Problems:

1.    A young aspiring DJ has saved up £4000 to buy the equipment she needs. She anticipates that the equipment will last for five years, after which it will be obsolete and have no disposal value. During these five years she believes she can use it to earn the following amounts, after allowing for her own wages and costs of travelling to clubs and events:

End of year             Net cash flow (£)

1                                              1200

2                                              1800

3                                              2000

4                                              2000

5                                              2000

(a)  Work out the accounting rate of return for the investment, allowing for depreciation of one-fifth of the cost of the equipment per year.

(b)  Find the payback period for the investment.

2. An advertisement offers a time share investment in a luxury apartment in the Algarve region of Portugal.  Investors can purchase the use of the apartment for an eight week period each year to rent out to tourists.  The cost of the time share is £ 15,000 for five years and it is claimed that the net rental income will be £4000 per year.

(a) What is the payback period for the investment?

(b) What is the net present value of the investment to an investor who would otherwise be able to earn 5% on their money?

(c) In the small print of the advertisement, it says “a service charge of £1000 per annum is charged for the cleaning and general maintenance of the property.”  Work out how this will alter the net present value of the investment.

3.  After a bad accident, Anton receives a large sum in compensation.  He is thinking about using it in a stretch limousine to hire out for special occasions.  The cost of the limousine is £ 100,000.  Anton is due to retire in six years, at which stage he thinks he will be able to sell the limousine for £ 40,000. The net cash inflows for the venture, after allowing for the driver’s wages and other direct expenses are:

End of year             Net cash flow (£)

1                                              10,000

2                                              15,000

3                                              20000

4                                              20000

5                                              15000

                                                                         6                                              15000

(a) Find the payback period for this venture.

(b) Calculate the net present value using a discount rate of 8%,

4.    Ricky Sadovnik, a geologist, discovered a deposit of decorative stone during a holiday in Scotland. He wants to establish a quarry to extract the stone and sell it to gardeners. The owner of the land is prepared to allow him to open and operate a quarry on the site for five years for a fee of £150,000. In addition he must landscape the site at the end of the period, at a cost of £50,000. Ricky intends to hire the digging equipment for the quarry. The net cash flows from the sale of the stone are predicted to be:

End of year             Net cash flow (£)

1                                              30,000

2                                              50,000

3                                              60,000

4                                              60,000

5                                              60,000

                                                                         6                                              60,000

(a) Determine the net present value for this project based on a discount rate of 15%.

(b) Find the net present value using a discount rate of 10%.

(c) Determine the internal rate of return for the project.

5. A Russian businessman offers a major Japanese car manufacturer an eight-year lease on a disused tank factory in Southern Russia.  The company could refit the factory and use it to manufacture low cost recreational off road vehicles for the holiday car-hire market in Southern Europe.  The total cost of the investment , including the lease and the installation of the equipment is $ 55 million.  Once the plant is operational, the following cash flows are expected:

End of year             Net cash flow ($millions)

       1                                       8

       2                                       12

       3                                       15

       4                                       20

       5                                       20

                                                                       6                                   10

                                                                       7                                         10

                                                                       8                                         5

At the end of the eighth year the lease would expire. The disposal value of the equipment is likely to be $5 m.

(a) Determine the net present value for this project based on a discount rate of 20%.

(b) Determine the internal rate of return for the project.