ACCA AFM Syllabus B. Advanced Investment Appraisal - Modigliani and Miller propositions - Notes ^{15 / 19}

Formulae

1. Proposition 1: value of company

   Vg = Vu

2. Proposition 2: cost of equity

   Keg = Keu+(Keu−Kd) Vd/Ve

3. Proposition 3: WACC

   WACCg = WACCu (Keu)

Formulae

1. Proposition 1: value of company

   Vg = Vu+Dt

   Dt = Tax on debt

2. Proposition 2: cost of equity

   Ke =  Keu + (1-T) x (Keu-Kd) x Vd/Ve

   Ke = cost of equity of a geared company, 
   Keu = cost of equity in an ungeared company
   Kd = cost of debt (pre-tax)
   Vd Ve = market value of debt & equity

   NB The formula is provided on the Formulae sheet.

3. Proposition 3: WACC

   WACCg = Keu (1 − (Vdt/( Ve + Vd))

Illustration

An ungeared company with a cost of equity of 15% is considering adjusting its gearing by taking out a loan at 10% and using it to buy back equity. 

After the buyback the ratio of the market value of debt to the market value of equity will be 1:1. Corporation tax is 20%.

Required

(a) Calculate the new Ke, after the buyback.
(b) Calculate and comment on the WACC after the buyback

• (a) Ke=15+(1-0.2)(15-10)x1=15+4=20%

• (b) WACC=(0.5x20)+(0.5x10x0.8)=10+4=14%

  The use of debt will bring benefit to the company because the lower WACC will enable future investments to bring greater wealth to the company's shareholders.

Example

Cow plc (an all equity company) has on issue 10,000,000 $1 ordinary shares at market value of $2.00 each.

Milk plc (a geared company) has on issue:
15,000,000 25p ordinary shares; and 
$5,000,000 10% debentures (quoted at 120)

Taking corporation tax at 30%, and assuming that:

1. The companies are in all other respects identical; and
2. The market value of Cow’s equity and the market value of Milk’s debt are “in equilibrium”.

Calculate the equilibrium price per share of Milk’s equity.

Solution

Vg = Vu+Dt

D = $5,000,000 x 120/100 = $6m

Vu = $10,000,000 x $2.00 = $20m

Dt = $6m x 30% = $1.8m

Vg = $20m + $1.8m = $21.8m

E = balancing figure ($21.8m - $6m) = $15.8m

Price per share = $15.8m / 15m = $1.05

Why do companies not attempt a 99.9% debt structure?

1. Bankruptcy costs

   The higher the level of gearing the greater the risk of bankruptcy with the associated “COSTS OF FINANCIAL DISTRESS”.

   Vg = Vu + Dt − Present value of costs of financial distress

2. Agency costs

   Costs of restrictive covenants to protect the interests of debt holders at high levels of gearing.

3. Tax exhaustion

   The value of the company will be reduced if advantage cannot be taken of the tax relief associated with debt interest.

4. Debt capacity

   Generally loans must be secured against a company’s assets and clearly some assets (eg property) provide better security for loans than other assets (eg high- tech equipment which may become obsolescent overnight). 

   The depth of the asset’s second hand market and its rate of depreciation are important characteristics.