financial analysis, planning and forecasting theory and application

Financial Analysis, Planning and Forecasting

Theory and Application

ByAlice C. Lee

San Francisco State UniversityJohn C. Lee

J.P. Morgan ChaseCheng F. Lee

Rutgers University

Chapter 17

Interaction of Financing, Investment,and Dividend Policies

1

Outline 17.1 Introduction 17.2 Investment and dividend interactions: the interval-vs.- external financing decision 17.3 Interactions between dividend and financing policies 17.4 Interactions between financing and investment decisions 17.5 Implications of financing and investment interactions for

capital budgeting 17.6 Debt capacity and optimal capital structure 17.7 The implication of different policies on the beta coefficient

determination 17.8 Summary and conclusion Appendix 17A. Stochastic dominance and its applications to

capital-structure analysis with default risk

2

17.2 Investment and dividend interactions: the interval-vs.-external financing decision Internal financing

3

Changes in equity accounts between balance-sheet dates are generally reported in the statement of retained earnings. Retained earnings are most often the major internal source of funds made available for investment by a firm.

TABLE 17.1 Payout ratio—Composite for 500 firms196219631964196519661967196819691970197119721973

0.5800.5670.5490.5240.5170.5480.5330.5470.6120.5390.4910.414

197419751976197719781979198019811982198319841985

0.4050.4620.4090.4290.4110.3800.4160.4350.4220.3990.6260.525

198619871988198919901991199219931994199519961997

0.3430.5590.8870.5380.4390.4180.1370.8520.3400.3460.3270.774

199819992000200120022003200420052006

0.2340.4350.2990.3830.0400.2590.3110.2820.301

17.2 Investment and dividend interactions: the interval-vs.-external financing decision

(17.1)

where p = Profit margin on sales, d = Dividend payout ratio,

L = Debt-to-equity ratio, t = Total asset-to-sales ratio.

rr = Retention Rate, ROE = Return on Equity

( )( )

1 ( )( )

p(1 - d)(1 + L) rr ROES* =

t - p(1 - d)(1 + L) rr ROE

10.5% = 0.88) + 0.33)(1 - (0.055)(1 - 0.73

0.88) + 0.33)(1 - (0.055)(1 =* S

Let c = Nominal current assets to nominal sales, f = Nominal fixed assets to real sales, j = Inflation rate.So real sustainable growth is

*rS

(17.2)*r

(1 + j)p(1 - d)(1 + L) - jc = .S

(1 + j)c + f - (1 + j)p(1 - d)(1 + L)4

17.2.2 External financing: External financing usually takes one of two forms, debt financing or equity financing.

17.3 Interactions between dividend and financing policies

Cost of equity capital and dividend policy Default risk and dividend policy

0 1 2 3/ ,P E a a g a p a Lev u (17.3)where g = Compound growth of assets over eight previous years; p = Dividend payout ratio on an annual basis; Lev = Interest charges/[operating revenues – operating expenses]; u = Error term.

(17.4)

where g = Compound growth rate, Lev = Financial risk measured by times interest earned, and F1, F2, F3, F4 = Dummy variables representing levels of new equity financing.

).()()(

)()()(/

473625

143210

FaFaFa

FaLevapagaaEP

5

17.3 Interactions between dividend and financing policiesTABLE 17.2 New-issue ratios of electric utility firms

From Van Horne, J. C., and J. D. McDonald, “Dividend policy and new equity financing,” Journal of Finance 26 (1971):507-519. Reprinted by permission.

F dummy variable grouping

A B C D E

New-issue ratio intervalNumber of firms in intervalMean dividend payout ratioDummy variable coefficientDummy variable t-statistic

0490.6811.86(1.33)

0.001-0.05160.6793.23(2.25)

0.05-0.1110.6781.26(0.84)

0.1-0.1560.7030.89(0.51)

0.15 and up40.728N.A.(N.A.)

(17.5) and (17.6)

Where S = Total value of the firm’s stock, V = Total firm value, C = Constant coupon payment on the perpetual bonds, r = Riskless rate of interest, L = A complicated risk factor associated with possible default on the required coupon payment.

