Question Tag: CAPM

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  • 8 Marks

AFM – Nov 2016 – L3 – Q3a – Sources of finance and cost of capital

Calculate the cost of equity for Sunland Co using the Capital Asset Pricing Model (CAPM) with a focus on deriving beta from industry data.

a) The directors of Sunland Company, a company which has 75% of its operations in the retail
sector and 25% in manufacturing, are trying to derive the firm’s cost of equity. However, since
the company is not listed, it has been difficult to determine an appropriate beta factor. The
following information was researched:

  •  Retail industry – quoted retailers have an average equity beta of 1.20, and an average
    gearing ratio of 20:80 (debt: equity).
  • Manufacturing industry – quoted manufacturers have an average equity beta of 1.45 and
    an average gearing ratio of 45:55 (debt: equity).
  • The risk free rate is 3% and the equity risk premium is 6%.
  • Tax on corporate profits is 30%.
  •  Sunland Co has gearing ratio of 50% debt and 50% equity by market values. Assume that
    the risk on corporate debt is negligible.

Required:
Calculate the cost of equity of Sunland Company using the Capital Asset Pricing Model.

Step 1: Calculate asset beta for the retail and manufacturing industries

  • Retail industry asset beta:
    Asset beta = Equity beta × [Equity / (Equity + Debt × (1 – Tax rate))]
    = 1.20 × [80 / (80 + 20 × (1 – 0.30))]
    = 1.20 × [80 / (80 + 14)]
    = 1.20 × 0.8511
    = 1.0213
  • Manufacturing industry asset beta:
    Asset beta = 1.45 × [55 / (55 + 45 × (1 – 0.30))]
    = 1.45 × [55 / (55 + 31.5)]
    = 1.45 × 0.6356
    = 0.9216

Step 2: Calculate weighted asset beta for Sunland Co
Weighted asset beta = (0.75 × Retail asset beta) + (0.25 × Manufacturing asset beta)
= (0.75 × 1.0213) + (0.25 × 0.9216)
= 0.7660 + 0.2304
= 0.9964

Step 3: Re-gear the asset beta to calculate Sunland Co’s equity beta
Equity beta = Asset beta × [1 + (Debt / Equity) × (1 – Tax rate)]
= 0.9964 × [1 + (50 / 50) × (1 – 0.30)]
= 0.9964 × [1 + 1 × 0.70]
= 0.9964 × 1.70
= 1.694

Step 4: Calculate the cost of equity using CAPM
Cost of equity = Risk-free rate + Equity beta × (Market risk premium)
= 3% + 1.694 × 6%
= 3% + 10.164%
= 13.164%

Thus, the cost of equity for Sunland Co is 13.16%.

  • 20 Marks

AFM – Nov 2017 – L3 – Q2 – Sources of finance and cost of capital

Calculation of the cost of capital using the WACC and CAPM methods for a company and discussing when to use the cost of equity or WACC for discounting.

Animal Farm Product Ltd, (AFP), a manufacturer of veterinary medicines for farm animals, wishes to estimate its current cost of capital.

The following figures have been extracted from their most recent accounts:

Other relevant data:

  • The current market value of AFP’s ordinary shares is GH¢12.50 per share cum-dividend. AFP’s beta is 1.4, the risk-free rate is 3%, and the return on the SEC index (the market proxy) is 8%. An annual dividend of GH¢800,000 is due for payment shortly.
  • The 8% debentures are irredeemable and are trading at a current market value of GH¢106.00, a GH¢6.00 premium over their issue price of GH¢100.00. Semi-annual interest of GH¢4 million has just been paid on the debentures.
  • The 6% preference shares are trading at a current market value of GH¢6.00, a GH¢1 above their issue price of GH¢5.00. Interest has just been paid on these preference shares.
  • There have been no issues or redemptions of ordinary shares or debentures during the past five years, and the corporation tax rate remains at 12.5%. Assume that tax relief on the debenture interest arises at the same time as the interest payment.

