ACCA F9 Financial Management - 2010 - Study text - Emile Woolf Publishing
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8 Baumol and Miller-Orr
(a) Optimum size of transaction for investment sales =
2 ×60 ×3,000,000
0.05
= $84,852, say $85,000.
The frequency of investment sales =
$85,000
$3,000,000
× 365 days = every 10.3 days
(b) Standard deviation of daily cash flows = 2,200.
Therefore the variance of daily cash flows = (2,200)
2
= 4,840,000.
Daily interest cost = 5%/365 days = 0.0137%.
(i)
Spread =
3 ×
¾ × 60 × 4,840,000
1/3
0.000137
(Note: ‘to the power of 1/3 = the cube root)
Spread = 3 × $11,671 = $35,013, say $35,000.
(ii) Upper limit = Minimum cash balance + Spread
= $20,000 + $35,000 = $55,000.
(iii) Return point = $20,000 + (1/3 × $35,000) = $31,667.
When the cash balance reaches $55,000, the entity will buy $23,333 of
investments, and the cash balance will return to $31,667.
Similarly, when the cash balance reaches $20,000, the entity will sell
$11,667 of investments, to return the cash balance to $31,667.
9 Appraisal
The cash outflow in Year 0 = cost of equipment + working capital investment =
$45,000 + $8,000 = $53,000.
The cash inflow for year 4 = project’s net cash profits + working capital recovered =
$4,000 + $8,000 = $12,000.
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Cost of capital 11% Cost of capital 15%
Year Cash flow Discount factor
PV
Discount factor PV
$
$
$
0 (53,000) 1.000 (53,000)
1.000 (53,000)
1 17,000 0.901 15,317
0.870 14,790
2 25,000 0.812 20,300
0.756 18,900
3 16,000 0.731 11,696
0.658 10,528
4 12,000 0.659 7,908
0.572 6,864
NPV
+ 2,221
(1,918)
(a) NPV at 11% cost of capital = + $2,221
(b)
()
()
⎥
⎦
⎤
⎢
⎣
⎡
−×
+
+= %1115
918,12,221
2,221
%11IRR
= 11% + 2.1% = 13.1%
(c)
Year
Cashflow
Cumulativecash
flow
$ $
0 (53,000) (53,000)
1 17,000 (36,000)
2 25,000 (11,000)
3 16,0005,000
4 12,000
Payback is during year 3.
If it is assumed that cash flows occur at an even rate through each year, the
payback period in years and months
= 2 years + [(11,000/16,000) × 12 months]
= 2 years 8.25 months.
The project has a positive NPV at a cost of capital of 11% and pays back within
three years. Without taking other factors into consideration (for example, risk
and uncertainty) the project should be undertaken.
10 Investment appraisal methods
(a) (i) Accounting rate of return: (ARR)
Project 1
Average annual profit = $200,000 - $100,000 depreciation = $100,000.
Average capital employed = Average carrying value of machine
= ½ ($556,000 + $56,000) = $306,000
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ARR =
$100,000
$306,000
×100% = 32.7%
Project 2
Average annual profit = $500,000 - $263,000 depreciation = $237,000.
Average capital employed = ½ ($1,616,000 + $301,000) = $958,500.
ARR =
$237,000
$958,500
×100% = 24.7%
(ii) Payback
Project 1
Payback period =
$556,000
$200.000
= 2.8 years,or 2 years 9 months
Project 2
Payback period =
$1,616,000
$500.000
= 3.2 years,or 3 years 2 months
(iii)
Net present value (NPV)
Project 1
Year Discount
factorat15%
Project1 Project2
Cashflow PV Cashflow PV
$ $ $ $
0 1.000 (556,000) (556,000) (1,616,000) (1,616,000)
1–5 3.352 200,000 670,400 500,000 1,676,000
5 0.497 56,000 27,832 301,000 149,597
NPV 142,232 209,597
(iv)
Internal rate of return (IRR)
Both projects have a positive NPV at 15%. Try a higher discount rate:
Try 20%
NPV of Project 1 = - 556,000 + (200,000 × 2.991) + (56,000 × 0.402)
= - 556,000 + 598,200 +22,512
= + $64,712
NPV of Project 2 = -1,616,000 + (500,000 × 2.991) + (301,000 × 0.402)
= - 1,616,000 + 1,495,500 + 121,002
= + $502
Try 25%
NPV of Project 1 = - 556,000 + (200,000 × 2.689) + (56,000 × 0.328)
= - 556,000 + 537,800 + 18,368
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= + $168
NPV of Project 2 = -1,616,000 + (500,000 × 2.689) + (301,000 × 0.328)
= -1,616,000 + 1,495,500 + 121,002
= - $172,772
IRR of Project 1 = 25% +
168
64,712 −168
()
× 25−20
()
%
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
= 25.01%, = 25% to the nearest 1%.
IRR of Project 2 = 20% +
502
502 +172,772
× 25−20
()
%
⎡
⎣
⎢
⎤
⎦
⎥
= 20.01%, = 20% to the nearest 1%.
