Chapter 5 – Cost of Capital Subject Coordinator

SECTION A – MULTIPLE CHOICE QUESTIONS

1. Which of the following is not part of a firm’s capital structure?
   (a) Assets
   (b) Debt
   (c) Equity
   (d) None of the above. (I.e. all of the above are part of the firm’s capital structure.)
2. Which of the following needs to be adjusted for tax in calculating a firm’s weighted average cost of capital?
   (a) The cost of debt
   (b) The cost of preference shares
   (c) The cost of ordinary shares
   (d) All of the above.
3. Which of the following is not an appropriate method of determining the cost of debt for a firm in calculating its
   WACC?
   (a) The debt‐rating approach
   (b) The coupon rate
   (c) The yield to maturity
   (d) None of the above. (I.e. All of the above are appropriate methods of determining the cost of debt for a
   firm in calculating its WACC.)
4. Which of the following is not something that must be true in order for a firm to use its WACC for project
   evaluation?
   (a) The WACC must have been calculated using market values for elements of the capital structure.
   (b) The WACC must be less than the project’s IRR.
   (c) The risk of the project must be similar to the risk of the frim overall.
   (d) The firm must intend to raise new capital based on its existing debt/equity ratio.
5. Firm E is planning takeover of Firm F. What discount rate should Firm E use in calculating the NPV of this
   investment?
   (a) Firm E’s WACC
   (b) Firm F’s WACC
   (c) The weighted average of Firm E’s WACC and Firm F’s WACC
   (d) None of the above.
6. If a firm has divisions in different industries, with different risks, what should is use to evaluate projects in a
   given division?
   (a) The firm’s overall WACC.
   (b) The cost of capital for that division.
   (c) Either (a) or (b) – whichever is lower.
   (d) Either (a) or (b) – whichever is higher.
   La Trobe University 4
   SECTION B – SHORT ANSWER QUESTIONS
7. Should you use book values or market values in calculating the WACC for a firm? Why?
8. What assumption regarding the risk of a project do we make if we use the firm’s WACC to evaluate the project,
   and why is this assumption important?
9. What assumption regarding the capital structure of a firm do we make if we use the firm’s WACC to evaluate
   its projects, and why is this assumption important?
   La Trobe University 5
   SECTION C – ESSAY QUESTIONS
10. What is a firm’s WACC, what does it represent, how is it used in project evaluation, and what assumptions do
    we make in using the firm’s WACC to evaluate a project the firm is planning to undertake?
    La Trobe University 6
    SECTION D – CALCULATION QUESTIONS
    Refer to the following information in answering Questions 11 to 21.
    The following information relates to the capital structure of XYZ Ltd.
     The firm has issued bonds with a face value (book value) of $10 million.
     The bonds pay a 7.5% annual coupon and have 8 years to maturity.
     The firm has an A+ debt rating.
     There are 1 million preference shares outstanding, which have a book value of $2 per share
    and which are trading for $2.40 per share.
     The preference shares pay an annual dividend of $0.30 per share.
     There are 16 million ordinary shares outstanding, which have a book value of $0.50 per
    share and which are currently priced at $0.80 per share.
     The ordinary shares are expected to pay a dividend next year of $0.10 per share. This
    dividend is expected to grow at a constant rate of 1.6% in perpetuity.
     The firm’s ordinary shares have a beta of 1.45.
     The yield on long‐term government bonds is 2.5% p.a.
     The long‐term market risk premium is 8% p.a.
     The corporate tax rate is 30%.
    The table at right is an extract from S&P’s latest
    debt rating report, showing the spread for debt
    with different debt ratings. (The spread is the
    amount by which the yield on the debt exceeds
    the risk‐free rate.)
    Debt rating Spread
    AA+ 3.2%
    AA 3.4%
    AA‐ 3.6%
    A+ 3.8%
11. What is the market value of debt?
12. What is the market value of preference shares?
13. What is the market value of ordinary shares?
    La Trobe University 7
14. What is the before‐tax cost of debt?
15. What is the cost of preferences shares?
16. What is the cost of ordinary shares based on the CAPM?
17. What is the cost of ordinary shares based on the Constant Dividend Growth Model?
18. What is XYZ’s weighted average cost of capital?
    La Trobe University 8
    Refer to the following information in answering Questions 19 to 21.
    This information is to be used in addition to the information provided earlier regarding XYZ Ltd.
    XYZ Ltd is a multidivisional firm, with operations in the
    mining, aerospace and publishing industries. The table at
    right gives the beta for typical firms operating solely within
    those industries and can be assumed to be an appropriate
    beta for the firm’s operation in those industries.
    Division Beta
    Mining 1.3
    Aerospace 0.9
    Publishing 1.7
    XYZ Ltd is considering three independent
    projects – one in each division. The table at right
    shows the internal rate of return for each of
    these projects.
    Project Division IRR
    A Mining 11.5%
    B Aerospace 10.5%
    C Publishing 17.5%
19. What is the cost of capital for each division?*
20. Which projects would be accepted if the firm’s used its overall WACC to evaluate the projects?*
21. Which projects would be accepted if the firm’s used divisional costs of capital to evaluate the projects?
    La Trobe University 9
    Hint, tips, advice and guidance
    SECTION D – CALCULATION QUESTIONS
    Refer to the following information in answering Questions 19 to 21.
    This information is to be used in addition to the information provided earlier regarding XYZ Ltd.
