Equivalent Annual Payment Method

COMPARE PROJECTS WITH DIFFERENT PERIODS

1. Alternative string method

 The life cycle of a long project must be a multiple of that of a short project.

 Capital invested in short-life projects will continue to be reinvested and the return level will remain unchanged.

=> Adjust projects with different life cycles to the same time period.

COMPARE PROJECTS WITH DIFFERENT PERIODS

2. Equivalent annual payment method

Equivalent annual annuity (EAA)

 Based on the NPV of each project, calculate the equivalent annual payments (EAA)

 Assume the project generates infinite constant cash flows (EAA)

NPV  EA A i

i r

 The project with the higher NPV (after adjustment) will be selected.

21 22

CHAPTER 8:

EFFICIENT MARKET THEORY

The concept of market efficiency

Forms of efficient market hypothesis

Six lessons of efficient markets

CONCEPT OF EFFICIENT MARKET

"A market is considered efficient if the price of a good reflects all available information related to that good" (Fama, 1970)

P t+1 = P t +  t+1

=> Investors cannot earn abnormal returns if the market is efficient.

LEVELS OF MARKET EFFICIENCY

(1)

weak form

Prices reflect all past information.

=> It is impossible to use past prices to predict future prices.

Semi-strong form

Prices reflect all information published in the market (monetary policy, exchange rates, interest rates, dividend announcements, stock splits)

LEVELS OF MARKET EFFICIENCY

(2)

=> Investors cannot make extraordinary profits by analyzing annual reports or publicly available information.

Strong form

Prices reflect all available information, including publicly available information and information within the company.

SIX LESSONS OF EFFICIENT MARKETS

Market without memory

Trust the price

There are no illusions about financial calculation methods.

Do it yourself

Look at a stock must see the whole market

Must collect information regularly

CHAPTER 9: OPERATING LEVERAGES AND

FINANCIAL LEVERAGE

CONTENT

 What is leverage?

 Operating leverage

 Financial leverage

 Total/combined leverage

OPERATING LEVERAGE

WHAT IS LEVERAGE?

- Leverage is the use of fixed costs to magnify a company's potential profits.

- Fixed costs include:

Fixed operating costs

OPERATING LEVERAGE (1)

- Operating leverage measures the extent to which a company uses fixed operating costs.

- Degree of Operating Leverage (DOL) measures the change in EBIT/operating profit in response to a change in revenue.

fixed financial costs

DOL

 EBIT / EBIT

 Q / Q

(9.1)

3 4

OPERATING LEVERAGE (2)

Break-even analysis

OPERATING LEVERAGE (3)

Company A

Total Operating

Q BE 

(9.2)

Units Variable Fixed Total Total Income

P V

Sold Costs $ Costs $ Costs Revenue $ (loss)

P: Selling price V: Variable cost F: Fixed cost

P – V: Contribution margin Q BE : Break-even quantity

0 $ 0 60,000 60,000 $ 0 (60,000)

20,000 16,000 60,000 76,000 40,000 (36,000)

40,000 32,000 60,000 92,000 80,000 (12,000)

50,000 40,000 60,000 100,000 100,000 0

60,000 48,000 60,000 108,000 120,000 12,000

80,000 64,000 60,000 124,000 160,000 36,000

100,000 80,000 60,000 140,000 200,000 60,000

OPERATING LEVERAGE (4)

Revenues and costs ($ thousands) 200

Total Revenue

OPERATING LEVERAGE (5)

Company B

total

Operating

Profile

160

Total

Units Variable Fixed Total Total Income Sold Costs Costs Costs Revenue (loss)

$ $ $

BE costs

0 $ 0 12,000 12,000 $

0 (12,000 . )

Loss

120

100

Variable costs

Fixed costs

20,000 32,000 12,000 44,000 40,000 (4,000 . )

30,000 48,000 12,000 60,000 60,000 0

40,000 64,000 12,000 76,000 80,000 4,000

60,000 96,000 12,000 108,000 120,000 12,000

80,000 128,000 12,000 140,000 160,000 20,000

100,000 160,000 12,000 172,000 200,000 28,000

20 40 50 60 80 100 120

Units produced and sold (thousands)

Fixed costs ($60,000) Price ($2) Variable costs per unit ($0.80)

