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第二章 財務管理基本理論

參考資料： Lee ect. Chap2 -Theory of Financial Management

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企業的經理人員負責計畫（ planning ）、執行（ implementing ）、控制（考核， controlling ）三種經濟行為—生產（ production ）、運銷（ marketing ）與財務（ financing ）管理（＋人事， personnel ）

財務經理的職責—負責目標的設定、發現及分析問題、做決策、執行並負責企業的財政庶務，其範圍包含生產與運銷事務

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企業管理目標（ Management Goal ）—最大利潤（ Profit maximization ）

timing risk & uncertainly

（時效性？ 風險與不確定性？ ） — Profit Max. 之二大缺失

↓ ↓ ↓

第三、四章 知道機率 不知機率

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企業風險（ Business Risk ）：與企業特性有關的獲利變動

農企業風險—氣候、病蟲害、價格變動 AgriBusiness Risk - (i) technical risk : weather, disease

-(ii) market risk : price

probility

expected returnmean

F

G

G has higher expected return & risk

G or F is preferred?

0

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財務風險（ Financial Risk ）：非自有資本的運用所帶來的風險。

— 要籌資多少 自己的、借的？ leverage =

(nonequity capital — borrowing , leasing , other arrangement or contracts) (interests) (rent) (obligations)

leverage↑ → risk↑ If rate or return ＞ cost of using nonequity capital, leverage↑ → profit↑, but at the same time ， risk↑

capitalequity

capitalnonequity

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Key elements of financial goal: profitability, risk & liquidity (timing) 目標－風險與報酬（ risk & return ） 兼顧－ utility maximization

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Measurement of Business Risk :

Variance

Risk--Return Trade-off 1. coefficient of variation CV = V/E 愈小愈好 2. highest lower bound L = E-2V 愈高愈好

mean (E)

iii

n

ii

YPYEn

EE 1

(expected return)

iVSVYiYiPV 2

22

11

2

2

n

n

iEiE

V

Standard deviation (S or V)

1

2

2

n

EEVVS i

(risk)

8

9

10

the risk-return basis for choice:

I1

more “conservative” decision maker (I)—prefers A less risk averser (I’)—prefers B

required rate of returnrisk averse

risk neutral

risk

risk preferring

I2

I3 I’1

I’2

I’3

B

A

‧‧

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Risk-reducing Strategy ( 風險分散策略）：Diversification : Holding combinations of investment

Portfolio Theory ( 投資組合理論 ) : ρ ＝ 0 ρ<0 （其實 ρ≠1 即可）

↑ ↑

If returns tend to be independent or negatively correlated, diversification will generally be desirable.

∵ the coefficient of variation (CV=V/E) for the “portfolio” will likely be less than that associated with each individual investment - the “portfolio effect”

Diversification as a risk – reducing strategy becomes more effective as the covariation (i.e. correlation) among investments is lower

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※coefficient of correlation (ρ): -1<ρ <1

BA

AB

bbiaai

bbiaaiBA VV

COV

EEEE

EEEE

22,

13

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Combinations of crops A and B will always dominate complete specialization in one or the other, as long as the returns from the two are less than perfectly correlated (ρ≠1 ).

100% A

V

I’2E

I’1

I1

I2

100% B

Comparatively

conservative ‧

‧

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Portfolio selection for risky assets ：

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Appendix : portfolio selection with risk-free assets

FP

FL

I’1 capital market line(the new efficient frontierwhen borrowing is possibleslope=market price of risk )

risk premiumof market portfolio

E

P

V

F

E*

V*

BI1

L

I2I3

I’2I’3

the dominantmarket portfolioof risky securities

(efficient frontier whenborrowing were prohibited )

Combination of P & F

‧‧

‧

O

portfolio risk-free assetsLender ：L: will be invested in the portfolio of risky assets P will be lent or used to buy risk-free assets F with rate of return OFBorrower ：B : all available funds will be invested in P, and PB/FB will be financed by borrowing (at the cost of OF)

FP

LP

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Separation Theorem :

The investment decision (which portfolio of risky assets to hold) is separate from the financing decision (how to allocate investable funds between the risk-free asset and the risky asset).

The dominant portfolio of risky assets (P) is optimal for every investor regardless of that investor's utility function.

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OFFP

LPOE

FP

FLEssEE fPFP

1,

22,

22222, 121 PFPFPFPFP VsVVssVsVSV 02 FVFV

If s=0.5 ： half in P, half in F s=1.0 ： all in P s=1.5 ： (all + borrowing) in P ↑ half of the equity is borrowed debt./equity=0.5 (leverage)

s=2.0 : L = D/E = 1

∵

3

1

FB

PB

，則 S=1.5 ， 1-S= -0.5

eg ：若

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Principle of Increasing Risk

- As the relative amount of nonequity capital used in a business ex

pands (leverage ↑) , the tendency for risk becomes greater.

leverage =E

D

net worth

ilitiestotal liab

italequity cap

capitalnonequity

ratio

非淨值資本

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eg:

I=(rA-iD)(1-t)

leverage ratio ( L )： 0 0.5 1 2

E ： equity capital 100 100 100 100

D ： nonequity capital ( debt ) 0 50 100 200

A ： total capital = D + E 100 150 200 300

(1)

rA ： if return (r=15%) 15 22.5 30 45

- iD ： cost of nonequity capita (i=9%) 0 4.5 9 18

before tax net return 15 18 21 27

Income tax (t=20%) 3 3.6 4.2 5.4

I ： after tax net return 12 14.4 16.8 21.6

I/E ： rate of return on equity capital 12% 14.4% 16.8% 21.6%

(2)

rA ： if return is –15% -15 -22.5 -30 -45

- iD ： cost of nonequity capital 0 4.5 9 18

net return -15 -27 -39 -63

rate of return -15% -27% -39% -63%

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(1) as leverage ↑ → the spread between possible gains and loss↑, risk↑

(2) as long as the marginal rate of return on capital > the marginal

cost of using nonequity capital, leverage↑→ income↑→ net worth↑

if some of the income is reinvested , saved , or used to repay bor

rowed funds , net worth will ↑

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net after-tax earnings ： I = ( rA – iD )( 1-t ) reinvestment ： G= ( rA – iD )( 1-t )( 1-c )

rate of growth in equity:

Theoretically, as long as r > i, ↑L to ↑G/E (assuming t, c, and r constant).

However, the hypothesis of constant t, c is not real realistic; the hypothesis that r

is constant for all size of business may also be unrealistic; finally, the assumption

that i remains constant as L↑ is also unrealistic.

∵external capital rationing & internal capital rationing

EctiDrAEG /11/ ctEDiEEDr 11//

ctrirL 11

A=D+E

L=D / E

as L↑ or (r-i)↑ G/E ↑

also, t↓ , c↓ G/E ↑

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external + internal capital rationing( the reluctance to use unlimited amount of nonequity financing )cost or return

optimal leveragedebtequity

Leverage (debt/equity)

i

i+R

external capital rationing ( the tendency for lenders to provide limit amount of credit )

diminishing marginal productivity of capital

r

• optimum degree of leverage : r = i + R• marginal rate of return = marginal cost of nonequity capital • debt / equity usually ≦ 3 or 2

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Factors limiting growth

A. external constraints

1. quantity rationing of credit use (L limited )

2. price rationing of credit use (i↑)

3. income tax payments (t↑)

B. internal constraints

1. quantity rationing of credit use

2. income withdrawals (c)

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short-run

level of input use : MPPi / Pi , for all factors are same level of production : MCi = MRi , for all products

long-run