FINM7006-Applied Foundations of Finance Study Notes & Practice | The Australian National University | AskSia

Mar 13, 2026

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summary lecture 2

Here's a comprehensive summary of Lecture 2 based on the provided materials:

Lecture 2: Valuing Shares & Dividend Policy

1. The Corporation: Features & Structure

2. Shareholder Rights & Cash Flows

3. Calculating the Value of a Share

General Valuation Principle

  • The theoretical value of a share ($P_0$) is the present value of all expected future dividends discounted by the required rate of return ($r_e$):

    $$ P_0 = \sum_{t=1}^{\infty} \frac{D_t}{(1 + r_e)^t} $$

[15][43][51]

Special Cases

A. Constant Dividends (“Preference Shares”, Perpetuity):

  • If dividends are constant ($D$) forever (as with preference shares):

    $$ P_0 = \frac{D}{r_e} $$

[3][43][51]

B. Constantly Growing Dividends (“Gordon Growth Model”):

C. Real-World Considerations:

4. Dividend Policy — Modigliani-Miller Theorem

5. Dividends in Australia: Tax Perspective

Key Takeaways

  • The intrinsic value of a share is the present value of all expected future dividends.
  • Two major dividend models: level (perpetuity, for preference shares) and growing (Gordon growth).
  • Dividend policy doesn't affect firm value in perfect markets, but taxes and other frictions matter in practice.
  • Australia uses an imputation system to reduce double taxation of dividends.

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summarize_document

Summary of Applied Foundations of Finance (FINM7006) and Foundations of Finance (FINM1001) Content

This summary covers key concepts related to business organization, shareholder liability, share types, and the valuation of financial securities, drawing from both FINM7006 and FINM1001.

I. Characteristics of Corporations vs. Other Business Organizations (FINM7006)

Corporations are distinguished from sole proprietorships and partnerships by three primary characteristics:

  • Widely Dispersed Ownership:
    • Ownership is typically spread across many shareholders.
    • Shareholdings are freely transferable without disrupting the corporation's operations.
  • Separation of Ownership and Management:
    • Shareholders do not participate in the daily running of the corporation.
    • The board of directors determines corporate objectives.
    • Shareholders elect and re-elect the board and receive reports on company operations and decisions.
  • Limited Shareholder Liability:
    • Shareholders' liability for corporate debts is generally limited.
    • This concept is further elaborated in the context of Question Two (not provided in detail here).

II. Shareholder Liability (FINM7006)

Understanding the extent of a shareholder's financial responsibility is crucial.

  • Limited Liability:
    • In a limited liability corporation, a shareholder's loss is capped at the amount they have paid for their shares, plus any unpaid portion of those shares.
    • Example: If a company goes bankrupt, the shareholder's total loss is their initial investment plus any outstanding amount due on their shares.
  • No Liability:
    • In a no liability company, a shareholder's loss is limited only to the amount they have already paid for their shares. No further payments are required.
  • Comparison with Sole Proprietorships and Partnerships:
    • Owners of sole proprietorships and partnerships have unlimited liability.
    • If these businesses fail to meet their obligations, creditors can seize the owners' personal assets to recover debts.

III. Types of Shares (FINM7006)

Shares represent ownership in a corporation, but different types offer distinct rights and priorities.

  • Ordinary Shares:
    • Represent ownership in the corporation.
    • Holders have the right to vote on corporate matters.
    • Holders are entitled to any dividends declared by the board.
    • Rank last in priority during liquidation.
  • Preference Shares:
    • Represent ownership in the corporation.
    • Receive priority over ordinary shares for fixed dividends.
    • Receive priority over ordinary shares in the event of liquidation.
    • Generally do not carry voting rights.

IV. Valuation of Preference Shares (FINM1001)

The price of a preference share can be calculated based on its dividend and the required rate of return.

  • Formula: Price = Annual Dividend / Required Rate of Return
  • Example:
    • A preference share paying a $0.50 annual dividend with a 10% required rate of return is priced at: $0.50 / 0.10 = $5.00

V. Valuation of Ordinary Shares (FINM1001)

The valuation of ordinary shares often involves considering dividends, growth rates, and required rates of return.

  • Dividend Growth Model (Gordon Growth Model):

    • Used for shares with dividends expected to grow indefinitely at a constant rate.
    • Formula: Price = D1 / (RE - g)
      • D1 = Expected dividend in the next period (D0 * (1 + g))
      • RE = Required rate of return
      • g = Constant growth rate of dividends
    • Example:
      • A company paid a $1.00 dividend, expects it to grow at 9% indefinitely, and investors require a 12% return. The share price is: $1.00 * (1.09) / (0.12 - 0.09) = $1.09 / 0.03 = $36.33

  • Valuation with No Growth:

    • If dividends are not expected to grow, the formula simplifies to Price = Dividend / Required Rate of Return.
    • Example:
      • A share priced at $5 pays a $0.25 annual dividend with no expected growth. The required rate of return is: ($0.25 / $5) = 0.05 = 5%

  • Required Share Price Appreciation:

    • To achieve a specific required rate of return, the share price must appreciate by a certain amount, considering the dividend received.
    • Formula: P0 * (1 + RE) = P1 + D1
    • Example:
      • To earn a 15% return on a $50 share paying a $6 dividend, the selling price (P1) needs to be: $50 * (1.15) - $6 = $57.50 - $6 = $51.50
      • This requires a share price appreciation of $1.50 ($51.50 - $50.00).

