Topic: Theories of capital structure

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  • 4 Marks

AFM – May 2016 – L3 – Q2c – Sources of finance and cost of capital, Theories of capital structure

Calculate the cost of debt after tax for a discounted debenture issued by Brown Limited.

c) Ten years ago, Brown Limited issued GH¢2.5 million of 6% discounted debentures at GH¢98 per 100 nominal. The debentures are redeemable in 5 years from now at GH¢2 premium over nominal value. They are currently quoted at GH¢80 per debenture ex-interest. Brown Limited pays corporate tax at the rate of 30%.

You are required to calculate the cost of debt after tax.

(4 marks)

 

  • 3 Marks

AFM – May 2018 – L3 – Q1d – Theories of capital structure

Determining the required rate of return for Lime Spider Ltd’s shares using CAPM.

The market is currently yielding a return of 16% while Treasury bills are yielding 10%. Shares of Lime Spider Ltd have a covariance of 7.5 with the market, while the market has a variance of 4.5.

Required:
Determine the required rate of return for Lime Spider Ltd’s shares

Using the Capital Asset Pricing Model (CAPM):

  • Market return (Rm) = 16%
  • Risk-free rate (Rf) = 10%
  • Covariance of Lime Spider shares with the market (CovLs) = 7.5
  • Market variance (σ²m) = 4.5

Step 1: Calculate Beta (β):
β = CovLs / σ²m
= 7.5 / 4.5
= 1.67

Step 2: Apply CAPM formula:
E(RLs)=Rf+β(Rm−Rf)E(R_{Ls}) = Rf + β (Rm – Rf)
= 10% + 1.67 × (16% – 10%)
= 10% + 1.67 × 6%
= 10% + 10.02%
= 20.02%

Conclusion:
The required rate of return for Lime Spider Ltd’s shares is 20%.

OR

  • 5 Marks

AFM – May 2018 – L3 – Q1c – Theories of capital structure

Calculating the WACC for different financing options and determining the optimal capital structure.

Paisley Brothers Ltd, a company producing loud paisley shirts, has a net operating income of GH¢20,000 and is faced with the following three options for how to structure its debt and equity:

i) Take no debt and pay shareholders a return of 9%.
ii) Borrow GH¢50,000 at 3% and pay shareholders an increased return of 10%.
iii) Borrow GH¢90,000 at 6% and pay a 13% return to shareholders.

Assuming no taxation and a 100% payout ratio:

Required:
Calculate the Weighted Average Cost of Capital (WACC) for each of the options and determine which method is optimal. (5 marks)

i) Option 1 (No Debt):

Income of GH¢20,000 is distributed to shareholders who require a return of 9%.

  • Market value of equity = GH¢20,000 / 0.09 = GH¢222,222
  • WACC = 9%

ii) Option 2 (GH¢50,000 Debt at 3%):

Interest on debt = GH¢50,000 × 3% = GH¢1,500
Dividends to shareholders = GH¢20,000 – GH¢1,500 = GH¢18,500

  • Required return of shareholders = 10%
  • Market value of equity = GH¢18,500 / 0.10 = GH¢185,000
  • Market value of debt = GH¢50,000
  • Total value of the company = GH¢185,000 + GH¢50,000 = GH¢235,000
  • WACC = (10% × GH¢185,000 + 3% × GH¢50,000) / GH¢235,000
    = (18,500 + 1,500) / 235,000
    = 8.51%

iii) Option 3 (GH¢90,000 Debt at 6%):

Interest on debt = GH¢90,000 × 6% = GH¢5,400
Dividends to shareholders = GH¢20,000 – GH¢5,400 = GH¢14,600

  • Required return of shareholders = 13%
  • Market value of equity = GH¢14,600 / 0.13 = GH¢112,308
  • Market value of debt = GH¢90,000
  • Total value of the company = GH¢112,308 + GH¢90,000 = GH¢202,308
  • WACC = (13% × GH¢112,308 + 6% × GH¢90,000) / GH¢202,308
    = (14,600 + 5,400) / 202,308
    = 9.9%

Conclusion:

The optimal capital structure is the one with the lowest WACC and highest market value. In this case, Option 2 is the optimal choice, with the lowest WACC of 8.51% and a total company value of GH¢235,000.

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