ACCA F9 Financial Management - 2010 - Study text - Emile Woolf Publishing
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Discount
factorat12%
1.000 0.893 0.797 0.636 0.567
Presentvalue (900,000) 360,772 324,953 159,297 186,346
NPV=+131,368
18 DCF and tax
Annual depreciation = $(800,000 – 200,000)/4 years = $150,000 per year.
Annual cash profits = Accounting profit + Deprecation = $250,000 + $150,000 =
$400,000.
Tax depreciation allowances (capital allowances)
Yearof
claim
Written
downvalue
Taxsaved
at30%
Yearof
cashflow
$ $
800,000
0 Allowance(25%) (200,000) 60,000 1
–
–––––––
600,000
1 Allowance(25%) (150,000) 45,000 2
–
–––––––
450,000
2 Allowance(25%) (112,500) 33,750 3
–
–––––––
337,500
3 Allowance(25%) (84,375) 25,313 4
–
–––––––
253,125
4 Disposalvalue (200,000)
–
–––––––
4 Balancingallowance 53,125 15,938 5
–
–––––––
Year 0 1 2 3 4 5
$ $ $ $ $ $
Equipment (800,000) 200,000
Capitalallowance 60,000 45,000 33,750 25,313 15,938
Cashprofit 400,000 400,000 400,000 400,000
Taxoncashprofit(120,000) (120,000) (120,000) (120,000)
––––––––
–
–––––––
–
–––––––
–
––––––– –––––––– ––––––––
Netcashflow (800,000) 460,000 325,000 313,750 505,313 (104,062)
Discount
factor,15%
1.000 0.870 0.756 0.658 0.572 0.497
Presentvalue (800,000) 400,200 245,700 206,448 289,039 (51,719)
NPV=+$289,668
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19 Risk in investment appraisal
(a) and (b)
MachineA
2,000
demand
3,000
demand
5,000
demand
Year
$ $ $
0 (15,000) (15,000) (15,000)
1 ($4‐$1)/unit 6,000 9,000 15,000
2 6,000 9,000 15,000
3 6,000 9,000 15,000
Discounted
cashflows
Discountfactorat
6%
PV PV PV
$ $ $
Year0 1.000 (15,000) (15,000) (15,000)
1 0.943 5,658 8,487 14,145
2 0.890 5,340 8,010 13,350
3 0.840 5,040 7,560 12,600
–
–––––––
–
––––––– ––––––––
NPV 1,038 9,057 25,095
–
–––––––
–
––––––– ––––––––
Expected value of NPV
= (0.2 × 1,038) + (0.6 × 9,057) + (0.2 × 25,095) = $10,661
2,000
demand
3,000
demand
5,000
demand
Year
$ $ $
0 (20,000) (20,000) (20,000)
1 ($4‐$0.5)/unit 7,000 10,500 17,500
2 7,000 10,500 17,500
3 7,000 10,500 17,500
Discounted
cashflows
Discountfactorat
6%
PV PV PV
$ $ $
Year0 1.000 (20,000) (20,000) (20,000)
1 0.943 6,601 9,902 16,503
2 0.890 6,230 9,345 15,575
3 0.840 5,880 8,820 14,700
–
–––––––
–
––––––– ––––––––
NPV (1,289) 8,967 26,778
–
–––––––
–
––––––– ––––––––
Expected value of NPV = (0.2 × (1,289)) + (0.6 × 8,067 + (0.2 × 26,778) = $9,938
Note: A quicker way of calculating expected values is to:
calculate the EV of annual sales (which is 3,200 units)
calculate the cash flows and NPV for annual sales of 3,200 units.
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However, this approach makes it more difficult to carry out risk and
uncertainty analysis.
On the basis of the figures, it would seem that Machine A should be
purchased.
It has a higher expected value of NPV.
It is also a lower risk option, because the NPV will be positive even when
sales are only 2,000 units each year. With machine B, the NPV would be
negative if the annual sales are just 2,000 units.
Machine A also gives a higher NPV if sales are 3,000 units, which is the
most likely outcome.
(c) Sensitivity analysis on the Machine A investment.
