QUESTION 1
Two investment projects are being considered.
i. Explain why comparing the two discounted payback periods or comparing the two payback periods are not generally appropriate ways to choose between two investment projects.
ii. The two projects each involve an initial investment of £3m. The incoming cash flows from the two projects are as follows:
Project A
In the first year, Project A generates cash flows of £0.5m. In the second year it will generate cash flows of £0.55m. The cash flows generated by the project will continue to increase by £0.05m per annum until the end of the sixth year and will then cease.
Assume that all cash flows are received in the middle of the year.
Project B
Project B generates cash flows of £0.64m per annum for six years. Assume that all cash flows are received continuously throughout the year.
(a) Calculate the non-discounted payback period from Project B.
(b) Calculate the discounted payback period from Project B at a rate of interest of 4% per annum effective.
iii. Show that there is at least one "cross-over point" for Projects A and B between 0% per annum effective and 4% per annum effective where the cross-over point is defined as the rate of interest at which the net present value of the two projects is equal.
iv. Explain why the net present value of Project A appears to fall more rapidly than the net present value of Project B as the rate of interest increases.
QUESTION 2
A country's football association is considering whether to bid to host the world
Cup in 2030. Several countries aspiring to host the World Cup will be making bids. Regardless of whether the bid is successful, the association will incur various costs.
For two years, starting on 1 January 2017, the association will incur costs at a rate of £2m per annum, assumed to be paid continuously, to prepare the bid.
If the football association is successful, the following costs will be incurred from 1 January 2020 until 31 December 2029:
• One stadium will be built each year for ten years. The first stadium will be built in 2020 and is expected to cost £200m; the stadium built in 2021 is expected to cost £210m; and so on, with the cost of each stadium rising by £10m each year. The costs of building each stadium are assumed to be incurred halfway through the relevant year.
• Administration costs at a rate of £100m per annum will be incurred, payable monthly in advance from 1 January 2029 until 31 December 2030.
• Revenues from television, ticket receipts, advertising and so on are expected to be £3,300m and are assumed to be received continuously throughout 2030.
Explain why the payback period is not a good indicator of whether this project is worthwhile.
The football association decides to judge whether to go ahead with the bid by calculating the net present value of the costs and revenues from a successful bid on 1 January 2017 at a rate of interest of 4% per annum effective.
Determine whether the association should make the bid.
The football association is discussing how it might factor into its calculations the fact that it is not certain to win the right to host the World Cup because other countries are also bidding.
Explain how you might adjust the above calculations if the probability of winning the right to host the World Cup is 0.1 and whether this adjustment would make it more likely or less likely that the bid will go ahead.