Tutorial note
The NPV of project 1 at 20% and the NPV of project 2 at 25% are close to
zero, indicating that the IRR to the nearest 1% must be 20% and 25%
respectively.
The calculations of the approximate IRR are shown here to illustrate the
technique, which you should learn.
(b) Project 2 should be recommended because it has a higher NPV.
When there are mutually exclusive projects, ignoring risk and uncertainty, the
NPV method should be used to make the project selection.
It does not matter that project 1 seems better on the basis of ARR, payback and
IRR.
11 NPV
Workings
Discount
factorat10%
Annuityfactor,years1–4 3.170
Discountfactor,Year1 0.909
Annuityfactor,years2–4 2.261
Annuityfactor,years1–10 6.145
Annuityfactor,years1–4 3.170
Annuityfactor,years5–10 2.975
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Costofcapital10%
Year Cash
flow
Discount
factor
PV
$$
0 (70,000) 1.000 (70,000)
1 15,000 0.909 13,635
2–4 12,000 2.261 27,132
5–10 8,000 2.975 23,800
NPV(5,433)
The project has a negative NPV and so should not be undertaken.
12 DCF and relevant costs
Year 0 1 2 3 4 5
$000 $000 $000 $00 $000 $000
Sales 7,400 8,300 9,800 5,800
Wages (550) (580) (620) (520)
Materials (340) (360) (410) (370)
Licencefee (300) (300) (300) (300) (300)
Overheads (100) (100) (100) (100)
Equipment (5,200) (5,200) 2,000
Specialisedequipment (150)
Workingcapital (650) 650
–––––––
–
–––––––
–
–––––––
–
––––––– –––––––– ––––––––
(5,200) (6,150) 5,960 6,960 8,370 7,160
Discountfactorat10% 1.000 0.909 0.826 0.751 0.683 0.621
Presentvalue (5,200) (5,590) 4,923 5,227 5,717 4,446
NPV = + $9,523,000
The project has a positive NPV. The project should be undertaken because it
will increase the value of the company and the wealth of its shareholders.
13 Annuities and perpetuities
(a) Present value of net cash flows of $75,000 in Years 1 – 6 =
$75,000
0.088
1−
1
1.088
()
6
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
= $852,273 (1 – 0.603)
= $338,352
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Costofcapital8.8%
Year Cashflow
Discount
factor
PV
$ $
0 (325,000) 1.000 (325,000)
1–6 75,000peryear 338,352
NPV +13,352
The project has a positive NPV and should be undertaken.
(b) The annuity PV formula can be used to calculate the ‘present value’ as at the
end of Year 1 for annual cash flows from Year 2 onwards.
End-of-Year 1 ‘present value’ of net cash flows of $75,000 in Years 2 – 6 =
$75,000
0.088
1−
1
1.088
()
5
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
= $852,273 (1 – 0.656)
= $293,182
Costofcapital8.8%
Year Cashflow
Discount
factor PV
$ $
0 (325,000) 1.000 (325,000)
1 50,000 1/1.088 45,956
2–6 293,182 1/1.088 269,469
NPV (9,575)
The project has a negative NPV and should not be undertaken.
(c)
Year Cashflow Costofcapital8.8%
Discount
factor
PV
$ $
0 (325,000) 1.000 (325,000)
1onwardsinperpetuity 50,000 1/0.088 568,182
NPV +243,182
The project has a positive NPV and should be undertaken.
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14 Investment appraisal and tax
Workings
Tax allowances on the investment
Yearof
claim
Taxsaving
(35%of
allowance)
Cashflow
year
$ $
Cost 250,000
0 Allowance(25%) (62,500) 21,875 1
–
–––––––
187,500
1 Allowance(25%) (46,875) 16,406 2
–
–
––––––
140,625
2 Allowance(25%) (35,156) 12,305 3
–
–––––––
105,469
3 Allowance(25%) (26,367) 9,228 4
–
–––––––
79,102
4 Disposal 100,000
–
–––––––
(20,898) (7,314) 5
–
–––––––
NPV calculation
Year 0 1 2 3 4 5
$ $ $ $ $ $
Capitalequipment (250,000) 100,000
Workingcapital (38,000) (12,000) 50,000
Cashprofitsbeforetax 120,000 120,000 120,000 120,000
Taxonprofits(35%)(42,000) (42,000) (42,000) (42,000)
Casheffectofallowances 21,875 16,406 12,305 9,228 (7,314)
––––––––
–
–––––––
–
–––––––
–
––––––– –––––––– ––––––––
Netcashflow (288,000) 129,875 94,406 90,305 237,228 (49,314)
DCFfactorat10% 1.000 0.909 0.826 0.751 0.683 0.621
PVofcashflow (288,000) 118,056 77,979 67,819 162,027 (30,624)
––––––––
–
–––––––
–
–––––––
–
––––––– –––––––– ––––––––
NPV +107,257
––––––––
The NPV is + $107,257. This indicates that the project should be undertaken.
