A manufacturing company is considering a new project in the more risky services industry. The cash flows from assets (CFFA) are estimated for the new project, with interest expense excluded from the calculations. To get the levered value of the project, what should these unlevered cash flows be discounted by?

Assume that the manufacturing firm has a target debt-to-assets ratio that it sticks to.

A firm is considering a new project of similar risk to the current risk of the firm. This project will expand its existing business. The cash flows of the project have been calculated assuming that there is no interest expense. In other words, the cash flows assume that the project is all-equity financed.

In fact the firm has a target debt-to-equity ratio of 1, so the project will be financed with 50% debt and 50% equity. To find the levered value of the firm's assets, what discount rate should be applied to the project's unlevered cash flows? Assume a classical tax system.

The US firm Google operates in the online advertising business. In 2011 Google bought Motorola Mobility which manufactures mobile phones.

Assume the following:

- Google had a 10% after-tax weighted average cost of capital (WACC) before it bought Motorola.
- Motorola had a 20% after-tax WACC before it merged with Google.
- Google and Motorola have the same level of gearing.
- Both companies operate in a classical tax system.

You are a manager at Motorola. You must value a project for making mobile phones. Which method(s) will give the correct valuation of the mobile phone manufacturing project? Select the most correct answer.

The mobile phone manufacturing project's:

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 new company's Firm Free Cash Flow (FFCF, same as CFFA) is forecast in the graph below.

To value the firm's assets, the terminal value needs to be calculated using the perpetuity with growth formula:

###V_{\text{terminal, }t-1} = \dfrac{FFCF_{\text{terminal, }t}}{r-g}###

Which point corresponds to the best time to calculate the terminal value?

An old company's Firm Free Cash Flow (FFCF, same as CFFA) is forecast in the graph below.

To value the firm's assets, the terminal value needs to be calculated using the perpetuity with growth formula:

###V_{\text{terminal, }t-1} = \dfrac{FFCF_{\text{terminal, }t}}{r-g}###

Which point corresponds to the best time to calculate the terminal value?

A new company's Firm Free Cash Flow (FFCF, same as CFFA) is forecast in the graph below.

To value the firm's assets, the terminal value needs to be calculated using the perpetuity with growth formula:

###V_{\text{terminal, }t-1} = \dfrac{FFCF_{\text{terminal, }t}}{r-g}###

Which point corresponds to the best time to calculate the terminal value?

**Question 345** capital budgeting, break even, NPV

Project Data | ||

Project life | 10 yrs | |

Initial investment in factory | $10m | |

Depreciation of factory per year | $1m | |

Expected scrap value of factory at end of project | $0 | |

Sale price per unit | $10 | |

Variable cost per unit | $6 | |

Fixed costs per year, paid at the end of each year | $2m | |

Interest expense per year | 0 | |

Tax rate | 30% | |

Cost of capital per annum | 10% | |

**Notes**

- The firm's current liabilities are forecast to stay at $0.5m. The firm's current assets (mostly inventory) is currently $1m, but is forecast to grow by $0.1m at the end of each year due to the project.

At the end of the project, the current assets accumulated due to the project can be sold for the same price that they were bought. - A marketing survey was used to forecast sales. It cost $1.4m which was just paid. The cost has been capitalised by the accountants and is tax-deductible over the life of the project, regardless of whether the project goes ahead or not. This amortisation expense is not included in the depreciation expense listed in the table above.

**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.

Find the break even unit production (Q) per year to achieve a zero *Net Income* (NI) and *Net Present Value* (NPV), respectively. The answers below are listed in the same order.

**Question 370** capital budgeting, NPV, interest tax shield, WACC, CFFA

Project Data | ||

Project life | 2 yrs | |

Initial investment in equipment | $600k | |

Depreciation of equipment per year | $250k | |

Expected sale price of equipment at end of project | $200k | |

Revenue per job | $12k | |

Variable cost per job | $4k | |

Quantity of jobs per year | 120 | |

Fixed costs per year, paid at the end of each year | $100k | |

Interest expense in first year (at t=1) | $16.091k | |

Interest expense in second year (at t=2) | $9.711k | |

Tax rate | 30% | |

Government treasury bond yield | 5% | |

Bank loan debt yield | 6% | |

Levered cost of equity | 12.5% | |

Market portfolio return | 10% | |

Beta of assets | 1.24 | |

Beta of levered equity | 1.5 | |

Firm's and project's debt-to-equity ratio |
25% | |

**Notes**

- The project will require an immediate purchase of $
**50**k of inventory, which will all be sold at cost when the project ends. Current liabilities are negligible so they can be ignored.

