 25

Taxes 125

Net income 375

EBIT 525

Depreciation 40+


Taxes of 125 euros is subtracted from the cash flow as such.

�Taxes 125−

Were a part of the taxes (or any other expenses, excluding interest expenses) still unpaid in the payables, or had taxes

(or any other expenses, excluding interest expenses) from earlier fiscal period(s) been paid during the fiscal period, had

they been adjusted in connection with the net working capital.




Current assets

Cash

Accounts receivable

Inventory

Fixed assets

Equipment

Current liabilities

Accounts payable


Long-term debt

Owners’ equity

Common stock

Retained earnings

120

185

250

690

210

310

300

425

140

200

260

720

220

225

310

565

Net sales 1500


Depreciation 40

EBIT 525

Interest paid 25

Taxes 125

Net income 375

EBIT 525

Depreciation 40+



Now we are at a point where all the remaining items in the income statement and the balance sheets are about the

claims of debtors of owners, and the cash flow statement provides the cash flow from assets.



Cash flow to debtors

Current assets

Cash

Accounts receivable

Inventory

Fixed assets

Equipment

Current liabilities

Accounts payable


Long-term debt

Owners’ equity

Common stock

Retained earnings

120

185

250

690

210

310

300

425

140

200

260

720

220

225

310

565

Net sales 1500


Depreciation 40

EBIT 525

Interest paid 25

Taxes 125

Net income 375

EBIT 525

Depreciation 40+



The net change in the amount of long-term debt is 225− 310 = −85

euros, and it is indeed a cash flow to debtors.

Change in long-term debt 85−

-

�

It is the net value of the new borrowing and the repayment of old debt.

Interest paid of 25 euros is the remaining part of the cash flow to debtors.

Interest paid 25−

�

�



Cash flow to owners

Current assets

Cash

Accounts receivable

Inventory

Fixed assets

Equipment

Current liabilities

Accounts payable


Long-term debt

Owners’ equity

Common stock

Retained earnings

120

185

250

690

210

310

300

425

140

200

260

720

220

225

310

565

Net sales 1500


Depreciation 40

EBIT 525

Interest paid 25

Taxes 125

Net income 375

EBIT 525

Depreciation 40+



Change in long-term debt 85−Interest paid 25−

The change in the value of the common stock is 310− 300 = 10 euros,

and it is a cash flow from owners due to issued new shares of stock.

-

�Common stock issued 10+

The change in the value of the retained earnings is 565− 425 = 140.

-

As the net income is 375, the dividends paid is 375− 140 = 235.

�

�Dividends paid 235−




Current assets

Cash

Accounts receivable

Inventory

Fixed assets

Equipment

Current liabilities

Accounts payable


Long-term debt

Owners’ equity

Common stock

Retained earnings

120

185

250

690

210

310

300

425

140

200

260

720

220

225

310

565

Net sales 1500


Depreciation 40

EBIT 525

Interest paid 25

Taxes 125

Net income 375

EBIT 525

Depreciation 40+





0

The cash flow from assets is 335 euros.

The cash flow to debtors is 85 + 25 = 110 euros.

The cash flow to owners is 235− 10 = 225 euros.


fundamentals of finance - university of oulucc.oulu.fi/~jope/fof/c12/printable/corporate cash...

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