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15 More investment appraisal and tax
Tax allowances on the investment
Yearof
claim
Taxsaving
(35%ofallowance)
Cashflow
year
$ $
Cost 600,000
0 Allowance(25%) (150,000) 52,500 1
–
–––––––
450,000
1 Allowance(25%) (112,500) 39,375 2
–
–––––––
337,500
2 Allowance(25%) (84,375) 29,531 3
–
–––––––
253,125
3 Allowance(25%) (63,281) 22,148 4
–
–––––––
189,844
4 Allowance(25%) (47,461) 16,611 5
–
–––––––
142,383
5 Disposal 0
–
–––––––
142,383 49,834 6
–
–––––––
Note: It is assumed that the company has taxable profits against which it can claim
an allowance in Year 0 (or early in Year 1).
Year 0 1 2 3 4 5 6
$000 $000 $000 $000 $000 $000 $000
Sales 250 250 300 350 400
Materials (50) (55) (58) (64) (70)
Labour (25) (25) (30) (30) (35)
–
–––––
–
–––––
–
–––––
–
––––– ––––––
Cashprofits 175 170 212 256 295
Taxat35% (61) (60) (74) (90) (103)
Capitalequipment (600)
Casheffectofallowances 53 39 30 22 17 50
––––––
–
–––––
–
–––––
–
–––––
–
––––– –––––– ––––––
Netcashflow (600) 228 148 182 204 222 (53)
DCFfactorat15% 1.000 0.870 0.756 0.658 0.572 0.497 0.432
PVofcashflow (600) 198 112 120 117 110 (23)
––––––
–
–––––
–
–––––
–
–––––
–
––––– –––––– ––––––
NPV 34
––––––
The project is just worthwhile, because the NPV is + $34,000. However, the NPV is
quite small in relation to the size of the capital investment, and in view of the fact
that it is a five-year project.
It might be appropriate to carry out some risk and uncertainty analysis on the
project, before deciding whether or not to undertake it.
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16 Investment appraisal and inflation
(a)
Contributioneachyear = $(15–3.75–2.50)×10,000 = $87,500
Minus:Productionoverheads = $37,500
Contribution = $50,000
Year
Capital
cost
Contribution
Netcash
flow
DCFfactor
at10%
Present
value
$ $ $ $
0 (205,000) (205,000) 1.000 (205,000)
1‐550,000 50,000 3.791 189,500
NPV (15,500)
Ignoring inflation, the project is not worthwhile.
(b) Workings
Year
Sales:
Inflation
at7%
Materials:
Inflation
at5%
Labour:
Inflation
at6%
Overheads:
Inflationat
2%
Net
cash
flow
$ $ $ $ $
Atcurrent
prices
150,000 (37,500) (25,000) (37,500)
1 160,500 (39,375) (26,500) (38,250) 56,375
2 171,735 (41,344) (28,090) (39,015) 63,286
3 183,756 (43,411) (29,775) (39,795) 70,775
4 196,619 (45,582) (31,562) (40,591) 78,884
5 210,382 (47,861) (33,456) (41,403) 87,662
Year
Capital
cost Contribution
Netcash
flow
DCFfactor
at10%
Present
value
$ $ $ $
0 (205,000)(205,000) 1.000 (205,000)
156,37556,375 0.90951,245
263,28663,286 0.82652,274
370,77570,775 0.75153,152
478,88478,884 0.68353,878
587,66287,662 0.62154,438
NPV 59,987
Allowing for inflation in the cash flows, the NPV of the project is about +
$60,000.
The effect of inflation, particularly because selling prices are expected to rise at
a faster rate than costs, is to turn a negative NPV into a positive NPV.
It would be a risky decision to invest in a project, when the project relies for its
positive NPV on estimates of future inflation rates.
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17 DCF exercises
(a)
Annuityfactorat8%,years1–8 5.747
Annuityfactorat8%,years1–4 3.312
Annuityfactorat8%,years5–8 2.435
Annuityfactorat8%,years1–10 6.710
Annuityfactorat8%,years1–8 5.747
Annuityfactorat8%,years9–10 0.963
The Year 10 value of a perpetuity of $100,000 each year in perpetuity from
Year 11 onwards:
= $100,000 ×1/0.08
= $1,250,000
Years Annualcash
flow
Discountfactorat
8%
PV
$ $
0 (3,000,000) 1.000 (3,000,000)
1–4 500,000 3.312 1,656,000
5–8 400,000 2.435 974,000
9–10 300,000 0.963 288,900
10 1,250,000 0.463 578,750
NPV +497,650
(b) (i)
Ignoring inflation
Year Annualcash
flow
Discountfactorat
12%
PV
$ $
0 (900,000) 1.000 (900,000)
1 400,000 0.893 357,200
2 400,000 0.797 318,800
3 250,000 0.636 159,000
4 300,000 0.567 170,100
+105,100
(ii)
Allowing for inflation
Year 0 1 2 3 4
$ $ $ $ $
Equipment (900,000) 243,101
Revenue824,000 848,720 655,636 450,204
Runningcosts(420,000) (441,000) (405,169) (364,652)
–
–––––––
–
–––––––
–
––––––– –––––––– ––––––––
Netcashflow (900,000) 404,000 407,720 250,467 328,653