(i) The NPV is + $1,038 even when sales are 2,00 units each year. The
probability of a negative NPV is 0%. (With machine B, the risk of a
negative NPV is 20%).
(ii) The project will achieve a 6% return if the NPV of annual cash profits is
$15,000.
Discount factor at 6% for years 1 – 3 = 2.673
Annual cash profits to achieve a PV of $15,000 = $15,000/2.673 = $5,612.
The contribution per unit is $3.
Therefore minimum annual sales to achieve an NPV of $0 = $5,612/$3
per unit
= 1,871 units.
If annual sales exceed 1,871 units, the NPV with Machine A will be
positive at a discount rate of 6%.
20 Lease or buy
(a) Evaluate the investment decision
Yearof
claim
Taxsaving(30%
ofallowance)
Cashflow
year
$ $
Cost 30,000
1 Allowance(25%) (7,500) 2,250 2
–
–––––––
22,500
2 Allowance(25%) (5,625) 1,688 3
–
–––––––
16,875
3 Allowance(25%) (4,219) 1,266 4
–
–––––––
12,656
4 Allowance(25%) (3,164) 949 5
–
–––––––
9,492
5 Disposal 6,000
–
––
–
––––
Balance (3,492) 1,048 6
–
–––––––
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Cashflows
Year 0 1 2 3 4 5 6
$ $ $ $ $ $ $
Equipment (30,000) 6,000
Taxrelief 2,250 1,688 1,266 949 1,048
Projectcashflows 10,000 10,000 10,000 10,000 10,000
Taxontheseat30% (3,000) (3,000) (3,000) (3,000) (3,000)
–––––––
–
–––––––
–
––––––
–
––––––
–
–––––– –––––––
–
–––––––
Netcashflow (30,000) 10,000 9,250 8,688 8,266 13,949 (1,952)
DCFfactorat
10%
1.000 0.909 0.826 0.751 0.683 0.621 0.564
Presentvalue (30,000) 9,090 7,641 6,525 5,646 8,662 (1,101)
NPV
= + $6,463
The acquisition is worthwhile.
(b) Evaluate the financing decision:
Now consider how it should be financed. The project cash flows and tax on
these are now irrelevant to this decision. Only the financing cash flows need
to be considered.
The cost of financing is the after-tax cost of borrowing, which is 8%.
Leasing Cashflows
Year 1 2 3 4 5 6
$ $ $ $ $ $
Leasepayments (7,000) (7,000) (7,000) (7,000) (7,000)
Taxrelief 2,100 2,100 2,100 2,100 2,100
––––––––
–
–––––––
–
–––––––
–
––––––– –––––––– ––––––––
Netcashflow (7,000) (4,900) (4,900) (4,900) (4,900) 2,100
DCFfactorat8% 0.926 0.857 0.794 0.735 0.681 0.630
Presentvalue (6,482) (4,199) (3,891) (3,602) (3,337) 1,323
PV of the cost of leasing = $20,188
Purchase Cashflows
Year 0 1 2 3 4 5 6
$ $ $ $ $ $ $
Equipment (30,000) 6,000
Taxrelief 2,250 1,688 1,266 949 1,048
––––––––
–
–––––
–
–––––
–
–––––
–
––––– ––––––
–
–––––
Netcashflow (30,000) 0 2,250 1,688 1,266 6,949 1,048
DCFfactorat8% 1.000 0.857 0.794 0.735 0.681 0.630
Presentvalue (30,000) 1,928 1,340 931 4,732 660
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PV of the cost of purchasing = $20,409
Leasing
has the lower PV of costs (although only by about $200) and is slightly
cheaper.
On this basis, the company might decide to lease the asset. However, the difference
in cost is so small that other non-financial factors might influence the decision.
