ACCA - P5 Study text - Emile Woolf INT - 2010
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Answers
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(1) Learning factor
Logarithm 0.85
Logarithm 2
=
-0.07058
0.30103
= -0.23446
(2) Average labour cost of producing the first five batches
0.23446
5
1
$2,000=y ×
= $2,000 (0.68568)
= $1,371 per batch
(3) Average labour cost of producing the first 12 batches
y - $2,000 x
1
12
0.23446
= $2,000 (0.55844)
= $1,117 per batch
(4) Labour cost of producing batches 6 – 12
$
Total cost for the first 12 batches (12 × $1,117) 13,404
Total cost for the first 5 batches (5 × $1,371)
6,855
Labour cost for batches 6
–
12
6,549
13 Regression
(a)
b=
5(254) - (15)(79)
5(55) - (15)(15)
=
1, 270 - 1,185
275 - 225
b = 85/50 = 1.7
a=
79
5
−
1.7(15)
5
a = 10.7
Forecast: Sales in $millions = 10.7 + 1.7x
(b)
Forecast for Year 6 (20X7) = 10.7 + 1.7(6) = 20.9 ($20.9 million)
Forecast for Year 7 (20X8) = 10.7 + 1.7(7) = 22.6 ($22.6 million).
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r =
85
(50)[5(1, 279)− (79)(79)
r = 85/87.75 = + 0.97
This is very close to + 1, suggesting that the forecast will be very reliable.
14 Replacement product
(a) Workings
If Product T is kept on the market for four more years:
Year
Unit sales
Unit
contribution
Annual
contribution
£ £
1 140,000 70
9,800,000
2 130,000 70
9,100,000
3 120,000 70
8,400,000
4 110,000 70
7,700,000
If Product V is introduced:
EV of annual sales = (0.2 × 100,000) + (0.5 × 80,000) + (0.3 × 50,000) = 75,000
units.
Unit contribution = $350 – $230 = $120.
EV of annual contribution = 75,000 units × $120 = $9,000,000.
Solution
Year
Extra
costs
Lost contribution
from T
Contribution
from V
Net cash
flow
Discount
factor 8%
PV
$000 $000 $000 $000 $000
0 (2,000)
(2,000)
1.000 (2,000)
1 (160) (9,800)
9,000
(960)
0.926 (889)
2 (160) (9,100)
9,000
(260)
0.857 (223)
3 (160) (8,400)
9,000
440
0.794 349
4 (160) (7,700)
9,000
1,140
0.735 838
NPV (1,925)
The NPV is – $1925,000, indicating that the immediate replacement of Product
T with Product V is not justified.
(b) The discount factor for Year 1- 4 at a cost of capital of 8% = 3.312.
To justify the immediate replacement of Product T with Product V, the annual
contribution from Product V would need to be higher by at least:
$1,925,000/3.312 = $581,220.
The annual contribution per unit from Product V is currently estimated to be
$120.
Annual sales in units from Product V would therefore need to be higher by at
least: $581,220/$120 per unit = 4,843.5 units – say 5,000 units.
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(c) Tutorial note: Annual sales of Product T are expected to fall by an additional
amount each year. It is therefore not possible to devise a simple computation
for the minimum fall in annual sales that would be required to justify
immediate replacement by Product V. The method used in the solution below
is therefore based on an interpolation method. The NPV is estimated
assuming a fall of 15,000 units in sales each year, rather than 10,000 units. A
net present value is calculated, and this is used together with the answer in (a)
to obtain a ‘break-even’ point.
Solution
If annual sales of Product T were to fall by 15,000 units in each subsequent
year from Year 2 onwards, the contribution lost by replacing Product T with
Product V would be as follows:
Year
Unit sales
Unit
contribution
Annual
contribution
£ £
1 135,000 70
9,450,000
2 120,000 70
8,400,000
3 105,000 70
7,350,000
4 90,000 70
6,300,000
The NPV of a decision to introduce Product V immediately would be:
Year
Extra
costs
Lost contribution
from T
Contribution
from V
Net cash
flow
Discount
factor 8%
PV
$000 $000 $000 $000 $000
0 (2,000)
(2,000)
1.000 (2,000)
1 (160) (9,450)
9,000
(610)
0.926 (565)
2 (160) (8,400)
9,000
440
0.857 377
3 (160) (7,350)
9,000
1,490
0.794 1,183
4 (160) (6,300)
9,000
2,540
0.735 1,867
NPV + 862
If annual sales of Product T fall by 10,000 units each year, the NPV would be
$(1,925,000).
If annual sales of Product T fall by 15,000 units each year, the NPV would be
$862,000.
The minimum fall in annual sales of Product T needed to justify its immediate
replacement by Product V is therefore approximately:
units 10,000)-(15,000
1,925)+(862
1,925
+10,000 ×
⎥
⎦
⎤
⎢
⎣
⎡
= 13,453 units = about 13,500 units.
