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From financial options to real options 4. Financing real options. Prof. André Farber Solvay Business School ESCP March 10,2000. Financing new ventures: . For new ventures, financing needs are greater than initial capital available. Outside financing required? How?

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from financial options to real options 4 financing real options

From financial options to real options4. Financing real options

Prof. André Farber

Solvay Business School

ESCP March 10,2000

Financing real options

financing new ventures
Financing new ventures:
  • For new ventures, financing needs are greater than initial capital available.
  • Outside financing required? How?
    • Debt ? principal source of outside financing for companies.
    • Equity ?
    • Convertible bonds (or bonds with warrants)?
  • An example:
  • Current value of company : 80, no debt, 100 shares
  • Financing needed: 70

Financing real options

slide3
Debt
  • Suppose it borrows by issuing a 2-year zero-coupon with a face value of 80.
  • If, at maturity, V*< 80: financial trouble….
  • Ultimate solution: bankruptcy, stockholders loose everything
  • Now, let’s look at the value of equity in 2 years:

V*<80 V*>80

Value of equity 0 V* - 80

  • This is like a call option: stocks of a levered company are similar to a call option on the company with a striking price equal to the face value of the debt.

Financing real options

pricing the equity and the debt
Pricing the equity and the debt
  • Let’s use Black Schole to value the equity and the debt
  • In our example: Maturity = 2, K = 100
  • Here: V = 150, r = 5%, Volatility = 40%
  • Using BS: C = 80 this is the market value of equity today
  • So : Equity = 80
  • Debt = 150 - 80 = 70 (thanks to Modigliani Miller)
  • Borrowing rate = 7.13%

Financing real options

more on debt value
More on debt value
  • Value of company = Value of equity + Value of debt
  • Now, remember put-call parity : S = C + PV(K) - P
  • Let’s map market value debt and equity onto option values

Value of company S Stock price

Value of equity C Call option

Value of debt PV(K) - P PV(Strike) - Put option

  • Why this put option?
    • Limited liability acts as an insurance for the stockholders
    • The amount that they borrow is the difference between
      • the value of a risk-free bond (72.4 in our example)
      • the value of a put option (2.4)

Financing real options

agency problems related to debt
Agency problems related to debt
  • We are now in a position to better understand conflicts of interests between stockholders and bonds holders:
    • incentive to take large risks
    • incentive toward underinvestment
    • milking the property
    • increasing debt

Financing real options

taking risk
Taking risk
  • By increasing the risk of the company, stockholders could fool bondholders by increasing the value of their stocks at the expense of the bonds
  • Remember, stocks similar to call option : value increasing function of volatility
  • Example:

 = 40%  = 50% 

Market value of equity 80.3 83.2 + 2.9

Market value of debt 69.7 66.8 -2.9

Financing real options

underinvesting
Underinvesting
  • Stockholders might decide not to invest in a project with positive NPV.
  • Example:
  • Following project has been identified: Cost = 49, NPV = 1
  • Going ahead with the project will increase the value to 200.
  • Should they go ahead if the project is equity-financed?

V = 150 V = 200 

Market value of equity 80.3 128.6 + 48.3

Market value of debt 69.7 71.4 +1.7

  • Stockholders loose: they invested 49 but the value of their equity increases only by 48.3
  • Bondholders gain : the risk on their debt has decreased

Financing real options

milking the property
Milking the property
  • Stockholders might be tempted to pay themselves a dividend at the expense of the bondholders
  • Example:
  • Stockholders sell assets worth 50 and use the proceed to pay a dividend. The value of the company drops to 100.

V = 150 V = 100 

Market value of equity 80.3 35.9 - 44.4

Market value of debt 69.7 64.1 -5.6

  • Stockholders gain: Dividend + Change in market value = + 5.6
  • Bondholders are 

Financing real options

borrowing
Borrowing
  • Another temptation in to increase debt.
  • Example:
  • Stockholders borrow an additional 50 (2-year zero-coupon with face value 60) and invest it in a project with NPV=0.

V = 150 V = 200 

Market value of equity 80.3 83.8 + 3.5

Market value of old debt 69.7 66.2 - 3.5

Market value of new debt - 50.0

Financing real options

controling conflicts of interests
Controling conflicts of interests
  • Bondholders should keep a close eye on the company
  • They will impose bond covenants
      • dividends
      • sales of assets
      • issuing new debt
      • minimum working capital
      • providing information to lender.

Financing real options

issuing equity
How to value the company ?

How to share the pie?

Issuing equity

New equity

Debt

Value of company

Financing real options

bonds with warrants
Bonds with Warrants
  • Give the right to its owner to buy a number of shares issued by a firm at a price set in advance.
  • Issued most frequently with bonds:
    • Price set for the "package" : Bond + Warrants
    • Traded separately after issue
  • Similar to call option but two main differences:
    • 1. Warrants are issued by the company:
      • If exercised, new stocks.are issued
    • 2.Proceeds of the sale of warrant goes to company

Financing real options

back to our example
Back to our example
  • V = 80 Equity = 80 (100 shares, price = 0.80/share)
  • Issue 50 bonds with 1 warrant, maturity 2 years.
  • Face value of bonds = 1.60/bond
  • Striking price of warrant = 1.60
  • Issue price = 1.40/ bond with warrant attached
  • Proceed of the issued:
  • If warrant exercised, the company
    • issues 50 new shares
    • collects the proceed of the issue 50 x 1.60 = 80

Financing real options

to exercise or not to exercise
To exercise or not to exercise..
  • Suppose V* = 300 at maturity
  • Value of company = VT - D + m * K = 300 - 80 + 80 = 300
  • Repartition of shares:
  • Number Fraction Value
  • Old 100 2/3 200
  • New 50 1/3 100
  • Total 150 300
  • Gain for warrant holders:
  • m * PT - m * K = 50 * 2.00 - 50 * 1.60
  • = 20 (0.40 / warrant)

Financing real options

when to exercise the warrants
When to exercise the warrants?
  • If they exercise their warrants, warrantholders will own a fraction q of the shares :
  • They will exercise if the value of their shares is greater than the amount to pay :

Exercise if : q (VT -D + m * K) > m * K

  • Warrant exercised if :q VT > (1 - q) m K + qD <=> VT > n * K-D
  • In our example :

1/3 (VT - 80 + 80) > 80 => VT > 240

Financing real options

warrants vs calls
Warrants vs calls
  • Value of warrants at maturity

V 180 210 240 270 300 330

50 Warrants 0 0 0 10 20 30

  • Now consider 100 call options on the shares of the company K = 2.4

V 180 210 240 270 300 330

100 Calls 0 0 0 30 60 90

  • At maturity, the 50 warrants are worth 1/3 of the value of the 100 calls

50 WT = (1/3)  Max(0, VT - 240)

  • More generally : m * WT = q * MAX ( 0, VT -D - n * K)
  • with q = m/(n+m)

Financing real options

valuing a warrant
Valuing a warrant
  • Step 1: Value n calls on the company using BS
    • (in our example: S=150, K=240, Maturity = 2, r = 5%,  = 40%)
    • Value of 100 calls = 15.41
  • Step 2: Calculate value of 1 warrant by dividing by m
    • Value of 50 warrant = 1/3 x 15.41 = 5.13
    • Value of 1 warrant = 5.13/50 = 0.10

Financing real options

bonds with warrants at maturity
Bonds with warrants at maturity

Financing real options