finance

Advanced Managerial Finance

In Ji Jang

Raising Capital

Ch.14,20

Raising Capital and Market Efficiency: Stock Price and NPV • Firm has no debt

• Existing assets generate earnings of $9mil. per year forever

• Discount rate=10%

• Firm has n shares (5 mil.) currently selling at P=$18 per share

Mkt. Value Balance Sheet Assets Equity Mkt Value V= E/R n shares x P0 =9/.10= 90 = 5 x 18 = 90

Share Price Effect of New Project • Now firm plans to invest I=$20mil. in a new project

• The project will generate $3 mil. in new earnings per year forever

• Firm will issue Δn new shares at price P0* to finance project

New Mkt. Value Balance Sheet Assets Equity Mkt Value

V= (9+3)/.10 = (5+n)P0* = 120 = 120

NPV and Share Price

• We would like to know the share price change with this new issue.

• NPV of the project:

• Wealth of original shareholders goes up by NPV of new project.

3 20 10

.10

E I

R

 − = − =

*

0

*

0 0

*

0 0

*

0

9 3 120 * ( )

.10 .10

90 20

3 ( ) 20 10

.10

20; 5 ; 1

E E V n n P

R R

E V nP nP I

R

E n P P I

R

P n mil n mil

 = = + = + = + 

= = =  = =

  − = − = − =

 = =  =

Efficient market and shareholder wealth

• Expected return for new shareholders:  EPS

 Return

 EMH

= $12mil / 6mil = 2

= EPS/Price = 2 /20 = 10%

→ Required return (discount rate) =10%

What if Market is Inefficient? • Suppose now new shares can only be sold for $18?

• How many new shares doe the firm needs to raise?

 Company must sell $20mil./$18=1.111mil. new shares (total of 6.11 mil. shares after issuance)

• Eventually, company will be recognized to be worth $120 mil.

 What would be the new price after the issuance?

 Share price will rise to 120mil / 6.111mil =$19.636

Inefficient Market and Shareholder Wealth • After company value is recognized, and share price rises, original

shareholder gain (5mil. shares)*(19.636-18) = 8.182 mil

• New shareholder gain: (1.11mil) * (19.636-18)=1.818 mil

• Expected return for new shareholders:  EPS = 12 / 6.111 = 1.964

 Return = EPS/Price = 1.964/18 = 10.91% > 10%

 (more than needed to attract capital)

Inefficient Market Transfers Wealth • Because new shares are sold too cheaply new shareholders gain

• At the expense of the original shareholders

• What happens if new shares can be sold at $22?

Timing of Securities Issues • If underpriced, new shareholders gain

• If overpriced, existing shareholders gain

Practice Problems

• Question 1