**Assumptions**

- The debt-to-equity ratio will be kept constant throughout the life of the project. The amount of interest expense at the end of each period has been correctly calculated to maintain this constant debt-to-equity ratio. Note that interest expense is different in each year.
- Thousands are represented by 'k' (kilo).
- 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 nominal. The inflation rate is 2% pa.
- All rates are given as effective annual rates.
- The 50% capital gains tax discount is not available since the project is undertaken by a firm, not an individual.

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

The hardest and most important aspect of business project valuation is the estimation of the:

A pharmaceutical firm has just discovered a valuable new drug. So far the news has been kept a secret.

The net present value of making and commercialising the drug is $**200** million, but $**600** million of bonds will need to be issued to fund the project and buy the necessary plant and equipment.

The firm will release the news of the discovery and bond raising to shareholders simultaneously in the same announcement. The bonds will be issued shortly after.

Once the announcement is made and the bonds are issued, what is the expected increase in the value of the firm's assets (ΔV), market capitalisation of debt (ΔD) and market cap of equity (ΔE)?

The triangle symbol is the Greek letter capital delta which means change or increase in mathematics.

Ignore the benefit of interest tax shields from having more debt.

Remember: ##ΔV = ΔD+ΔE##

The CAPM can be used to find a business's expected opportunity cost of capital:

###r_i=r_f+β_i (r_m-r_f)###

What should be used as the risk free rate ##r_f##?

**Question 418** capital budgeting, NPV, interest tax shield, WACC, CFFA, CAPM

Project Data | ||

Project life | 1 year | |

Initial investment in equipment | $8m | |

Depreciation of equipment per year | $8m | |

Expected sale price of equipment at end of project | 0 | |

Unit sales per year | 4m | |

Sale price per unit | $10 | |

Variable cost per unit | $5 | |

Fixed costs per year, paid at the end of each year | $2m | |

Interest expense in first year (at t=1) | $0.562m | |

Corporate tax rate | 30% | |

Government treasury bond yield | 5% | |

Bank loan debt yield | 9% | |

Market portfolio return | 10% | |

Covariance of levered equity returns with market | 0.32 | |

Variance of market portfolio returns | 0.16 | |

Firm's and project's debt-to-equity ratio |
50% | |

**Notes**

- Due to the project, current assets will increase by $
**6**m now (t=0) and fall by $**6**m at the end (t=1). Current liabilities will not be affected.

**Assumptions**

- The debt-to-equity ratio will be kept constant throughout the life of the project. The amount of interest expense at the end of each period has been correctly calculated to maintain this constant debt-to-equity ratio.
- Millions are represented by 'm'.
- All rates and cash flows are real. The inflation rate is 2% pa. All rates are given as effective annual rates.
- The project is undertaken by a firm, not an individual.

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

**Question 419** capital budgeting, NPV, interest tax shield, WACC, CFFA, CAPM, no explanation

Project Data | ||

Project life | 1 year | |

Initial investment in equipment | $6m | |

Depreciation of equipment per year | $6m | |

Expected sale price of equipment at end of project | 0 | |

Unit sales per year | 9m | |

Sale price per unit | $8 | |

Variable cost per unit | $6 | |

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

Interest expense in first year (at t=1) | $0.53m | |

Tax rate | 30% | |

Government treasury bond yield | 5% | |

Bank loan debt yield | 6% | |

Market portfolio return | 10% | |

Covariance of levered equity returns with market | 0.08 | |

Variance of market portfolio returns | 0.16 | |

Firm's and project's debt-to-assets ratio |
50% | |

**Notes**

- Due to the project, current assets will increase by $
**5**m now (t=0) and fall by $**5**m at the end (t=1). Current liabilities will not be affected.