L), - (1 r

C - V = S *C(1 - T)

S = V - (1 - )Lr

6

17.4 Interactions between financing and investment decisions Risk-free debt case

Maximize dV (xj, yt, Dt, Et) = W,

a) Uj = xj - 1 0 (j = 1, 2, ..., J); b) = yt - Zt 0 (t = 1, 2, ..., T); c) = -Ct - [yt - yt-1 (1 + (1 - τ)r)] + Dt - Et 0 (17.7)

FtU

CtU

Max W’ = W - Lj(xj - 1) - Lft(yt - Zt) - Lct {-Ct - [yt - yt-1(1 + (1 - τ) r)]} + Dt - Et). (17.7′)

(17.8) T

j ft jt ct jjtt=0

+ [ + ] - 0CA L Z L L

7

Ft - Lft + Lct - Lc,t-1 [1 + (1 - τ) r] 0. (17.9)

(17.10) and (17.11)

(17.12)

0; L - dD

dWct

t

0. L + dE

dWct

t

F Z + A = APV tjt

T

=0tjj

17.4 Interactions between financing and investment decisions

8

Risky debt caseRendleman (1978) not only examined the risk premiums associated

with risky debt, but also considered the impact that debt financing could have on equity values, with taxes and without. The argument is to some extent based on the validity (or lack thereof) of the perfect-market assumption often invoked, which, interestingly enough, turns out to be a double-edged sword.

Without taxes, the original M&M article claims, the investment decision of a firm should be made independent of the financing decision. But the financing base of the firm supports all the firm’s investment projects, not some specific project. From this we infer that the future investments of a firm and the risk premiums embodied in the financing costs must be considered when the firm takes on new projects.

17.5 Implications of financing and investment interactions for capital budgeting

Equity-residual method After-tax weighted-average, cost-of-capital

method Arditti and Levy method Myers adjusted-present-value method

9


Table 17.3 Definitions of variables Rt = Pretax operating cash revenues of the project during period t; Ct = Pretax operating cash expenses of the project during period t;dept = Additional depreciation expense attributable to the project in period t; τc = Applicable corporate tax rate; I = Initial net cash investment outlay; Dt = Project debt outstanding during period t; NP = Net proceeds of issuing project debt at time zero; rt = Interest rate of debt in period t; ke = Cost of the equity financing of the project; kw = After-tax weighted-average cost of capital (i.e., debt cost is after-tax); kAL = Weighted average cost of capital -- debt cost considered before taxes; ρ = Required rate-of-return applicable to unlevered cash-flow series, given the risk class of the project.r, ke, and ρ are all assumed to be constant over time. 10

1N

t t t t tt ctt

t=1 e

[( - - - )(1 - ) + ] - ( - )depCR rD D D DNPV(ER) = - [I - NP].(1 + )k

(17.13)

17.5.1 Equity-Residual Method


17.5.2 After-tax weighted-average, cost-of-capital method

(17.14)

17.5.3 Arditti and Levy method

(17.15)

17.5.4 Myers adjusted-present-value method

(17.16)

Nt t ct t

twt=1

( - - )(1 - ) + dep depCRNPV = I.

(1 + )k

Nt t tt ct t

tt=1 AL

[( - - - )(1 - ) + ] + dep depCR rD rDNPV(AL) = I(1 + )k

.)r + (1

rD + I - ) + (1

dep + ) - )(1dep - C - R( = APV t

tcN

=1tt

tctttN

=1t

11


Table 17.4 Application of four capital budgeting techniques

From Chambers, D. R., R. S. Harris, and J. J. Pringle, “Treatment of financing mix in analyzing investment opportunities,” Financial Management 11 (Summer 1982): 24-41. Reprinted by permission.

Inputs: 1. = 0.112 2. r = 0.041 3. = 0.46 4. = 0.0802 5. w = .6

Method NPV results Discount rates

1. Equity-residual2. After-tax WACC3. Arditti-Levy WACC4. Myers APV

$230.55 270.32 261.67 228.05

= .112 = .058 = .069r = .041 and = .0802

ek c

ek

wk

ALk

12

17.5 Implications of financing and investment interactions for capital budgetingTable 17.5 Inputs for simulation

From Chambers, D. R. , R. S. Harris, and J. J. Pringle, “Treatment of financing mix in analyzing

investment opportunities,” Financial Management 11 (Summer 1982): 24-41. Reprinted by permission.

