In order to determine the net present value of the project, the cash flows must be adjusted to take account of specific inflation, and the nominal cash flows produced discounted by the nominal cost of capital.
Question 1 Starfish plc
(1) For Project 1:
Year Cash flow £ Tax (£) NCF (£) DF (10%) OV (£)
0 Investment (25,000) (25,000) 1.000 (25,000)
1 Income 5,000 5,000 0.877 4,385
2 Tax benefit 6,200 6,200 0.769 4,768
2 NCF 6,000 (1,550) 4,450 0.769 3,422
3 NCF 7,000 (1,860) 5,140 0.675 3,469
4 NCF 8,000 (2,170) 5,830 0.592 3,452
5 NCF 9,000 (2,480) 6,520 0.519 3,384
5 Scrap+WC 13,000 13,000 0.519 6,747
6 Tax on NCF (2,790) (2,790) 0.456 (1,272)
6 Balancing* (2,480)* (2,480) 0.456 (1,131)
NPV 2,224
*(8,000 X 0.31) = £2,480 = balancing charge because 100% initial capital allowance gave too much tax benefit, as scrap value was not allowed for.
For Project 2:
Year £ Tax (£) NCF(£) DF (10%) PV (£)
0 (36,000) (36,000) 1.000 (36,000)
1 6,000 6,000 0.877 5,262
2 8,000 7,440 15,440 0.769 11,873
3 9,000 (2,480) 6,520 0.675 4,401
4 9,000 (2,790) 6,210 0.592 3,677
5 36,000 (2,790) 33,210 0.519 17,236
6 (3,100) (3,100) 0.456 (1,414)
6 (6,200) (6,200) 0.456 (2,827)
NPV 2,208
(2) IRR (Project 1):
Year NCF (£) DF (20%) PV (£)
0 (25,000) 1.000 (25,000)
1 5,000 0.833 4,165
2 6,200 0.694 4,303
2 4,450 0.694 3,088
3 5,140 0.579 2,976
4 5,830 0.482 2,810
5 6,520 0.402 2,621
5 13,000 0.402 5,226
6 (2,790) 0.335 (935)
6 (2,480) 0.335 (831)
NPV (1,577)
Hence IRR = 14% + (20% – 14%) x 2,224)/ (2,224 + 1,577) = 17.5%
IRR (Project 2):
Year £ Tax (£) NCF (£) DF PV (£)
0 (36,000) (36,000) 1.000 (36,000)
1 6,000 6,000 0.833 4,998
2 8,000 7,440 15,440 0.694 10,715
3 9,000 (2,480) 6,520 0.579 3,775
4 9,000 (2,790) 6,210 0.482 2,993
5 36,000 (2,790) 33,210 0.402 13,350
6 (3,100) (3,100) 0.335 (1,038)
6 (6,200) (6,200) 0.335 (2,077)
NPV (3,284)
Hence IRR = 14% + ((20% – 14%) x 2,208)/ (2,208 + 3,284) = 16.4%
(3) According to the NPV rule project 1 should be taken (higher NPV)
According to the IRR rule project 1 should be taken (higher IRR)
Both NPV and IRR confirm that Project 2 should be selected as this will maximise shareholder wealth.
Question 2 Darla Kinsett plc
In order to determine the net present value of the project, the cash flows must be adjusted to take account of specific inflation, and the nominal cash flows produced discounted by the nominal cost of capital.
Year 0 1 2 3 4 5
£,000 £,000 £,000 £,000 £,000 £,000
Freeze Dryer (600) (400) (10)
Working Capital (100) 100
Revenue 874 1,090 1,155 1,225 1,298
Packaging/Labour (196) (243) (255) (267) (281)
Frozen Food (432) (539) (572) (606) (642)
Net Cash Flow (600) (254) 308 328 352 465
14% DCF 1.000 0.877 0.769 0.675 0.592 0.519
Present Values (600) (223) 237 221 208 241
NPV = (600) + 223 + 237 +221 + 208 + 241 = +£84,000
Accept investment as NPV is positive
£
Sales: Year 1: 85,000 x 9.70 x 1.06 = 873,970
Year 2: 100,000 x 9.70 x 1.062 = 1,089,892
Year 3: 100,000 x 9.70 x 1.063 = 1,155,286
Year 4: 100,000 x 9.70 x 1.064 = 1,224,603
Year 5: 100,000 x 9.70 x 1.065 = 1,298,079
£
Packaging Year 1: 85,000 x 2.20 x 1.05 = 196,350
and Labour: Year 2: 100,000 x 2.20 x 1.052 = 242,550
Year 3: 100,000 x 2.20 x 1.053 = 254,678
Year 4: 100,000 x 2.20 x 1.054 = 267,411
Year 5: 100,000 x 2.20 x 1.055 = 280,782
£
Frozen Food Year 1: 85,000 x 4.80 x 1.06 = 432,480
and Year 2: 100,000 x 4.80 x 1.062 = 539,328
Processing: Year 3: 100,000 x 4.80 x 1.063 = 571,688
Year 4: 100,000 x 4.80 x 1.064 = 605,989
Year 5: 100,000 x 4.80 x 1.065 = 642,348
Question 3 Matrix Ltd
£
Present value of sales revenue = 9.00 x 750,000 x 3.170 = 21,397,500
Present value of variable costs = 5.45 x 750,000 x 3.170 = 12,957,375
Present value of contribution 8,440,125
Initial investment 8,000,000
Net present value 440,125
We can now calculate the change needed in each variable to make the NPV zero
Initial investment
The NPV becomes zero if the initial investment increases by an absolute amount equal to the NPV (£440,125), which is a relative increase of 5.5% (100 x (440,125/ 8m))
Sales price
The relative decrease in sales revenue or selling price per unit that makes the NPV zero is the ratio of the NPV to the present value of sales revenue:
100 x (440,125/ 21,397,500) = 2.06%
This is an absolute decrease of £9.00 x 0.0206 = 18.5 pence, so the selling price that makes the NPV zero is 9.20 – 0.185 = £9.015
Variable cost
Since a decrease of 18.5 pence in selling price makes the NPV zero, an increase of 18.5 pence or 3.4% in variable cost will have the same effect
Sales volume
The relative decrease in sales volume that makes the NPV zero is the ratio of the NPV to the present value of contribution:
100 x (440,125/ 8,440,125) = 5.2%
This is an absolute decrease of 750,000 x 0. 052 = 39,000 units, so the sales volume that makes the NPV zero is 750,000 – 39,000 = 711,000 units.
