Question

Company “AIBM” has debt with a market value of £2,500,000 and equity with a market value of £5,500,000. The financial management estimates that the company’s shares have a beta of 1.85. The risk premium on the market is 8%, and the current Treasury bill rate is 5%. Debt is risk-free, and company “AIBM” has a corporate tax rate of 35%. Company “AIBM” is now considering whether investing in two new independent projects X and Y. Each project has an expected life of 6 years. Project X requires an initial cash outflow of £100,000, and subsequent annual cash inflows of £50,000 (year 1), £60,000 (year 2), £50,000 (year 3), £60,000 (year 4), £100,000 (year 5), and £50,000 (year 6). Project Y requires an initial cash outflow of £100,000, and subsequent annual cash inflows of £40,000 (year 1), £100,000 (year 2), £30,000 (year 3), £50,000 (year 4), £50,000 (year 5), and £50,000 (year 6). Both projects X and Y are similar to the company’s existing operations.

Required:

A. Calculate the beta of the assets of company “AIBM”. [5 marks] (the answer is 1.27)

B. Calculate the cost of equity capital and the weighted average cost of capital (WACC) after tax of company “AIBM”, assuming validity of the capital asset pricing model (CAPM). [8 marks] (answers: cost of equity capital is 0.193 and WACC after tax is unknown)

C. Calculate the net present value (NPV) of projects X and Y, and discuss which project(s) should be accepted according to the NPV method. [10 marks]

D. Calculate the profitability index (PI) of projects X and Y. Which project(s) should be accepted according to the PI method? [5 marks]

E. Introduce the notion of “average accounting return” (AAR) and illustrate strengths and weaknesses of the AAR method within the framework of strategic investment appraisal decisions.

Answer #1

As per rules I will answer the first 4 subparts of the question

1: MV of company = Debt + Equity

= 2500,000+ 5500,000

= $8000,000

Beta= Beta of equity*Equity/MV + Beta of debt*Debt/ MV

=1.85*5500,000/ 8000,000 + 0

= 1.27

2: Cost of equity = Rf+ Beta of equity*Risk premium

= 5%+ 1.85*8%

=19.8%

3: WACC= Cost of equity* Equity/MV + Cost of debt*(1-Tax)*Debt/ MV

=0.198*5500,000/8000,000 + (5%*(1-0.35)*2500,000/ 8000,000

=14.63%

Years | Project X | Y |

0 | -100000 | -100000 |

1 | 50000 | 40000 |

2 | 60000 | 100000 |

3 | 50000 | 30000 |

4 | 60000 | 50000 |

5 | 100000 | 50000 |

6 | 50000 | 50000 |

NPV | $129,789.69 | $107,174.87 |

Accept Project X since it has higher NPV.

WORKINGS

Question
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Year
K’000
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