Week 11 - Tutorial 10 Flashcards
Question A:
A small manufacturing company has decided to buy a new machine that will cost £100,000 and can be sold after 5 years for £20,000. The projected sales of the
products made by this machine are as follows:
Year Sales (units) 1 5,000 2 10,000 3 15,000 4 15,000 5 5,000 Each product is expected to make a net profit of £4 (before depreciation). However, the financial advisor to the company feels this is a risky investment and is thus suggesting a very high cost of capital of 20%.
i. What is the payback period for this investment?
ii. What is the net present value and internal rate of return of this investment?
The relevant entries in the present value table for 30% are: year 1 - 0.769, year 2 – 0.592, year 3 – 0.455, year 4 – 0.350, year 5 – 0.269.
The cash flows of this investment are as follows:
Year Actual (£) Cumulative (£) 0 (100,000) (100,000) 1 20,000 (80,000) 2 40,000 (40,000) 3 60,000 20,000 4 60,000 80,000 5 40,000 120,000
Therefore the payback period is 2 years plus 40/60 = 2 years and 8 months
The NPV can be calculated as follows:
Year Expenditure Income Net Discount PV
(£) (£) (£)
0 (100,000) - (100,000) 1 (100,000)
1 - 20,000 20,000 0.833 16,660
2 - 40,000 40,000 0.694 27,760
3 - 60,000 60,000 0.579 34,740
4 - 60,000 60,000 0.482 28,920
5 - 40,000 40,000 0.402 16,080
NPV 24,160
The NPV at a discount rate of 30% is as follows:
Year Expenditure Income Net Discount PV
(£) (£) (£)
0 (100,000) - (100,000) 1 (100,000)
1 - 20,000 20,000 0.769 15,380
2 - 40,000 40,000 0.592 23,680
3 - 60,000 60,000 0.455 27,300
4 - 60,000 60,000 0.350 21,000
5 - 40,000 40,000 0.269 10,760
NPV (1,880)
Therefore, the IRR is 20% + 10% * 24,160/26,040 = 29.3%
Question B:
A logistics company is considering expanding its fleet by purchasing 10 delivery vans that will cost £15,000 each. The annual running costs (i.e. petrol, maintenance and road tax, but not depreciation) per van will be £20,000 and they are expected to sell for £3,000 each after 6 years of operation. The finance
director has calculated that the annual charge to customers will be £230,000 every year for all the vans. She also feels, given the risky nature of this
investment, that the cost of capital should be 15%.
i. What is the payback period for this investment?
ii. What is the net present value and internal rate of return of this investment?
The cash flows of this investment are as follows:
Year Actual (£) Cumulative (£) 0 (150,000) (150,000) 1 30,000 (120,000) 2 30,000 (90,000) 3 30,000 (60,000) 4 30,000 (30,000) 5 30,000 0 6 60,000 60,000
Therefore the payback period is 5 years
The NPV can be calculated as follows:
Year Expenditure Income Net Discount PV
(£) (£) (£)
0 (150,000) - (150,000) 1 (150,000)
1 - 30,000 30,000 0.870 26,100
2 - 30,000 30,000 0.756 22,680
3 - 30,000 30,000 0.658 19,740
4 - 30,000 30,000 0.572 17,160
5 - 30,000 30,000 0.497 14,910
6 - 60,000 60,000 0.432 25,920
NPV (23,490)
The NPV is negative and therefore it is not worth investing in the project
The NPVs at a discount rate of 10% and 9% are as follows:
Year Net (£) Discount (10%) PV Discount (9%) PV
0 (150,000) 1 (150,000) 1 (150,000)
1 30,000 0.909 27,270 0.917 27,510
2 30,000 0.826 24,780 0.842 25,260
3 30,000 0.751 22,530 0.772 23,160
4 30,000 0.683 20,490 0.708 21,240
5 30,000 0.621 18,630 0.650 19,500
6 60,000 0.564 33,840 0.596 35,760
NPV (2,460) 2,430
Therefore, the IRR is just over 9.5% - we can’t use the usual calculation as there is no positive NPV and the figures are irregular; i.e. the original NPV was negative.
Question C:
A manufacturing company is deciding whether to close one of its factories due to the long term prospects for their industry being bleak. The lease for the factory premises has a further four years to run; however, should they decide to cease operations another company has offered to sublease the premises for the remaining four years at a cost of £40,000 per year.
The company could also sell their machinery for £220,000. They also have working capital of £420,000 that can either be liquidated immediately, or at the end of the lease. However, if they were to close the factory they would have to pay immediate redundancy payments of £180,000, as opposed to £150,000 at the end of the lease period. Moreover, if the factory was to continue its operations it would make the following profits (losses) over the next four years:
Year 1 (£000) 2 (£000) 3 (£000) 4 (£000) Profit (loss) 160 (40) 30 20
The above figures include an annual depreciation charge of £90,000 for the
machinery. The residual value of the machinery at the end of four years is
expected to be £40,000. The company has a cost of capital of 12%.
i. Using the above information, calculate whether is it more financially viable for the company to close immediately, or continue operations until the end of the lease period.
Remember, any money foregone by not closing is an opportunity cost.
The calculations are as follows:
Year Expenditure/ Income/money Net Discount PV
lost income (£) saved (£) (£)
0 (640,000) 180,000 (460,000) 1 (460,000)
1 (40,000) 250,000 210,000 0.893 187,530
2 (40,000) 50,000 10,000 0.797 7,970
3 (40,000) 120,000 80,000 0.712 56,960
4 (190,000) 570,000 380,000 0.636 241,680
NPV 34,140
- The year 0 expenditure/lost income is the foregone income from the sale of the machinery and working capital; however the company does not have to make any redundancy payments, thus some money is saved
- The years 1-3 expenditure/lost income is the foregone rent from subletting the premises; the income is the net profit (loss) plus the depreciation charge
- In year 4 the expenditure/lost income is the foregone rent and the final redundancy payments; the income is the net profit, depreciation, liquidation of the working capital and residual value of the machinery
- On a purely financial basis it would be worthwhile continuing in operations for the next four years
- However, the company would need to check the accuracy of any forecasts and the creditworthiness of the company that are offering to sublease the premises
- Once the factory is closed it will not be possible to reverse the decision
- Giving the workforce four years to find another job might also be considered more ethical