  • Calculating Share Value with Growth:

    • Formula: VE = D1 / (RF - g)
    • Example:
      • Header Motors paid a $3.50 dividend, expects 5% growth, and investors require 20%. The share value is: $3.50 * (1.05) / (0.20 - 0.05) = $3.675 / 0.15 = $24.50

  • Investment Decision Rule:

    • Compare the expected rate of return (implied by the market price) with your required rate of return.
    • Compare the calculated value of the share with its current market price.
    • Decision: Invest if the expected return is greater than the required return, OR if the calculated value exceeds the market price.
    • Example (NCP Ltd):
      • Current Market Price: $23.50
      • Dividend (D0): $1.32
      • Growth Rate (g): 8%
      • Required Rate of Return (RE): 10.5%
      • a) Expected Rate of Return: RE = (D0 * (1 + g) / Market Price) + g RE = ($1.32 * 1.08 / $23.50) + 0.08 = (1.4256 / 23.50) + 0.08 = 0.06067 + 0.08 = 14.07%
      • b) Value of Share for You: Value = D0 * (1 + g) / (RE - g) Value = $1.32 * 1.08 / (0.105 - 0.08) = 1.4256 / 0.025 = $57.02
      • c) Investment Decision: Yes, invest because 14.07% (expected return) > 10.5% (required return), and $57.02 (calculated value) > $23.50 (market price).

  • Multi-Period Valuation:

    • The price of a share is the present value of all expected future dividends and the expected future selling price.
    • Formula: P0 = D1 / (1 + RE) + D2 / (1 + RE)^2 + ... + Dn / (1 + RE)^n + Pn / (1 + RE)^n
    • Example (Acap Corporation):
      • D1 = $2.80, D2 = $3.00, Expected P2 = $52.00, RE = 10%
      • a) Price if held for two years (P0): P0 = $2.80 / (1.10) + $3.00 / (1.10)^2 + $52.00 / (1.10)^2 P0 = $2.545 + $2.479 + $42.975 = $48.00
      • b) Expected selling price in one year (P1): P1 = (D2 + P2) / (1 + RE) P1 = ($3.00 + $52.00) / 1.10 = $55.00 / 1.10 = $50.00
      • c) Price if held for one year (P0): P0 = D1 / (1 + RE) + P1 / (1 + RE) P0 = $2.80 / 1.10 + $50.00 / 1.10 = $2.545 + $45.455 = $48.00
        • This price is the same as holding for two years because the expected future selling price ($52.00) was determined using the same required rate of return and dividend expectations.
请根据所有资料，给出Tutorial 2的答案

根据提供的资料，以下是Tutorial 2（Foundations of Finance/APPLIED Foundations of Finance）的答案与详细解析：

Question 1:

Describe the characteristics of a corporation that differentiate it from other forms of business organization such as partnerships and sole proprietorships?

答案：

  1. 广泛分散的所有权：
    公司的所有权通常比合伙制和独资企业更为分散，且股份可以在不同股东之间自由转让，而不会影响公司的运营。
  2. 所有权与经营的分离：
    股东不能参与公司日常运营，公司的目标由董事会决定。董事会由股东选举/重选，并且必须向股东报告公司运营和决策。
  3. 有限责任：
    股东的责任仅限于他们为股份支付的金额，加上任何未支付的部分。即使公司破产，股东的最大损失就是初始投资和任何尚未支付的股份金额[2]。

Question 2:

What is meant if a shareholder has limited liability? How does this differ from a situation where a shareholder has no liability?

答案：

Question 3:

What is the difference between a preference share and an ordinary share?

答案：

Question 4:

Preference Share Valuation

Calculate the price of a preference share paying a dividend of $0.50 p.a. given a required rate of return of 10% p.a. Assume the company has just paid the last dividend.

答案：
$$ P = \frac{D}{r} = \frac{0.50}{0.10} = $5.00 $$ [5][8][19]

Question 5:

Constant-Growth Ordinary Share Valuation

A company has just paid a dividend of $1.00 per share. Dividends are expected to grow at 9% p.a. indefinitely. Calculate the price if the required rate of return is 12%.