    XYZ Ltd is a multidivisional firm, with operations in the
    mining, aerospace and publishing industries. The table at
    right gives the beta for typical firms operating solely within
    those industries and can be assumed to be an appropriate
    beta for the firm’s operation in those industries.
    Division Beta
    Mining 1.3
    Aerospace 0.9
    Publishing 1.7
    XYZ Ltd is considering three independent
    projects – one in each division. The table at right
    shows the internal rate of return for each of
    these projects.
    Project Division IRR
    A Mining 11.5%
    B Aerospace 10.5%
    C Publishing 17.5%
22. What is the cost of capital for each division?
    Use the CAPM and the beta for each division.
23. Which projects would be accepted if the firm’s used its overall WACC to evaluate the projects?
    Use the IRR decision rule. Compare the IRR of each project to the required rate of return.
    La Trobe University 10
    Solutions
    SECTION A – MULTIPLE CHOICE QUESTIONS
24. Which of the following is not part of a firm’s capital structure?
    (a) Assets
    (b) Debt
    (c) Equity
    (d) None of the above. (I.e. all of the above are part of the firm’s capital structure.)
25. Which of the following needs to be adjusted for tax in calculating a firm’s weighted average cost of capital?
    (a) The cost of debt
    (b) The cost of preference shares
    (c) The cost of ordinary shares
    (d) All of the above.
26. Which of the following is not an appropriate method of determining the cost of debt for a firm in calculating its
    WACC?
    (a) The debt‐rating approach
    (b) The coupon rate
    (c) The yield to maturity
    (d) None of the above. (I.e. All of the above are appropriate methods of determining the cost of debt for a
    firm in calculating its WACC.)
27. Which of the following is not something that must be true in order for a firm to use its WACC for project
    evaluation?
    (a) The WACC must have been calculated using market values for elements of the capital structure.
    (b) The WACC must be less than the project’s IRR.
    (c) The risk of the project must be similar to the risk of the frim overall.
    (d) The firm must intend to raise new capital based on its existing debt/equity ratio.
28. Firm E is planning takeover of Firm F. What discount rate should Firm E use in calculating the NPV of this
    investment?
    (a) Firm E’s WACC
    (b) Firm F’s WACC
    (c) The weighted average of Firm E’s WACC and Firm F’s WACC
    (d) None of the above.
29. If a firm has divisions in different industries, with different risks, what should is use to evaluate projects in a
    given division?
    (a) The firm’s overall WACC.
    (b) The cost of capital for that division.
    (c) Either (a) or (b) – whichever is lower.
    (d) Either (a) or (b) – whichever is higher.
    La Trobe University 11
    SECTION B – SHORT ANSWER QUESTIONS
30. Should you use book values or market values in calculating the WACC for a firm? Why?
     Market values
     The WACC is used to make decision about the future
     It is used to decide which projects the firm should undertake, and capital that needs to be acquired to
    invest in those projects must be obtained based on current market prices.
31. What assumption regarding the risk of a project do we make if we use the firm’s WACC to evaluate the project,
    and why is this assumption important?
     That the risk of the project is equal to the average risk of the firm’s current projects.
     The WACC is based on the riskiness of the firm (from the point of view of capital providers), which in
    turn is based on the riskiness of the projects undertaken by the firm.
     A project that differs in risk from the firm’s existing projects must be evaluated using a discount rate
    that reflects the risk of the project.
32. What assumption regarding the capital structure of a firm do we make if we use the firm’s WACC to evaluate
    its projects, and why is this assumption important?
     That the firm will maintain its current debt/equity ratio as it raises new capital.
     The WACC is based on the firm’s current debt/equity ratio. If this changes (because new capital is
    raised with a different proportion of debt to equity) this will change the WACC.
    La Trobe University 12
    SECTION D – CALCULATION QUESTIONS
    Refer to the following information in answering Questions 11 to 21.
    The following information relates to the capital structure of XYZ Ltd.
     The firm has issued bonds with a face value (book value) of $10 million.
     The bonds pay a 7.5% annual coupon and have 8 years to maturity.
     The firm has an A+ debt rating.
     There are 1 million preference shares outstanding, which have a book value of $2 per share
    and which are trading for $2.40 per share.
     The preference shares pay an annual dividend of $0.30 per share.
     There are 16 million ordinary shares outstanding, which have a book value of $0.50 per
    share and which are currently priced at $0.80 per share.
     The ordinary shares are expected to pay a dividend next year of $0.10 per share. This
    dividend is expected to grow at a constant rate of 1.6% in perpetuity.
     The firm’s ordinary shares have a beta of 1.45.
     The yield on long‐term government bonds is 2.5% p.a.
     The long‐term market risk premium is 8% p.a.
     The corporate tax rate is 30%.
    The table at right is an extract from S&P’s
    latest debt rating report, showing the spread
    for debt with different debt ratings. (The
    spread is the amount by which the yield on
    the debt exceeds the risk‐free rate.)
    Debt rating Spread
    AA+ 3.2%
    AA 3.4%
    AA‐ 3.6%
    A+ 3.8%
33. What is the market value of debt?
       