21 Asset replacement
(a) Replace every year
Year
Cash
flow
Discount
factorat10%
PV
$ $
0 Purchasecost (40,000) 1.000 (40,000)
1 Runningcosts (8,000)
1 Disposalvalue 25,000
1 Netcashflow,Year1 17,000 0.909 15,453
––––––––
(24,547)
––––––––
Annuityfactorat10%,Year1 0.909
Equivalentannualcost$(27,004)
––––––––
(b)
Replace every two years
Year
Cash
flow
Discount
factorat10%
PV
$ $
0 Purchasecost (40,000) 1.000 (40,000)
1 Runningcosts (8,000) 0.909 (7,272)
2 Runningcosts (12,000)
2 Disposalvalue 20,000
2 Netcashflow,Year2 8,000 0.826 6,608
––––––––
(40,664)
––––––––
Annuityfactorat10%,Years1–2 1.736
Equivalentannualcost$(23,424)
––––––––
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(c) Replace every three years
Year
Cash
flow
Discount
factorat10%
PV
$ $
0 Purchasecost
(
40,000
)
1.000
(
40,000
)
1 Runnin
g
costs
(
8,000
)
0.909
(
7,272
)
2 Runnin
g
costs
(
12,000
)
0.826
(
9,912
)
3 Runnin
g
costs
(
20,000
)
3 Dis
p
osalvalue 10,000
3 Netcashflow,Year3
(
10,000
)
0.751
(
7,510
)
––––––––
(
64,694
)
–
–––––––
Annuit
y
factorat10%,Years1
–
3 2.487
E
q
uivalentannualcost $
(
26,013
)
––––––––
(d)
Replace every four years
Year
Cash
flow
Discount
factorat10%
PV
$$
0 Purchasecost (40,000) 1.000 (40,000)
1 Runningcosts (8,000) 0.909 (7,272)
2 Runningcosts (12,000) 0.826 (9,912)
3 Runningcosts (20,000) 0.751 (15,020)
4 Runningcosts (25,000) 0.683 (17,075)
(89,279)
Annuityfactorat10%,Years1–4 3.170
Equivalentannualcost$(28,164)
Recommendation
The machine should be replaced every two years, because this replacement policy
gives the lowest equivalent annual cost.
22 Capital rationing
(a) Assume that all the investments are divisible
Total NPV is maximised by maximising the NPV per $1 invested.
Investment
Capital
investment NPV
NPVper$1
invested
Ranking
$ $ $
A 60,000 12,000 0.20 3rd
B 80,000 21,600 0.27 1st
C 50,000 8,500 0.17 5th
D 45,000 10,800 0.24 2nd
E 55,000 9,900 0.18 4th
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Investments to maximise NPV
Investment Capital
investment
NPV
$ $
B 80,000 21,600
D 45,000 10,800
125,000
A (balance) 25,000 5,000
Total 150,000 37,400
(b) Assume that all investments are indivisible
The combination to maximise total NPV is found by identifying possible
combinations of investments within the $150,000 investment limit and
calculating the total NPV from that combination.
Investments
Capital
investment
Total
NPV
$ $
A+B (60,000+80,000) 140,000 33,600
C+D+E (50,000+45,000+55,000) 150,000 29,200
B+D (80,000+45,000) 125,000 32,400
(B + D) is clearly better than (B + C) or (B + E).
Conclusion
If the projects are indivisible, the combination of investments to maximise
total NPV is investment in A and B.
23 Misteri Company
Workings
WACC
WACC = (70% × 10%) + [(30%) × (8.9%)(1 – 0.25)]
= 7% + 2% = 9%.