(d) Limitations of analysis:
(1) Expected value used for sales of Product V. Actual sales could be higher
or lower than 75,000 each year.
(2) Estimates of falls in sales of Product T cannot be predicted accurately.
(3) The calculations have ignored taxation and inflation, which is
inappropriate in practice.
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(4) A cost of capital of 8% has been assumed. This may be inappropriate.
(5) There has been no consideration of the options to introduce Product V at
the beginning of Year 3, or Year 4 or Year 5.
(6) The option to reduce the selling price of Product T to increase annual
sales has not been considered. Similarly an option to sell Product V at a
lower price to increase annual sales has not been considered.
(7) Non-financial factors have been ignored: for example, there could be a
longer-term marketing advantage to be gained from introducing
Product V as soon as possible.
15 Probabilities
Cash inflows for the project can be calculated as an EV of expected annual cash
inflows.
The first step is to establish a probability distribution of possible outcomes.
Factor 1
Factor 2
Factor 3
Joint
probability
Yes, No, No 0.2 0.7 0.6 0.084
Yes, Yes, Yes
0.2
0.3
0.4
0.024
Yes, No, Yes 0.2
0.7
0.4
0.056
Yes, Yes, No 0.2
0.3
0.6
0.036
No, No, No 0.8
0.7
0.6
0.336
No, Yes, Yes 0.8
0.3
0.4
0.096
No, No, Yes 0.8
0.7
0.4
0.224
No, Yes, No 0.8
0.3
0.6
0.1440
Probability of
outcome
Cash inflows as a
proportion of expectation
EV
0.084 (- 25%) 0.75 0.0630
0.024 (- 25%
–
10% + 5%)
0.70 0.0168
0.056 (- 25% + 5%)
0.80 0.0448
0.036 (- 25%
–
10%)
0.65 0.0234
0.336 1.00 0.3360
0.096 (- 10% + 5%)
0.95 0.0912
0.224 (+ 5%) 1.05 0.2352
0.144 (- 10%) 0.90 0.1296
1.000
0.9400
The EV of cash inflows, allowing for the three additional factors, will be 94% of the
original estimates.
Year
Cash inflows (0.94 of
original estimate)
Cash
outflows
Net cash
flow
Discount
factor at 10%
PV
$m $m $m $m
0 (6.25)
(6.25)
1.000 (6.25)
1 2.82
1.50
1.32
0.909 1.20
2 3.76
1.80
1.96
0.826 1.62
3 4.70
2.40
2.30
0.751 1.73
4 3.76
1.70
2.06
0.683 1.41
5 1.88
1.00
1.88
0.621 1.17
NPV + 0.88
Answers
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16 Sensitivity
(a) The residual value of the equipment at the end of year 5 will be 30% × $3
million = $900,000.
Year Cash flow Discount factor at 8% Present value
$ $
0 (3,000,000)
1.000
(3,000,000)
1 400,000
0.926
370,400
2 800,000
0.857
685,600
3 800,000
0.794
635,200
4 700,000
0.735
514,500
5 400,000
0.681
272,400
5 900,000
0.681
612,900
Net present value
+ 91,000
(b) Sensitivity analysis
(i) Cost of equipment
The estimated PV of the cost of the equipment, allowing for a residual
value of 30% of cost after five years, is:
3,000,000 – (0.681 × 0.30 × 3,000,000) = 2,387,100.
This estimate can be wrong by $105,400 before the project ceases to have
a positive NPV. The cost of the equipment can therefore be higher by
(91,000/2,387,100) = 3.8%.
(ii)
Residual value of equipment
The estimated PV of the residual value is $612,900. This estimate can be
wrong by $105,400 before the project ceases to have a positive NPV. The
PV of the residual value could therefore be (612,900 – 105,400) =
$521,900.
The residual value (without discounting) could therefore be
$507,500/0.681 = $745,228. This is 24.8% of the original cost of
$3,000,000.
The residual value could therefore be as low as about 25% of cost before
the project ceased to have a positive NPV.
((iii),(iv) and (v)) Sales revenue and annual costs
Workings
The estimated contribution/sales ratio is 40%, therefore sales revenue will be
100/40 = 2.5 times annual contribution. Variable costs will be 60/40 = 1.5
times annual contribution. Fixed costs are $200,000 each year; therefore total
contribution is $200,000 more than the annual net cash flow.