     8  8
    7.5% 10,000,000 $750,000
    2.5% 3.8% 6.3%
    1 1 1
    1 1
    750,000 1 1 1 10,000,000 $10,736,408
    0.063 1.063 1.063
    n n
    CPN
    y
    D CPN FV
    y y y
      
      
     
         
         
     
          
     
     
34. What is the market value of preference shares?
    P  $2.401,000,000  $2,400,000
35. What is the market value of ordinary shares?
    E  $0.8016,000,000  $12,800,000
36. What is the before‐tax cost of debt? 6.3% D r 
    La Trobe University 13
37. What is the cost of preferences shares?
    0.30 12.5%
    2.40
    P
    P
    P
    r Div
    P
      
38. What is the cost of ordinary shares based on the CAPM?
        0.025 1.450.08 14.1% E f Mkt f r  r  β E R  r   
39. What is the cost of ordinary shares based on the Constant Dividend Growth Model?
    1 0.10 0.016 14.1%
    E 0.80
    E
    r Div g
    P
        
40. What is XYZ’s weighted average cost of capital?
     
       
      
       
             
       
          
     
    % % 1 %
    0.141 12,800,000 0.125 2,400,000
    25,936,408 25,936,408
    0.063 1 0.3 10,736,408 9.94%
    25,936,408
    WACC E P D C r rE rP r T D
    Refer to the following information in answering Questions 19 to 21.
    This information is to be used in addition to the information provided earlier regarding XYZ Ltd.
    XYZ Ltd is a multidivisional firm, with operations in the
    mining, aerospace and publishing industries. The table at
    right gives the beta for typical firms operating solely within
    those industries and can be assumed to be an appropriate
    beta for the firm’s operation in those industries.
    Division Beta
    Mining 1.3
    Aerospace 0.9
    Publishing 1.7
    XYZ Ltd is considering three independent
    projects – one in each division. The table at
    right shows the internal rate of return for each
    of these projects.
    Project Division IRR
    A Mining 11.5%
    B Aerospace 10.5%
    C Publishing 17.5%
41. What is the cost of capital for each division?
        0.025 1.30.08 12.9% M f M Mkt f r  r  β E R  r   
        0.025 0.90.08 9.7% A f A Mkt f r  r  β E R  r   
        0.025 1.70.08 16.1% P f P Mkt f r  r  β E R  r   
42. Which projects would be accepted if the firm’s used its overall WACC
    to evaluate the projects?
43. Which projects would be accepted if the firm’s used divisional costs
    of capital to evaluate the projects?
    All projects
    Projects B and C