Project Net cash inflows per year Project life

1234

$300 per year$253.77 per year$124.95 per year$200 per year, years 1-4$792.58 in year 5

5 years5 years20 years5 years

For each project the initial outlay is $1000 at time t = 0, with all subsequent outlays being captured in the yearly flows.

Debt Schedule1.Market value of debt outstanding remains a constant proportion of the project ’s market value.2.Equal principal repayments in each year.3.Level debt, total principal repaid at termination of project.

Inputs: = 0.112 = 0.085 = 0.085W = 0.3

r = 0.041 = 0.0986 = 0.46

ekwkM

c( & )M M

13


Table 17.6 Simulation results

From Chambers, D. R. , R. S. Harris, and J. J. Pringle, “Treatment of financing mix in analyzing investment opportunities,” Financial Management 11 (Summer 1982): 24-41. Reprinted by permission.

Net-present-value under alternative debit schedule

Project Capital budgeting Constant debt ratio Equal Principal Level debt

1

2

3

4

After-tax WACCArditti-Levy WACCEquity-ResidualMyers APV (M&M)Myers APV (M)

After-tax WACCArditti-Levy WACCEquity-ResidualMyers APV (M&M)Myers APV (M)

After-tax WACCArditti-Levy WACCEquity ResidualMyers APV (M&M)Myers APV (M)

After-tax WACCArditti-Levy WACCEquity ResidualMyers APV (M&M)Myers APV (M)

1821821821601820 00

-180

182182182138182182182182155182

182179167157182

0-1-3

-190

182169128119182182174147146182

1821872021661820732-100

182186194150182182182183156182

14

17.5 Implications of financing and investment interactions for capital budgetinga) Operating flows = (Rt - Ct - dept)(1 - τc) + dept = ($4000 - $1000 - $500)(1 - 0.46) + $500 = $1850.b) Financial flows = τc rDt

= (0.46)(0.09)($3600) = $149.04c) kw = wr(1 - τc) + (1 - w)ke

= (0.6)(0.09)(1 - 0.46) + (1 - 0.6)(0.15) = (0.029) + (0.06) = 0.089.d) (1 )

0.089

(1 (0.46)(0.6))

0.1229

w

c

k

w

15

17.6 Debt capacity and optimal capital structureTable 17.7 Acceptance-rejection criteria

*In the special instance where both relationships are strict equalities the firm is, of course, indifferent in attitude toward the project.

Accept Reject Indeterminate

and and and

Or

and

*r QR R p QS S p QR R

p QS S p QR Rp QS S

p QR R p QS S

Re = WRp - Rd(W - 1), Re = Rd + W(Rp - Rd)

(17.17) and (17.17a)

Se = WSp. (17.18)

(17.19) and (17.20)

(17.18a)

,ee d p d

p

S = + ( - )R R R RS

.S

R - R =

dS

dR

p

dp

e

e

.SW = S pe 16

17.6 Debt capacity and optimal capital structure

(17.21) and (17.22)

(17.22a)

,e d p d = + W ( - )R R R R ,R )W

1 - (1 + R

W

1 = k dpp

).R - R( W

1 + R = k dpdp

(17.22a′)

where = Cost of financing a project, ρpe = Correlation between Rp and Re, Sp = Estimated standard deviation of Rp, Se = Estimated standard deviation of Re.

' pped e dP

e

Sk = + ( - ),r R R

S

'Pk

,0 t-10

S = ( )

S ),z - C P(C = 0) P(C c

(17.23) and (17.24)

17


(17.25) and (17.26)

(17.27) and (17.28)

(17.29)

.k

) - NOI(1 = V

a

L

,V

) - kD(k + k = k L

issa

a s i

L

( - )dk k dk = dD dDV

D,k - r

rD +

k

) - NOI(1 = V i

s

L

,S

) - D(1 +

S

S =

0

D

00

ks = 0.09 + (0.16 - 0.09)(1.5) = 0.195.