Required:

a) Calculate the cost of capital that AFP should use as a discount rate when appraising new marginal investment opportunities. (11 marks)

b) Explain when firms should discount projects using:

  • The cost of equity;
  • The WACC instead; and
  • When should they use neither? You may use the information and your results in part (a) as examples. (6 marks)

c) Discuss what type of covenants might be attached to bonds. (3 marks)

 

Cost of Capital Calculation

Cost of Equity (Using CAPM):

Cost of Preference Shares:

  • Dividend = 6% of GH¢5 = GH¢0.30
  • Market price = GH¢6.00

Cost of Preference Shares=0.30 / 6.00  = 5%

Market Value of Components:

b) When to Use Cost of Equity or WACC:

  • Firms should discount projects using cost of equity when they have no debt in their capital structure or when the project being evaluated is very similar to existing equity-financed operations.
  • WACC should be used when firms are considering projects that reflect their existing mix of debt and equity financing. In AFP’s case, the WACC of 7.85% is appropriate for evaluating marginal investments.
  • Neither cost of equity nor WACC should be used when a firm is considering a project significantly different from its current operations or when the investment would alter the firm’s financial structure.

c) Types of Covenants Attached to Bonds:

  • Financial Covenants: These may include restrictions on the company’s financial ratios, such as maintaining a minimum interest coverage ratio or maximum debt-to-equity ratio.
  • Asset Covenants: These restrict the disposal of significant assets without bondholder approval.
  • Dividend Covenants: These limit dividend payments to ensure that sufficient funds are retained to meet debt obligations.
  • 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

  • 10 Marks

FM – Nov 2020 – L2 – Q1b – Cost of capital | Portfolio theory and the capital asset pricing model (CAPM)

Calculate the appropriate discount rate for a new subsidiary in the U.S. using CAPM and Modigliani-Miller Proposition II.

The directors of Fameko Ltd (Fameko), a courier delivery services company based in Ghana, are considering a proposal for setting up a subsidiary in the United States of America to provide courier services in North America. The capital of this new subsidiary will be structured as 20% equity and 80% debt.

The directors are not sure of what would be an appropriate discount rate for appraising the North American business. You have been asked to recommend an appropriate discount rate for this project. You have gathered the following information for this exercise.

  • Competition in the U.S. Courier industry:
    The U.S. courier services industry is highly competitive. If Fameko sets up in the U.S., its main competitor will be ExFed Corporation. ExFed’s capital structure is 70% equity and 30% debt.
  • Market risk:
    The following statistics have been computed from historical excess returns on the equity stock of ExFed Corporation and that on the S&P 500 Index (a proxy for the market portfolio):
S&P 500 Index ExFed Equity Stock
Average return 0.0628 0.0321
Standard Deviation 0.1875 0.1521
Sample Variance 0.0352 0.0231
Kurtosis -1.4335 -1.1121
Skewness -0.2178 -0.1601

You analyzed the correlation between the excess returns on ExFed and excess returns on the S&P 500 Index and obtained a correlation coefficient of 0.91.

  • The annual risk-free rate and market return:
    The annual rate of interest on the 10-year U.S. Treasury bond is 2.1%. The expected return on the S&P 500 Index is 7%.
  • Taxation:
    ExFed pays corporate income tax at the rate of 30%. However, the effective corporate income tax rate on profits from Fameko’s North American operations will be 35%.

Required:

i) Compute the equity beta of ExFed. (3 marks)

ii) Derive an appropriate equity beta for Fameko’s U.S. subsidiary. (4 marks)

iii) Using the capital asset pricing model or the Modigliani and Miller Proposition II with tax, compute an appropriate cost of equity for Fameko’s U.S. subsidiary. (3 marks)

i) Equity beta:

ii) Appropriate equity beta for Fameko’s subsidiary:

Since Fameko’s subsidiary would be carrying out a similar business, the level of business risk will be the same as that of ExFed. However, since the capital structure of the subsidiary will differ from that of ExFed, the financial risk will also differ. We can derive an appropriate equity beta for Fameko’s subsidiary by un-gearing the equity beta of ExFed and then re-gearing it to reflect the capital structure of the subsidiary:

iii) The appropriate required rate of return on the equity of the Ghana subsidiary:

Using CAPM:

  • 6 Marks

FM – NOV 2015 – L2 – Q5d – Portfolio theory and the capital asset pricing model (CAPM)

Calculate the expected return and the value of shares using the CAPM and the dividend discount model.

 I, me, and myself have shares in a company which paid a dividend of GH₵10 to its shareholders. The shares have a beta factor of 1.2. The risk-free rate of return and the market return are 15% and 20% respectively.

Required:
i. Calculate the return on the shares. (4 marks)
ii. Calculate the value of the shares. (2 marks)

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