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Year Contribution PV factor at 8% Revenue Variable costs
Total PV Total PV
$000 $000 $ $000 $000
1 600 0.926
1,500
1,389,000
900 833,400
2 1,000 0.857
3,500
2,142,500
1,500 1,285,500
3 1,000 0.794
2,500
1,985,000
1,500 1,191,000
4 900 0.735
2,250
1,653,750
1,350 992,250
5 600 0.681
1,500
1,021,500
900 612,900
8,191,750
4,915,050
The PV of annual fixed costs = $200,000 × discount factor for years 1 – 5 at 8%
= $200,000 × 3.993 = $798,600.
Sales revenue: The PV of sales revenue could be lower by $91,000 before the
project ceases to have a positive NPV. Sales revenue could therefore be lower
by 91,000/8,245,750 = about 1.3%.
Similarly,
variable costs could be higher by (91,000/4,947,450) 2.1% before the
project ceases to have a positive NPV.
Similarly,
fixed costs could be higher by (91,000/798,600) 13.2% before the
project ceases to have a positive NPV.
(c) The positive NPV of the project appears to depend on the accuracy of the cash
flows. If these are only a small amount worse than estimated, the NPV will be
negative. The project is particularly sensitive to estimates of sales revenue,
variable costs (and the contribution/sales ratio), the cost of the equipment and
its residual value.
This suggests that the project could be high-risk.
17 The Jin Company
(a) Tutorial note. There are two ways of calculating the taxation cash flows. One
approach is to calculate the tax on the cash profits ignoring capital allowances,
and then to calculate the savings in tax payments because of the capital
allowances separately. The second approach is to calculate the profit liable to
tax in each year and the tax on that profit. Both methods should produce the
same net cash flows. The second approach is used here.
Machine A
Workings
Year 1 Year 2 Year 3 Year 4
Cost $600,000 $
$
$ $
Capital allowance (25%) 150,000
112,500
84,375 253,125
Written down value (WDV) 450,000
337,500
253,125 0
Operating cash flow 470,000
520,000
490,000 450,000
Capital allowance 150,000
112,500
84,375 253,125
Profit liable for tax 320,000
407,500
405,625 196,875
Tax at 30% on the profit 96,000
122,250
121,688 59,063
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Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
$
$
$
$ $
Machine (600,000)
Working capital
(100,000)
100,000
Operating cash flow
470,000
520,000
490,000 450,000
Tax (one year in arrears)
(96,000)
(122,250) (121,688) (59,063)
Net cash flow (700,000)
470,000
424,000
367,750 428,312 (59,063)
Discount factor 10% 1.000
0.909
0.826
0.751 0.683 0.621
Present value (700,000)
427,230
350,224
276,180 292,537 (36,678)
NPV = + $609,493
Machine B
Workings
Year 1 Year 2 Year 3 Year 4 Year 5
Cost $750,000 $
$
$
$ $
Capital allowance (25%) 187,500
140,625
105,469
79,102 237,304
Written down value (WDV) 562,500
421,875
316,406
237,304 0
Operating cash flow 580,000
640,000
500,000
500,000 400,000
Capital allowance
(187,500)
(140,625)
(105,469)
(79,102) (237,304)
Profit liable to tax
392,500
499,375
394,531
420,898 162,696
Tax at 30% on the profit 117,750
149,813
118,359
126,269 48,809
Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6
$
$
$
$
$
$
Machine (750,000)
Working capital
(200,000)
200,000
Operating cash flow
580,000
640,000
500,000
500,000 400,000
Tax (one year in arrears)
(117,750)
(149,813)
(118,359) (126,269)
(48,809)
Net cash flow (950,000)
580,000
522,250
350,187
381,641 473,731
(48,809)
Discount factor 10% 1.000
0.909
0.826
0.751
0.683 0.621
0.564
Present value (950,000)
527,220
431,379
262,990
260,661 294,187
(27,528)
NPV = + $798,909
(b)
Machine A
Machine B
$
$
Year 0 spending (700,000)
(950,000)
Year 1 net cash flow 470,000
580,000
(230,000)
(370,000)
Year 2 net cash flow 424,000
522,250
194,000
152,250
Payback will be during year 2 for both machines.
Machine A. Payback = 1 year + (230,000/424,000) years = 1.54 years.
Machine B. Payback = 1 year + (370,000/522,250) years = 1.71 years.
(c) Here is no information to assess whether strategic factors and non-financial
factors might affect the choice between Machine A and Machine B.
On purely financial grounds, Machine B has the higher NPV, but this is for a
five-year project whereas the Machine A project would be only four years.
Machine A has the slightly earlier payback period.
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The recommendation on financial grounds should be to select the machine
that will provide the higher equivalent annual value.
Machine A Machine B
NPV $609,493
NPV $798,909
Annuity factor at 10%,
Years 1 - 4
3.170
Annuity factor at 10%,
Years 1 - 5
3.791
Equivalent annual value $192,269
$210,738
Machine B will provide the higher equivalent annual value of benefits, and should
therefore be chosen in preference to Machine A.