Project discount rate
What is the cumulative present value factor that makes the NPV zero?
We have:
((9.00 - 5.45) x 750,000 x CPVF) – 8,000,000 = 0
and so:
CPVF = (8,000,000/ (9.00 5.45) x 750,000) = 3.005
Using annuity tables, and looking along the row of values for a life of four years (as project life remains constant), we find that 3.005 corresponds to a discount rate of almost exactly 12.5%, an increase in the discount rate of 2.5% in absolute terms or 25% in relative terms.
The project is most sensitive to changes in selling price and variable cost per unit and so these are the key project variables.
Question 4
(a) Inflation can have a serious effect on capital investment decisions, both by reducing the real value of future cash flows and by increasing the uncertainty associated with the values of those cash flows. Future cash flows must be adjusted to take account of any expected inflation in the prices of individual goods and services in order to express them in ‘nominal’ (or money) terms, that is, in terms of the actual amounts of cash to be received or paid on a future date. These nominal cash flows can then be discounted by a nominal cost of capital using the net present value method of investment appraisal. Hence estimation of future inflation is an important part of the investment appraisal process.
As an alternative to the nominal approach to dealing with inflation in investment appraisal, it is possible to deflate nominal cash flows by the general rate of inflation in order to obtain cash flows expressed in real terms, that is, with inflation stripped out. These real cash flows can then be discounted by a real cost of capital to determine the net present value of the investment project. Whichever method is used, whether nominal terms or real terms, care must be taken to determine and apply the correct rates of inflation to the correct cash flows.
(b) Depreciation can affect projects at two levels. From a company’s balance sheet perspective is not important as it determined by company management and does not affect cash flows. For taxation perspective however, depreciation is written off against taxable profits in a manner laid down by government and enforced by the tax authorities. Under this system, companies write off capital expenditure by means of capital allowances, also known as writing down allowances. These clearly do affect a project’s cash flows and therefore need to be taken into account in the investment appraisal process – in terms of savings on the payment of corporation tax.
Question 5 Bleak plc
(a) Calculation of ENPV
Year 1 PV P Y2 PV P PV Sum P ENPV
£
£8,930 0.25 nil 0.25 £8,930 0.0625 558
£11,955 0.50 £20,885 0.125 2,611
£19,925 0.25 £28,855 0.0625 1,803
£17,860 0.50 £15,940 0.25 £33,800 0.125 4,225
£23,910 0.50 £41,770 0.250 10,442
£31,880 0.25 £49,740 0.125 6,218
£26,790 0.25 £23,910 0.25 £50,700 0.0625 3,169
£31,880 0.50 £58,670 0.125 7,334
£39,850 0.25 £66,640 0.0625 4,165
40,525
Less initial investment 30,000
Expected net present value 10,525
Probability of negative NPV = 0.0625 + 0.125 + 0.0625 = 25%
While the expected NPV is £10,525, this does not represent a value expected to occur in reality. Managers must decide whether they are prepared to accept a 25% chance of a negative NPV.
(b) A company which is restricted in the amount of capital available for investment is said to be in a capital rationing situation and will not be able to undertake all positive NPV projects. Hard capital rationing (due to external factors) may arise because:
(1) The capital markets may be depressed
(2) Investors may consider the company to be too risky
(3) The cost of raising tiny amounts of capital may be too high
(c) If projects are ranked by net present in a capital rationing situation, projects with large net present values will be favoured for selection, rather than several small projects with cumulatively larger net present values but lower cumulative outlays. The profitability index relates the present value of future cash flows to the initial capital invested, and so provides a more appropriate ranking if capital is rationed and projects are divisible and non-repeatable. If projects are non-divisible, combinations of projects must be evaluated in order to find the combination offering the highest net present value.
Question 6
Class discussion
