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Finance Lecture 10(the last lecture)

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Lecture 10 L t

Lecture 1-4: Time value of money and project evaluation Missing ingredient: Required rate of return

Cost of Capital

Lecture 9: CAPM

Lectures Le t e 5 and 6: nd 6 Valuation of debt and equity

Lecture 7 and 8: Portfolio analysis

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Lec 1-4
Time value of money → technique of discounting cash flows Use technique to calculate NPV (discounted stream of future cash flows net of cost)
Focus on relevant cash flows to include

Lec 5-pricing of debt
Bonds:
Regular interest payments Face value at maturity Price is P i i payment stream discounted at t t di t d t current market yield

Project evaluation Key: required rate of return was given
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Bond Pricing
Regular interest payments of:
A = FV × (coupon rate) ÷ (# coupons per year)

Bond Pricing

Number of coupon payments:
n = (# coupons per year) × (# years)

FV

Payment of face value at maturity
A 0 1 A 2 A 3 A 4 A 5 A n-3 3 A n-2 2 A n-1 1
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⎡1 − (1 + r per )−n ⎤ FV PV = A ⎢ ⎥+ n r per ⎥ (1 + r per ) ⎢ ⎣ ⎦
A 0 1 A 2 A 3 A 4 A 5 … A n-3 3 A n-2 2 A n-1 1

FV

…

A n

A n
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Lec 6-pricing of equity
Basic valuation principle: Share price is the p present value of expected future cash flows p from the share
If hold share forever, receive an infinite stream of dividends: di id d

Dividend Valuation Models
Constant dividend model

P0 =

d3 d2 d1 + + + 2 (1 + re ) (1 + re ) (1 + re )3
∞

d P0 = re
Assumes the same dividend is paid forever … it is an application of a simple perpetuity!
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Usually for preferred share valuation.

dt =∑ t 1 t =1 ( + re )
dt is the dividend paid in year t Discount rate (re) is return on equity, the opportunity cost

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Constant Dividend Growth Model
Assumes dividends grow at a constant rate of g per annum. ate o pe a u
0 1 2 3 4

Lec 8-9: the CAPM

...

The return you can expect to earn on asset i

The magnitude of the risk premium earned is proportional to asset i’s beta

d0

d0(1+g) d0(1+g)2 d0(1+g)3 d0(1+g)4

g , p Under constant growth of divs, share price is given by: d 0 (1 + g ) d1

E (ri ) = rf + βi ⎡E(rm ) − rf ⎤ ⎣ ( ⎦
The riskfree Rate, plus
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P0 =

re − g

=

re − g

Need re > g

A premium for bearing risk (the market risk premium)
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The Role of the Firm

Valuing the Firm
Value of firm is present value of all future free cash flows to the firm
Shareholders

Real Assets

Net Cash Flow Re-investment Free cash flows to the firm

E

V =∑

Ft t 1 t =1 ( + r )
∞

V

Debtholders

D

Value of firm is market value of debt plus equity V =D +E
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Project evaluation
Two key factors in project evaluation are
Future cash flow estimation Discount rate

Cost of capital
Suppose 2 projects-one riskless, another risky How should one estimate the cost of capital? What rate of return would our shareholders require from these projects?
Riskless project will only increase shareholder value if earns at least as much as risk-free asset (e.g. government debt) Risky project will increase shareholder wealth only if earns similar returns as other projects with similar risk

The appropriate discount rate is the pp p investors’ expected return=opportunity cost of capital=rate of return that could be earned on another investment of similar risk
It I cannot be observed; must be estimated b b d b i d

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Alternative Approaches to Estimation of pp Cost of Capital
• Direct use of CAPM to estimate the

But..
Most companies are also financed by debt Estimate the project’s beta by a weighted average of the debt and equity beta:
βproject = βdebt × ⎜ ⎟ + βequity × ⎜ ⎟ V V
⎛ D⎞ ⎝ ⎠ ⎛E⎞ ⎝ ⎠

project’s beta.

rproject = rf + β project ( E (rM ) − rf

)

Can rf , rM and the project’s beta be accurately observed? Would be OK if the company’s projects were all of the same systematic risk and if the company was financed solely by equity, since then:

β equity =β assets =β project
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Calculation of debt beta? Difficult
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WACC
Most common approach is to use the weighted-average cost of capital (WACC) Assume that project’s risk is similar to A h j ’ i k i i il risk of other projects, then return required by equity holders and q y q y debtholders from project same as that from the company as a whole Company s Company’s average cost of capital is the minimum rate of return it needs to earn on its assets to meet the costs of debt finance and provide the rate of return that shareholders require
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WACC
Annual interest cost on debt: interest rate (after tax)*market value of tax) market debt Minimum net cash flow required by shareholders: Required return on equity market value equity*market equity WACC sum WACC=sum of above/total market value

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Weighted Average Cost of Capital
To estimate WACC for a project, the first step is to determine the permanent sources of capital used by the firm. Then, Then each source’s cost of capital is source s calculated at market values, weighted, and summed to arrive at WACC

Permanent sources of capital
Include all classes of equity Include long term debt long-term Exclude seasonal short-term debt and accounts payable (these are working capital) Exclude deferred taxes.

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WACC
After-tax WACC is summarised by the equation… q

Market Value and Return for Equity
Marketable equity
Use current market price for value Use CAPM for expected return

⎡E ⎤ ⎡D ⎤ WACC = ⎢ × re ⎥ + ⎢ × ( rd × (1 −Tc ) ) ⎥ ⎣V ⎦ ⎣V ⎦
where: V = market value of firm E = market value of equity D = market value of debt Tc = corporate tax rate rd = before-tax cost of debt re = cost of equity
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Non-marketable equity N k t bl it
Estimate beta for CAPM using
Similar companies Industry averages

Compute present value of projected dividends
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Market Value and Return for Debt
Marketable debt
Use current market price to compute yield Or compute p p price using market y g yield

After-tax cost of capital
Interest payments on debt are taxdeductible
Therefore cost of debt must be adjusted

Non-marketable debt
Estimate current market yield based on
Credit ratings Bank loan rates

Dividend payments to shareholders are a e not ta ded ctible tax-deductible
Therefore, no adjustment is necessary for f equity. it

Estimate value by computing present value of interest payments
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WACC
After-tax WACC is summarised by the equation… q

WACC
Assumptions:
Proposed project’s risk is the same as the average risk for the firm Acceptance of the project will not affect the optimal capital structure

⎡E ⎤ ⎡D ⎤ WACC = ⎢ × re ⎥ + ⎢ × ( rd × (1 −Tc ) ) ⎥ ⎣V ⎦ ⎣V ⎦
where: V = market value of firm E = market value of equity D = market value of debt Tc = corporate tax rate rd = before-tax cost of debt re = cost of equity
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WACC Example
Mango Ltd’s book capital structure as at 30 June, 2004 is shown below: Liabilities
2,000,12%, $100 debentures (maturing 30 June, 2006) June $200,000 $200 000

WACC Example
Additional information:
Corporate tax rate is 30% Debentures are currently priced at $106 Preference shares are selling for $1 Ordinary shares: y Dividend of $0.50 just paid Dividends have been growing at 5% Market price is $5

Shareholders’ Equity
500,000 ordinary shares, d h $2.00 each 50,000, 4% preference shares, , , p , $3.00 each $1,000,000 $150,000

Required: Calculate the cost of capital for Mango

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WACC Example
Step 1: Identify permanent sources of capital
Debentures (D) Ordinary shares (E1) Preferred shares (E2)

WACC Example
Step 2 (a): Calculate the cost of capital for each S ( ) C l l h f i lf h source of capital. The CAPM can be used to estimate the cost of equity capital. capital An alternative is to use the Dividend Growth Model

P0 =

d 0 (1 + g ) re − g

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WACC Example
Similarly, Similarly using the Constant Dividend Model, Model we can calculate the cost of preference shares

WACC Example
What is the cost of debt, rd? We can use the bond pricing formula formula.

P0 =

d re

⎡1 − (1 + r )−n per PV = A ⎢ ⎢ r per ⎣
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⎤ FV ⎥+ ⎥ (1 + r )n per ⎦
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WACC Example

WACC Example
Using Excel:
PV FV n C rper 106 100 4 6 4.3340%

⎡1 − (1 + r )−4 ⎤ per ⎥ + 100 106 = 6 ⎢ ⎢ ⎥ (1 + r )4 r per per ⎣ ⎦
Unfortunately, Unfortunately we cannot solve for rper by simply rearranging
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Since this is compounded semip annually, the annual equivalent is:

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WACC Example
Step 2 (b): Calculate the market values for sources of capital Ordinary Sh O di Shares: $5 x 500 000 =$2,500,000 500,000 $2 500 000 Preference Shares: $1 x 50,000 = 50,000 Debentures: $106 x 2,000 = 212,000 Total Value: $2,762,000

WACC Example
Step 3: Calculate WACC
⎡E ⎤ ⎡E ⎤ ⎡D ⎤ WACC = ⎢ 1 × re 1 ⎥ + ⎢ 2 × re 2 ⎥ + ⎢ × ( rd × (1 −Tc ) ) ⎥ ⎦ ⎣V ⎦ ⎣V ⎦ ⎣V

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Cost of Capital Summary
Discount rate depends on project risk, risk not company risk Company cost of capital is only p y p y appropriate for projects that
Have similar systematic risks to the company as a whole Will not change the company’s target g p y g leverage

Example
Calculate the WACC of Tristan Ltd, using the following information: Balance sheet extract Liabilities 10% debentures ($100 issue price)$150,000,000 Shareholders’ funds Paid-up capital – ordinary shares ($1 issue price)$50,000,000 Additional information Ordinary shares will pay a dividend of 66 cents at the end of this year, and dividends are expected to grow by 2.4% per annum indefinitely. Commonwealth government bonds trade at 4%. g The return on the market portfolio is 12% Tristan Ltd’s beta is 1.3. Its debentures are priced at $110 and pay coupons annually. The current return on Tristan Ltd debentures is 2% above the government bond rate. No company or personal taxes are levied levied. The existing capital structure is unlikely to change. Should Tristan Ltd go ahead with an expansion of their factory that costs $2 million today and will generate a cash flow of $350 000 per year for ten years? Show all $350,000 computations and explain why you chose any additional numbers needed to make this decision.

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Step 1
Identify permanent sources of capital
Debentures Ordinary shares O dina sha es

Step 2a
Calculate cost of capital
Cost of Debt (rd): =Govt bond rate +2%

= 4%+2% = 6%
Cost of Equity (re): =rf + β[E(Rm) - Rf]

= 4% + 1 3[12% 4%] = 14.4% 1.3[12%-4%] 14 4%

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Step 2b
Calculate market value of sources of capital
Market Value of Debt(D): Number of Debentures = ($150M/$100) =1,500,000 , , Market value = number * price =1,500,000*$110 = $165M Market Value of Equity (E): Number of ordinary shares = ($ y ($50M/$1) = 50M $ )

Price per share = $0.66/(0.144-0.024) = $5.50 Market value = number*price = 50M*$5.50 50M*$5 50 =$275M
Total Market Value(V) =D+E = 165M+$275M

$440M =$440M
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Step 3
Calculate WACC

(b)

Tristan should go ahead since NPV is positive. Use WACC (11.25%) from part (a) as the discount rate in NPV computations for the expansion project NPV =-2,000,000 + 350,000

⎡E ⎤ ⎡D ⎤ W =⎢ ×re ⎥ +⎢ ×(rd ×(1−Tc ) )⎥ ACC ⎣V ⎦ ⎣V ⎦
WACC= 275/440 x .144 + 165/440 x .06 WACC = 11.25%

= 39,801

⎡1 − (1 + 0.1125)−10 ⎤ ⎢ ⎥ 0.1125 0 1125 ⎣ ⎦

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Evidence on cost of capital calculations p in practice
J. Graham and C. Harvey, “The Theory of and Practice of Corporate Finance: Evidence from the Field, Field,” Journal of Financial Economics, 2001, p.199 Short version: “How do CFOs make capital g g p budgeting and capital structure decisions?” Journal of Applied Corporate Finance, 2002, p. 8 Question: Do firms finance themselves in ways y that are consistent with the theory? Data:
Current practice of corporate finance Survey CFOs on cost of capital, capital budgeting, capital structure in 1999 Sample of 4,440 firms, 392 CFOs responded

Cost of equity capital method
CAPM Arithmetic average historical return Multibeta CAPM Dividend discount Model Investor expectations Regulatory decisions 0% 10% 20% 30% 40% 50% 60% 70% 80%

Percent of CFO's who always or almost always use a given method

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Fig. 3. Survey evidence on the popularity of different methods to calculate the cost of equity capital We report the percentage of CFOs who always or almost capital. always use a particular technique. CAPM represents the Capital Asset Pricing Model. The survey is based on the responses of 392 CFOs.

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Description: Finance - Master of Commerce- The University of Queensland Australia