18 Growth objective
Sales
Sales growth: Year 2 compared with Year 1 20.0%
Sales growth: 1
s
t
six months of Year 2 compared with 1
s
t
six months of Year 1
28.1%
Sales growth: 2
n
d
six months of Year 2 compared with 2
n
d
six months of Year 1
5.0%
Sales increased by 20% in Year 2 compared with Year 1. However, the strong
growth in sales occurred in the first six months of the year (28% compared with the
same period in Year 1). In the second half of the year, sales growth compared with
the same period in Year 1 was down to 5%. There is insufficient information to
judge whether the growth in sales revenue is slowing down or coming to an end.
Net profit
There was no increase in net profit between Year 1 and Year 2. The increase in sales
(20%) is offset by an increase of 30.4% in operating costs and some interest charges.
In terms of annual net profit, the business is therefore not growing.
If a part-time employee is the equivalent of 50% of a full-time employee, there were
415 equivalent full time employees in Year 1 (260 + 50% × 310). There were 565
equivalent full time employees in Year 2 (318 + 50% × 494). Sales revenue per
equivalent full-time employee was therefore $62,651 in Year 1 and $55,221 in Year 2.
This fall in employee productivity is one reason for the failure to achieve growth in
the annual net profit.
Investment
The investment in non-current assets has risen by just 5%, but the investment in
working capital has doubled. The increase in net assets has been almost entirely
financed by borrowing. (Presumably, this means that most of the profits earned in
Year 1 have been paid in taxation or distributed as dividends to shareholders.)
It is difficult to draw definite conclusions from the limited amount of data, but
management should be concerned about a 100% increase in working capital, when
the increase in annual sales is only 20%. Could there be large quantities of unsold
inventory as a result of the decline in sales growth in the second half of the year?
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It is not clear why it was considered necessary to borrow $9,000,000 when increases
in non-current assets have been only $1,300,000. It would appear that the new
borrowing might be financing unnecessary working capital investment, and not
investment in non-current assets for longer-term development.
On the other hand, investment in non-current assets will probably need to exceed
5% per year (by a large amount) if the company is to achieve significant long-term
growth in its business.
Product range/new product sales
The data about new products is difficult to interpret, because there is no information
about the total size of the product portfolio and no information about whether the
new products sold well or badly.
19 Gap analysis
(a) Workings
Budgeted variable costs per unit
$000
Material and labour costs 16,000
Variable other production costs (25% × 8,000) 2,000
Variable marketing and distribution costs (1/3 × 12,000) 4,000
Total variable costs 22,000
Volume of production and sales $80,000
Budgeted variable cost per unit 275
Budgeted contribution per unit (600 – 275) 325
Budgeted annual fixed costs
$000
Fixed other production costs (75% × 8,000) 6,000
Fixed marketing and distribution costs (2/3 × 12,000) 8,000
Administration costs 10,000
Total annual fixed costs 24,000
Strategy 1
Increase in sales (units) 5,000
$000
Increase in total annual contribution ($325 × 5,000) 1,625
Increase in annual fixed costs 1,200
Increase in annual profit 425
Strategy 2
Increase in sales price and unit contribution $25
$000
Increase in total annual contribution ($25 × 80,000 units) 2,000
Increase in annual fixed costs 1,500
Increase in annual profit 500
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Strategy 2
Reduction in variable cost per unit (20% × $275) $55
Therefore increase in unit contribution $55
$000
Increase in total annual contribution ($55 × 80,000 units) 4,400
Increase in annual fixed costs 3,500
Increase in annual profit 900
(b)
Taking all three strategies together
$000 $000
Sales (85,000 units at $625 per unit) 53,125
Variable costs (85,000 × $220 per unit) 18,700
Total contribution
Fixed costs 34,425
In the original budget 24,000
Extra fixed costs of strategies 1, 2 and 3 6,200
30,200
Profit 4,225
$000 $000
Profit taking all three strategies together 4,225
Original budget profit 2,000
Difference 2,225
Extra profit from Strategy 1 only 425
Extra profit from Strategy 2 only 500
Extra profit from Strategy 3 only 900
1,825
Balancing figure 400
The balancing figure comes from the combination of the three strategies. The
company will sell 5,000 units more than in the original budget, and the
contribution per unit will be $80 per unit higher ($25 per unit from strategy 2
and $55 per unit from strategy 3).
5,000 extra units of sale × $80 extra contribution per unit = Extra total
contribution of $400,000.
Gap analysis
$000 $000
Target profit 4,000
Original budget profit 2,000
Profit gap 2,000
Extra profit from Strategy 1 only 425
Extra profit from Strategy 2 only 500
Extra profit from Strategy 3 only 900
Extra profit from combination of three strategies 400
2,225
Profit in excess of the ‘gap’ 225