.$84,285.23 =

))(8,000 + )000)(8,0002(0.5)(80, + )((80,000 = 1/222c

1.25. = $80,000

$100,000 =

0 - C =z

c1.40. =

$84,285

$118,000 = z

18


Table 17.8Valuation information for Project X A. Project Cash-Flow Information 1. NOI = $18,000 2. Project maturity = infinity 3. Marginal tax rate for ABC = 45% 4. Initial cash outlay = $800,000 B. Required Return Information 1. Rf = 0.09 2. Rm = 0.16 3. β0 = 1.5 C. Debt-Capacity Information 1. Standard deviation in project cash flows = $8,000 2. Correlation between firm and project cash flows = 0.5 3. Cost of new debt, r = 0.10

19


Fig. 17.1 (a) Distribution of unencumbered cash flows for ABC Company.

Fig. 17.1 (b) Distribution of unencumbered cash flows after project is undertaken.

20


D = DSC/kd = ($12,643.75) (0.10) = $126,438.

(17.25′)

c

( C - C ) (118,000 - C )z = = = 1.25.

84,285

s

(1 - ) rDV = NOI + .

rk

($18,000)(1- 0.45) (126,438)(0.10)(0.45)

0.195 0.10 $50,769 $56,897 $107,666.

V

21

17.7 The implication of different policies on the beta coefficient determination

Impact of Financing Policy on Beta Coefficient Determination

Impact of Production Policy on Beta Coefficient Determination

Impact of Dividend Policy on Beta Coefficient Determination

(1 )(1 ) (17.25')c

L U

B

S

0.320.23.

[1 (0.64)(1 0.4)]U

(17.31)a bQ K L22


Where r = the risk-free rate, = return on the market portfolio, = random price disturbances with zero mean, ,

an elasticity constant b = contribution of labor to total output, = the market price of systematic risk,

(1 ) ( , )

(17.32)( ) [1 (1 ) ]

m

m

r Cov e R

Var R E b

mRe

( / )( / )E P Q Q P 1 cov( , )mv R

(1 )[ ( 1) ] (17.33)s sQ K L K 30,0 1,0 1, / (1 ) / (1 ) .s s L K s 23


(17.34)Where p = expected price of output, µ = reciprocal of the price

elasticity of demand, w = expected wage rate, = random shock in the wage rate with zero mean;

are as defined in Equation (17.30)

1 1

1

(1 ) ( , ) [ (1 ) ( ) (1 ) ] ( , )

( ) [ (1 ) ( ) (1 )

m m

m

r Cov e R E s w pQ K Cov v R

Var R E s w pQ K

v1 cov( , )me R

, , , , ,mr R e E

= the firm’s systematic risk when the market is informationally imperfect and the information asymmetry can be resolved by dividends; = the firm’s systematic risk when market is informaitonally perfect. = a signaling cost incurred if firm’s net after-tax operating cash flow X falls below the promised dividend D. = firm’s dividend payout ratio. = cumulative normal density function in term of payout ratio.

[1 ( )] (17.35)i pi iF d

i

pi

id ( )iF d24

17.8 Summary and conclusion In this chapter we have attacked many of the irrelevance propositions of the

neoclassical school of finance theory, and in so doing have created a good news-bad news sort of situation. The good news is that by claiming that financial policies are important, we have justified the existence of academicians and a great many practicing financial managers. The bad news is that we have made their lot a great deal more difficult as numerous tradeoffs were investigated, the more general of these comprising the title of the chapter.

In the determination of dividend policy, we examined the relevance of the internal-external equity decision in the presence of nontrivial transaction costs. While the empirical evidence was found to be inconclusive because of the many variables that could not be controlled, there should be no doubt in anyone’s mind that flotation costs (incurred when issuing new equity to replace retained earnings paid out) by themselves have a negative impact on firm value. But if the retained earnings paid out are replaced whole or in part by debt, the equity holders may stand to benefit because the risk is transferred to the existing bondholders -- risk they do not receive commensurate return for taking. Thus if the firm pursues a more generous dividend-payout policy while not changing the investment policy, the change in the value of the firm depends on the way in which the future investment is financed.

