CIMA F3 Syllabus B. Sources of long term funds - Cost of equity and WACC (M&M) - Notes ^{2 / 4}

Formulae

1. Value of company

   Vg = Vu

2. Cost of equity

   Keg = Keu+(Keu−Kd) Vd/Ve

3. WACC

   WACCg = WACCu (Keu)

Formulae - given in the exam

Where:

• Vg = value of geared company
  Vu = value of ungeared company
  TB = Tax on debt
  Keg = 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
  t = tax

Example 1

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)

Corporation tax at 30%.

Assume that the companies are in all other respects identical.

Calculate the value of Milk’s plc.

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

Example 2

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

Calculate the new Ke, after the buyback.

• Keg = Keu + (Keu - Kd) x [ VD (1 - t) / Ve]

  Keg = 15 + (15 - 10) x [1 (1 - 0.20) / 1]
  Keg = 15 + 5 x 0.80
  Keg = 19%

Example 3

A Company has:

- an ungeared cost of equity of 10%
- market value of equity of $200
- market value of debt of $100
- a tax rate of 20%.

Required:

Calculate WACC using M&M formulae

• WACC = Keu x [1 - ( Vdt / (Ve + Vd))]

  WACC = 10% x  [ 1 - ( 0.2 x 100 / ( 200 + 100))]
  WACC = 9.3%