答案：
$$ P = \frac{D_0(1 + g)}{r - g} = \frac{1.00 \times 1.09}{0.12 - 0.09} = \frac{1.09}{0.03} = $36.33 $$ [5][8][10][12][19]

Question 6:

Required Rate of Return (No Growth)

A share price为$5，每年派息$0.25，无增长。年回报率为？

答案：
$$ r = \frac{D}{P} = \frac{0.25}{5} = 0.05 = 5% $$ [10][12][18][20]

Question 7:

Share Price Appreciation for Target Return

以$50价格买入，每年分红$6，需要达到15%回报，年底股价须涨多少？

答案：
$$ 50 \times (1 + 0.15) = 50 + 6 + \text{价格上涨} \ 57.5 = 56 + \text{价格上涨} \ \text{价格上涨} = 1.5 $$ 即股价需上涨$1.50[12][17][18][20]

Question 8:

Constant Growth Valuation

Header Motors派息$3.50，分红增速5%，所需回报率20%，股价？

答案：
$$ P = \frac{D_0(1+g)}{r-g} = \frac{3.5 \times 1.05}{0.20-0.05} = \frac{3.675}{0.15} = $24.50 $$ [7][16][17][18]

Question 9:

NCP Ltd派息$1.32，预期增长8%，市场价$23.50。

Question 10:

Acap Corporation今年末派息$2.80，明年$3，2年后股价$52。资本成本为10%。

  • (a) 持有2年，今天最多付多少钱？

$$ P_0 = \frac{2.80}{1.10} + \frac{3.00}{1.10^2} + \frac{52.00}{1.10^2} = 2.545 + 2.479 + 42.975 = $48 $$

  • (b) 持有1年，明年能卖多少钱？

$$ P_1 = \frac{3.00 + 52.00}{1.10} = $50.00 $$

  • (c) 持有一年，今天最多付多少？

$$ P_0 = \frac{2.80 + 50.00}{1.10} = 52.80 / 1.10 = $48.00 $$ [1][3][9][11][13][15]

如需更详细推导、相关定理或LaTeX版完整解析，可以随时告知！

所有答案依据：Tutorial 2 Solutions (1).docx 提供的内容，引用详见括号。

英文

Here are detailed answers for Tutorial 2, based on the content from the current file [Tutorial 2 Solutions (1).docx]:

Question 1:

Describe the characteristics of a corporation that differentiate it from other forms of business organization such as partnerships and sole proprietorships.

Answer: A corporation is distinct in three main ways:

  1. Widely Dispersed Ownership: Ownership is usually spread among many shareholders, and shares are freely transferable between them without interrupting the operation of the corporation.
  2. Separation of Ownership and Management: Shareholders do not have the right to participate in daily management. Corporate objectives are determined by a board of directors, who are elected and re-elected by shareholders. The board must report to them on company operations and decisions.
  3. Limited Liability: Shareholders' financial risk is limited to the amount unpaid on their shares (if any). In bankruptcy, their total loss is what they’ve paid plus any unpaid outstanding share amounts, compared to sole proprietorships or partnerships, where personal assets are at risk for company debts [4][12][14].

Question 2:

What is meant if a shareholder has limited liability? How does this differ from a situation where a shareholder has no liability?

Answer:

Question 3:

What is the difference between a preference share and an ordinary share?

Answer:

Question 4:

Calculate the price of a preference share paying a dividend of $0.50 p.a. given a required rate of return of 10% p.a. Assume the company has just paid the last dividend.

Answer:
The price of a preference share is: $$ P = \frac{D}{r} = \frac{0.50}{0.10} = $5.00 $$ [2][10][19]

Question 5:

A company has just paid a dividend of $1.00 per share. Dividends are expected to grow at 9% p.a. indefinitely. Calculate the price of a share if the required rate of return is 12%.

Answer:
Use the Gordon Growth Model: $$ P = \frac{D_0(1 + g)}{r - g} = \frac{1.00 \times 1.09}{0.12 - 0.09} = \frac{1.09}{0.03} = $36.33 $$ [10][17][19]

Question 6:

What is the per annum required rate of return on a share whose price is $5 and pays dividends at a rate of $0.25 p.a.? Assume dividends are not expected to grow and the company has just paid a dividend.

Answer:
$$ r = \frac{D}{P} = \frac{0.25}{5} = 0.05 = 5% $$ [15][17]

Question 7:

If you buy a share for $50 and expect a dividend of $6, how much must the share price rise by year-end for a 15% required return?

Answer:
Total return required: $$ 50 \times 1.15 = 57.5 $$ Return from dividend: $6
Required price appreciation: $$ 57.5 - 50 - 6 = 1.5 $$ So, the share price must increase by $1.50 [9][15][17]

Question 8:

Header Motors just paid a $3.50 ordinary share dividend. Dividends are expected to grow at 5% p.a. If investors require a 20% return, find the share price.

Answer:
$$ P = \frac{D_0(1+g)}{r-g} = \frac{3.50 \times 1.05}{0.20 - 0.05} = \frac{3.675}{0.15} = $24.50 $$ [3][8][15]

Question 9:

NCP Ltd just paid $1.32 dividend, with expected growth of 8%. Current price is $23.50.

Question 10:

Acap Corporation will pay a dividend of $2.80 at year-end and $3 next year. Expected share price in 2 years is $52. Equity cost of capital is 10%.

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