OPERATING LEVERAGE (6)

Revenues and costs ($ thousands)

Total Revenue

OPERATING LEVERAGE (7)

200

160

Profit

Total costs

EBIT = PQ – (VQ +F) = Q(PV) + F

 Q ( P V )

120

80 BE

Variable costs

DOL Q

  EBIT / EBIT

 Q / Q

 Q ( P  V )  F

 Q

Loss

Fixed costs

DOL Q

 Q ( P  V )

Q ( P  V )  F

(9.3)

20 40 60 80 100 120

Units produced and sold (thousands)

Fixed costs ($12,000) Price ($2) Variable costs per unit ($1.60)10

OPERATING LEVERAGE (8)

Dividing the numerator and denominator of (9.3) by (PV), we get:

Q ( P V )

OPERATING LEVERAGE (9)

Q	Company A	Company B
0	- 60,000	- 12,000
20,000	- 36,000	- 4,000
40,000	- 12,000	4,000
60,000	12,000	12,000
80,000	36,000	20,000
100,000	60,000	28,000

Maybe you are interested!

Operating profits of companies A and B at different Q levels:

DOL Q

 ( P  V ) 

Q ( P  V )  F

P V

Q Q BE

(9.4)

DOL S

Q ( P  V )

Q ( P  V ) F

S  V

S  V F

 EBIT  F

EBIT

(9.5)

11 12

OPERATING LEVERAGE (10)

DOL of company A at levels Q = 60,000:

DOL

60,000

 60,000 (2  0.8)  6

60,000 (2  0.8)  60,000

FINANCIAL LEVERAGE

DOL of company B at levels Q = 60,000:

DOL

60,000

 60,000 (2  1.6)  2

60,000 (2  1.6)  12,000

RELATIONSHIP BETWEEN EBIT AND EPS (1)

C&T Company has current equity of 10 million USD (200,000

RELATIONSHIP BETWEEN EBIT AND EPS (2)

CP). The company needs to raise an additional 5 million USD to expand its production and business. The company is considering 3 capital raising options: (1) Issuing common shares, (2) issuing bonds with an interest rate of 12%.

EP S 

(EBIT

- I)(1 - t) - PD NS

and (3) issue preferred shares with a dividend of 11%. The company's current annual EBIT is 1.5 million USD, but if it expands its business, the company expects EBIT to increase to 2.7 million USD. Corporate income tax is 40%. If using the first method, the company will issue 100,000 more shares ($50/share). Calculate EPS for the above 3 options?

I: Annual interest payable

t: Corporate income tax rate PD: Dividends payable on preferred shares NS: Number of common shares

15 16



	Funding options
Target
Target		Common stock	Bonds	Preferential CP
EBIT		2,700,000	2,700,000	2,700,000
I		-	600,000	-
EBT		2,700,000	2,100,000	2,700,000
Corporate income tax		1,080,000	840,000	1,080,000
Profit after tax		1,620,000	1,260,000	1,620,000
PD		-	-	550,000
LN for common stock		1,620,000	1,260,000	1,070,000
NS		300,000	200,000	200,000
EPS		5.40	6.30	5.35

RELATIONSHIP BETWEEN EBIT AND EPS (3)

RELATIONSHIP BETWEEN EBIT AND EPS (4)

Is there an EBIT value such that the EPS of the financing options are equal?

That point is called the Indifference point (Indifference or Financial leverage break-even point).

EBIT 1,2 = Indifference point between 2 PA 1 and 2 I 1 , I 2 : Annual interest payable corresponding to PA 1 and 2 PD 1 , PD 2 : Preferred stock dividends corresponding to PA 1 and 2 t: Corporate income tax rate

NS 1 , NS 2 : Number of common CPs corresponding to PA 1 and 2



	Funding options
Target
Target		Common stock	Bonds	Preferential CP
EBIT		1,800,000	1,800,000	2,700,000
I		-	600,000	-
EBT		1,800,000	1,200,000	2,700,000
Corporate income tax		720,000	480,000	1,080,000
Profit after tax		1,080,000	720,000	1,620,000
PD		-	-	550,000
LN for common stock		1,080,000	720,000	1,070,000
NS		300,000	200,000	200,000
EPS		3.60	3.60	5.35