Lecture 2 DEF (part b) PDF

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Time Value of Money: Lecture 2-B of Financial Engineering Dr. Daan Schraven Drs.ir. Jules Verlaan Section of Infrastructure Design and Management Department of Structural Engineering

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Contents 1.

Background to Time Value of Money (part a) – – – –

2.

Valuing Bonds (part a) – – – –

3.

Bonds Valuation and Mechanics Duration and Term Structure Real and Nominal interest Risk of Default

Valuing Common Stock (part b) – – – –

4.

Future and Present Values Perpetuities and Annuities Growing Perpetuities and Growing Annuities Continuous Compounding

Stock Valuation and Mechanics Estimating Cost of Equity Capital Present value for growth opportunities Valuing business by DCF

Valuing Civil engineered Projects (part b) – –

Project evaluation methods Project evaluation

2

3. Valuing Common Stock

3

Common Stock • Common stock  are securities issued by organizations to transfer partial ownership. – These never expire, unlike bonds. As long as the company exists, its stocks will be tradeable.

• Common stock are traded by – Primary Market (new securities) – Secondary Market (previously-issued securities) 4

Value of Common Stock •

Several indirect ways exist to value stocks by Comparable indicators: – Book Value: Net worth of firm according to balance sheet – Dividend: Periodic cash distribution from firm to the shareholders – P/E Ratio: Price per share divided by earnings per share – Market Value Balance Sheet: Financial statement that uses market value of assets and liabilities

•

The more direct measure is the valuation by the Discounted Cash Flow (DCF) Formula: – Value of a stock = present value of future cash flows –    󰇛 󰇜 5

Return on Common Stock • Expected Return: Percentage yield forecast from specific investment over time period – It is also called market capitalization rate

• Example – Fledgling Electronics sells for $100 per share today; they are expected to sell for $110 in one year. What is expected return if dividend in one year is forecasted to be $5.00?    

     5  110  100  .15  100  6

Price of Common Stock • Price of share of stock is present value of future cash flows • For a stock, future cash flows are dividends and ultimate sales price

• Example: Fledgling Electronics price     

   5  110   100 1 1.15

• Price is also used to estimate the Market Capitalization Rate – This is estimated using perpetuity formula – It is also called cost of equity capital

   

  r    7

Dividend Discount Model •

Computation of today’s stock price: share value equals present value of all expected future dividends – H: Time horizon for investment

 

 1

  

   •



Example

 1  1

 ⋯  



   1 

 1



– XYZ Company will pay dividends of $3, $3.24, and $3.50 over next three years. After three years, stock sells for $94.48. What is the price of stock given 12 % expected return?

 

3.00 1  .12





3.24 1  .12



 ⋯

3.50  94.48  $75.00 1  .12 

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Estimating cost of equity capital • Dividend yield plus expected dividend growth (Gordon’s Growth Formula) – Similar to capitalization rate –    

 

–     

• Example

 



• Northwest Natural Gas shares sold for $47.30 at start of 2012. Dividend payments for 2013 were $1.86. Analysts forecasted an annual growth 6.1%. What is the cost of equity? • 

.  .

.061  .1, or10%

But, how can we forecast this growth? 9

Estimating Growth Rate •

Dividend Growth Rate (g) is derived by applying return on equity (ROE) to percentage of earnings reinvested in operations, the so-called “plowback ratio”. But, how does growth affect stock price?

 

    

 

    

  1    

  10

Valuing Non-Constant Growth •

Non-Constant Growth: is the notion that growth is temporary. – Hence, growing dividend payments will stop at some at the horizon (H).       1 1   

•

 

     ⋯ 1   

    1 1



 ⋯

 1   1 1





   

PH is the price at the horizon.

Example: Phoenix pays dividends in three consecutive years of 0, .31, and .65. Year-4 dividend is estimated at .67 with perpetuity growth at 4%. With 10% discount rate, what is stock price?  

0 1  .1





.31 1  .1





.65 1  .1





1 1  .1





.67 .1  .04

 9.13 11

Payout and Plowback ratio •

If firm pays lower dividend and reinvests funds, stock price may increase due to higher future dividends – –

Payout Ratio: Fraction of earnings paid out as dividends Plowback Ratio: Fraction of earnings retained by firm

•

Plowback ratio is used to calculate Present Value of Growth Opportunities (PVGO)     

•

Example with Common Stock: Company plans $8.33 dividend next year (100% of earnings). Investors will get 15% expected return. Instead, company plows back 40% of earnings at firm’s current return on equity of 25%. What is the stock value before and after plowback decision? –

No growth, with no earnings ‘plowed back:

–

With growth, with earnings plowed back:

     %  .25  .4  .1

   

   

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Valuing a Business by DCF • •

Usually computed as discounted value of FCF to valuation horizon (H) Valuation horizon is sometimes called terminal value and calculated like PVGO –

PVGO = NPV of firm’s future investments

PV (free cash flows)   •

     ⋯      1 1 1 1

PV (horizon value) 

 

 

PVh is often chosen in the year starting a stable pattern of free cash flows.

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