A company has:

- 100 million ordinary shares outstanding which are trading at a price of $5 each. Market analysts estimated that the company's ordinary stock has a beta of 1.5. The risk-free rate is 5% and the market return is 10%.
- 1 million preferred shares which have a face (or par) value of $100 and pay a constant annual dividend of 9% of par. The next dividend will be paid in one year. Assume that all preference dividends will be paid when promised. They currently trade at a price of $90 each.
- Debentures that have a total face value of $200 million and a yield to maturity of 6% per annum. They are publicly traded and their market price is equal to 110% of their face value.

The corporate tax rate is 30%. All returns and yields are given as effective annual rates.

What is the company's after-tax Weighted Average Cost of Capital (WACC)? Assume a classical tax system.

**Question 207** income and capital returns, bond pricing, coupon rate, no explanation

For a bond that pays fixed semi-annual coupons, how is the annual coupon rate defined, and how is the bond's annual income yield from time 0 to 1 defined mathematically?

Let: ##P_0## be the bond price now,

##F_T## be the bond's face value,

##T## be the bond's maturity in years,

##r_\text{total}## be the bond's total yield,

##r_\text{income}## be the bond's income yield,

##r_\text{capital}## be the bond's capital yield, and

##C_t## be the bond's coupon at time t in years. So ##C_{0.5}## is the coupon in 6 months, ##C_1## is the coupon in 1 year, and so on.

Value the following business project to manufacture a new product.

Project Data | ||

Project life | 2 yrs | |

Initial investment in equipment | $6m | |

Depreciation of equipment per year | $3m | |

Expected sale price of equipment at end of project | $0.6m | |

Unit sales per year | 4m | |

Sale price per unit | $8 | |

Variable cost per unit | $5 | |

Fixed costs per year, paid at the end of each year | $1m | |

Interest expense per year | 0 | |

Tax rate | 30% | |

Weighted average cost of capital after tax per annum | 10% | |

**Notes**

- The firm's current assets and current liabilities are $3m and $2m respectively right now. This net working capital will not be used in this project, it will be used in other unrelated projects.

Due to the project, current assets (mostly inventory) will grow by $2m initially (at t = 0), and then by $0.2m at the end of the first year (t=1).

Current liabilities (mostly trade creditors) will increase by $0.1m at the end of the first year (t=1).

At the end of the project, the net working capital accumulated due to the project can be sold for the same price that it was bought. - The project cost $0.5m to research which was incurred one year ago.

**Assumptions**

- All cash flows occur at the start or end of the year as appropriate, not in the middle or throughout the year.
- All rates and cash flows are real. The inflation rate is 3% pa.
- All rates are given as effective annual rates.
- The business considering the project is run as a 'sole tradership' (run by an individual without a company) and is therefore eligible for a 50% capital gains tax discount when the equipment is sold, as permitted by the Australian Tax Office.

What is the expected net present value (NPV) of the project?

A company announces that it will pay a dividend, as the market expected. The company's shares trade on the stock exchange which is open from 10am in the morning to 4pm in the afternoon each weekday. When would the share price be expected to fall by the amount of the dividend? Ignore taxes.

The share price is expected to fall during the:

In the dividend discount model:

### P_0= \frac{d_1}{r-g} ###

The pronumeral ##g## is supposed to be the:

Acquirer firm plans to launch a takeover of Target firm. The deal is expected to create a present value of synergies totaling $**105** million. A **40**% **scrip** and **60**% **cash** offer will be made that pays the fair price for the target's shares plus **75**% of the total synergy value. The cash will be paid out of the firm's cash holdings, no new debt or equity will be raised.

Firms Involved in the Takeover | ||

Acquirer | Target | |

Assets ($m) | 6,000 | 700 |

Debt ($m) | 4,800 | 400 |

Share price ($) | 40 | 20 |

Number of shares (m) | 30 | 15 |

Ignore transaction costs and fees. Assume that the firms' debt and equity are fairly priced, and that each firms' debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money.

Calculate the merged firm's share price and total number of shares after the takeover has been completed.

**Question 433** Merton model of corporate debt, real option, option, no explanation

A risky firm will last for one period only (t=0 to 1), then it will be liquidated. So it's assets will be sold and the debt holders and equity holders will be paid out in that order. The firm has the following quantities:

##V## = Market value of assets.

##E## = Market value of (levered) equity.

##D## = Market value of zero coupon bonds.

##F_1## = Total face value of zero coupon bonds which is promised to be paid in one year.

What is the payoff to equity holders at maturity, assuming that they keep their shares until maturity?

Find the cash flow from assets (CFFA) of the following project.

One Year Mining Project Data | ||

Project life | 1 year | |

Initial investment in building mine and equipment | $9m | |

Depreciation of mine and equipment over the year | $8m | |

Kilograms of gold mined at end of year | 1,000 | |

Sale price per kilogram | $0.05m | |

Variable cost per kilogram | $0.03m | |

Before-tax cost of closing mine at end of year | $4m | |

Tax rate | 30% | |

Note 1: Due to the project, the firm also anticipates finding some rare diamonds which will give before-tax revenues of $1m at the end of the year.

Note 2: The land that will be mined actually has thermal springs and a family of koalas that could be sold to an eco-tourist resort for an after-tax amount of $3m right now. However, if the mine goes ahead then this natural beauty will be destroyed.

Note 3: The mining equipment will have a book value of $1m at the end of the year for tax purposes. However, the equipment is expected to fetch $2.5m when it is sold.

Find the project's CFFA at time zero and one. Answers are given in millions of dollars ($m), with the first cash flow at time zero, and the second at time one.

A $**100** stock has a continuously compounded expected **total** return of **10**% pa. Its **dividend** yield is **2**% pa with continuous compounding. What do you expect its price to be in **one** year?

Which of the following is **NOT** a valid method for estimating the beta of a company's stock? Assume that markets are efficient, a long history of past data is available, the stock possesses idiosyncratic and market risk. The variances and standard deviations below denote total risks.