Capital allowances
Year Tax
WDV
Capital
allowance
Taxsaved
at25%
Yearof
saving
$ $ $
1,200,000
1 Allowance (300,000) 300,000 75,000 2
–
–––––––––
900,000
2 Allowance (225,000) 225,000 56,250 3
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–
–––––––––
675,000
3 Allowance (168,750) 168,750 42,188 4
–
–––––––––
506,250
4 Disposalvalue (200,000)
–
–––––––––
4 Balancingallowance 306,250 306,250 76,562 5
–
–––––––––
Year1 Year2 Year3 Year4
Sales(units) 400,000 600,000 700,000 700,000
Contributionperunit:$2
$ $ $ $
Totalcontribution 800,000 1,200,000 1,400,000 1,400,000
Fixedcosts(cash) (500,000) (520,000) (540,000) (560,000)
––––––––
–
–––––––
–
––––––– ––––––––
Cashprofit 300,000 680,000 860,000 880,000
––––––––
–
–––––––
–
––––––– ––––––––
Taxat25% (75,000) (170,000) (215,000) (220,000)
Project cash flows
Year1 Year2 Year3 Year4 Year5
$ $ $ $ $
Cashprofits 300,000 680,000 860,000 880,000
Taxonprofits(75,000) (170,000) (215,000) (220,000)
Taxbenefitofcap.allowances 75,000 56,250 42,188 76,562
Disposalofmachine200,000
––––––––
–
–––––––
–
–––––––
–
––––––– ––––––––
Netcashflow 300,000 680,000 746,250 907,188 (143,438)
––––––––
–
–
––––––
–
–––––––
–
––––––– ––––––––
NPV calculation
Year Netcash
flow
Discount
factorat9%
Present
value
$$
0 (1,200,000) 1.000 (1,200,000)
1 300,000 0.917 275,100
2 680,000 0.842 572,560
3 746,250 0.772 576,105
4 907,188 0.708 642,289
5 (143,438) 0.650 (93,235)
–
–––––––
NPV+772,819
–
–––––––
Recommendation
The NPV of the project is + $772,819.
The project would appear to provide a DCF return well in excess of the WACC, and
on financial considerations (assuming that the estimates of costs and revenues are
reasonably reliable) the project should be undertaken.
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24 Valuation model
(a)
Expected share price =
$0.24
0.08
= $3.00
(b)
Expected share price =
$0.24 1.03
(
)
0.08 −0.03
()
= $4.94
(c) Expected growth rate in dividends = 60% × 9% = 5.4%.
Expected share price =
$0.24 1.054
(
)
0.08 −0.054
()
= $9.73
25 Rights
(a)
$
4shares haveacurrentmarketvalueof(
×
$5.50)
22.00
1newshare‐issueprice 4.50
––––––
5shares Haveatheoreticalvalueof 26.50
––––––
Theoretical ex-rights price = $26.50/5 = $5.30 per share.
(b)
Valueofrights $
Currentmarketprice 5.50
Theoreticalex‐rightsprice 5.30
–
–––
Valueofrights 0.20
–
–––
This is the theoretical value of the rights, for each existing share.
26 Rights issue
(a)
(i) Number of shares in issue = total earnings/EPS
= $1,200,000/$0.15 = 8,000,000
$m
Valueoftheexistingshares=8,000,000×$2.70 21.6
Cashraisedfromnewshares 3.8
––––––
Total 25.4
––––––
Number of shares issued = $3,800,000/$1.90 per share
= 2,000,000 shares
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The rights issue is therefore a 1 for 4 rights issue (2,000,000:8,000,000)
The number of shares after the issue = 10 million
$
Currentvalueof4existingshares (
×$2.70) 10.80
Rightsissuepriceof1share1.90
––––––
Theoreticalvalueof5shares12.70
––––––
Theoreticalex‐rightsprice (12.70/5) $2.54
(ii)
$
Currentmarketvalueofexistingshare 2.70
Theoreticalex‐rightsprice 2.54
––––––
Thevalueofaright 0.16
––––––
(iii) Existing P/E ratio = $2.70/$0.15 = 18.0
The revised profit after tax = $1.8 million
The revised total market value = 18 × $1.8 million = $32.4 million
Therefore, the market value per share =
$32.4 million
10 million shares
= $3.24
(b) The shareholder can do any of the following:
Buy all the shares offered to him in the rights issue. This would maintain
his percentage shareholding in the company.
Sell the rights. Rights can be sold on the stock market. The theoretical
market price is $0.16 for the rights attached to one existing share.
Buy some of the shares offered to him in the rights issue and sell some
rights.
Do nothing. This is a bad choice. Shareholders will see a fall in the value of
their shares because the new shares will be issued at a discount to the
current market price. The company may try to sell any rights that are not
taken up on behalf of the shareholder, but the shareholder should not rely
on getting any money from the company.