25

17.8 Summary and conclusion The effect that debt financing has on the value of the firm was analyzed

in terms of the interest tax shield it provides and the extent to which the firm can utilize that tax shield. In Myers’ analysis we also saw a that a limit on borrowing could be incorporated so that factors such as risk and the probability of insolvency would be recognized when making each capital-budgeting decision. When compared to other methods widely used in capital budgeting, Myers’ APV formulation was found to yield more conservative benefit estimates. While we do not wish to discard the equity-residual, after-tax weighted cost-of-capital method or the Arditti-Levy weighted cost-of-capital method, we set forth Myers’ method as the most appropriate starting point when a firm is first considering a project, reasoning that if the project was acceptable following Myers’ method, it would be acceptable using the other methods -- to an even greater degree. If the project was not acceptable following the APV criteria, it could be reanalyzed with one of the other methods. The biases of each method we hopefully made clear with the introduction of debt financing.

26

17.8 Summary and conclusion Section 17.6 outlined practical procedures for attaining optimal capital structures

subject to probability-of-insolvency constraints or costs incurred attributable to the risky debt financing. If management is able to specify the tolerance for risk, or the rate at which monitoring costs are incurred, then an upper limit on debt capacity can be stated as the amount of interest expense the firm can afford. In the case of regulated firms, we also consider capital-structure decisions, in light of the inability of the equity holders to acquire the benefits of the interest tax shield; and we concluded that regulated firms, in the best interests of their shareholders and of society, should issue debt only to the extent it does not jeopardize the equity stake or the existence of the firm. In section 17.7, we have discussed how different policies can affect the determination of beta coefficient.

In essence, this chapter points out the vagaries and difficulties of financial management in practice. Virtually no decision concerning the finance function can be made independent of the other variables under management’s control. Profitable areas of future research in this area are abundant; some have already begun to appear in the literature under the heading “simultaneous-equation planning models.” Any practitioner would be well advised to stay abreast of developments in this area.

27

Appendix 17A. Stochastic dominance and its applications to capital-structure analysis with default risk

17.A.1 INTRODUCTION

17.A.2 CONCEPTS AND THEOREMS OF

STOCHASTIC DOMINANCE

17.A.3 STOCHASTIC-DOMINANCE APPROACH TO

INVESTIGATING THE CAPITAL-

STRUCTURE PROBLEM WITH DEFAULT

RISK

17.A.4 SUMMARY

28


(17.A.1)

(17.A.2a)and(17.A.2b)

where G(t) ≠ F(t) for some t. (17.A.3)

( ) ( )F GE U X E U X

( ) ( ) ( ) ,x

F

x

E U X U X f X dx

( ) ( ) ( )x

F

x

E U X U X g X dx

[ ( ) ( )] 0x

x

G T F t dt

29


(17.A.4)

(17.A.5)

(17.A.6)

(17.A.7)

(17.A.8)

(17.A.9)

10,

(1 )Y X T if 0,if 0,

XX

1(0) ( ) ( /(1 )

FG Y F Y T if 0,if 0.

YY

2

2

0 (1 ) (1 ) ( (1 )

Y k X TX T TrD

2 2

2 2

if 0, if 0 (1 ) ,if (1 ) ,

XX T D rD

x T D rD

2

2

(0) ( ) [ / (1 )(1 )]

[ / (1 ) ]

FG Y F Y k T

F Y T TrD

2 2

2 2

if 0, if 0 (1 )[ ],if [ ].

Yy k D rD

Y D rD

1 2( ) ( )G Y G Y 2 2if 0 ( ),Y D rD 2 2( ) ( )G Y G Y 2 2if ( ),Y D rD

30


17.A.4 SUMMARY In this appendix we have tried to show the basic

concepts underlying stochastic dominance and its application to capital-structure analysis with default risk. By combining utility maximization theory with cumulative-density functions, we are able to set up a decision rule without explicitly relying on individual statistical moments. This stochastic-dominance theory can then be applied to problems such as capital-structure analysis with risky debt, as was shown earlier.

31

financial analysis, planning and forecasting theory and application

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