**Assumptions**

- The debt-to-assets ratio will be kept constant throughout the life of the project. The amount of interest expense at the end of each period has been correctly calculated to maintain this constant debt-to-equity ratio.
- Millions are represented by 'm'.
- All rates and cash flows are real. The inflation rate is 2% pa.
- All rates are given as effective annual rates.
- The 50% capital gains tax discount is not available since the project is undertaken by a firm, not an individual.

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

A mining firm has just discovered a new mine. So far the news has been kept a secret.

The net present value of digging the mine and selling the minerals is $**250** million, but $**500** million of new equity and $**300** million of new bonds will need to be issued to fund the project and buy the necessary plant and equipment.

The firm will release the news of the discovery and equity and bond raising to shareholders simultaneously in the same announcement. The shares and bonds will be issued shortly after.

Once the announcement is made and the new shares and bonds are issued, what is the expected increase in the value of the firm's assets ##(\Delta V)##, market capitalisation of debt ##(\Delta D)## and market cap of equity ##(\Delta E)##? Assume that markets are semi-strong form efficient.

The triangle symbol ##\Delta## is the Greek letter capital delta which means change or increase in mathematics.

Ignore the benefit of interest tax shields from having more debt.

Remember: ##\Delta V = \Delta D+ \Delta E##

Which of the following is **NOT** a valid method to estimate future revenues or costs in a pro-forma income statement when trying to value a company?

A young lady is trying to decide if she should attend university or not.

The young lady's parents say that she must attend university because otherwise all of her hard work studying and attending school during her childhood was a waste.

What's the correct way to classify this item from a capital budgeting perspective when trying to decide whether to attend university?

The hard work studying at school in her childhood should be classified as:

A young lady is trying to decide if she should attend university. Her friends say that she should go to university because she is more likely to meet a clever young man than if she begins full time work straight away.

What's the correct way to classify this item from a capital budgeting perspective when trying to find the Net Present Value of going to university rather than working?

The opportunity to meet a desirable future spouse should be classified as:

A young lady is trying to decide if she should attend university or begin working straight away in her home town.

The young lady's grandma says that she should not go to university because she is less likely to marry the local village boy whom she likes because she will spend less time with him if she attends university.

What's the correct way to classify this item from a capital budgeting perspective when trying to decide whether to attend university?

The cost of not marrying the local village boy should be classified as:

A man is thinking about taking a day off from his casual painting job to relax.

He just woke up early in the morning and he's about to call his boss to say that he won't be coming in to work.

But he's thinking about the hours that he could work today (in the future) which are:

A man has taken a day off from his casual painting job to relax.

It's the end of the day and he's thinking about the hours that he could have spent working (in the past) which are now:

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.

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

Project Data | ||

Project life | 2 years | |

Initial investment in equipment | $6m | |

Depreciation of equipment per year for tax purposes | $1m | |

Unit sales per year | 4m | |

Sale price per unit | $8 | |

Variable cost per unit | $3 | |

Fixed costs per year, paid at the end of each year | $1.5m | |

Tax rate | 30% | |

Note 1: The equipment will have a book value of $4m at the end of the project for tax purposes. However, the equipment is expected to fetch $0.9 million when it is sold at t=2.

Note 2: Due to the project, the firm will have to purchase $0.8m of inventory initially, which it will sell at t=1. The firm will buy another $0.8m at t=1 and sell it all again at t=2 with zero inventory left. The project will have no effect on the firm's current liabilities.

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

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

Project Data | ||

Project life | 2 years | |

Initial investment in equipment | $8m | |

Depreciation of equipment per year for tax purposes | $3m | |

Unit sales per year | 10m | |

Sale price per unit | $9 | |

Variable cost per unit | $4 | |

Fixed costs per year, paid at the end of each year | $2m | |

Tax rate | 30% | |

Note 1: Due to the project, the firm will have to purchase $40m of inventory initially (at t=0). Half of this inventory will be sold at t=1 and the other half at t=2.

Note 2: The equipment will have a book value of $2m at the end of the project for tax purposes. However, the equipment is expected to fetch $1m when it is sold. Assume that the full capital loss is tax-deductible and taxed at the full corporate tax rate.

Note 3: The project will be fully funded by equity which investors will expect to pay dividends totaling $10m at the end of each year.

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

The 'time value of money' is most closely related to which of the following concepts?