Pike Robert, Neal Bill. Corporate finance and investment: decisions and strategy
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Appendix B Solutions to selected questions 705
The option writer receives 73.5p. If neither option is exercised, the writer gains all of this. However, this
is the outcome only if
If the call is exercised, if the put is exercised.
The writer will gain from the strategy if the intrinsic value of the exercised option is less than the 73.5
premiums received. Hence the writer will only profit if is within the range 726.5 to 873.5.
If the put is exercised, the writer must take delivery at 800, therefore losing 73.5, which exact-
ly cancels the written premiums of 73.5, so net
If the call is exercised, the writer must deliver the share at price 800, therefore losing 73.5,
which exactly cancels out the written premiums, so net
Thus at any share price outside of that range the writer of the short straddle has an overall loss. If share
price at expiration is within the range the writer makes a net profit.
In general, the profit to short value of the option that is exercised.
Losses could be very high, e.g. if (i.e. ), if
It is extremely risky.
ˇ 126.5 173.5 2002.
S
T
1000 loss73.5 150S
T
650 loss 76.5
straddle written premiums intrinsic
profit 0.
S
T
873.5
profit 0.
S
T
726.5
S
T
800 6 S
T
S
T
7 800
S
T
800.
CHAPTER 13
6 Hercules Wholesalers Ltd
(a) The liquidity position may be examined by calculating the following ratios:
The current ratio reveals that the current assets exceed the short-term liabilities of the company.
However, the ratio of 1.1:1 seems rather low. If current assets were to be liquidated, they would only have
to be sold off at a small discount on the cost to be insufficient to meet the short-term liabilities. The acid-
test ratio excludes stocks from the calculation and represents a more stringent test of liquidity. The ratio of
0.6:1 is also low and suggests the company has insufficient liquid assets to meet its maturing obligations.
When interpreting these ratios, it should be borne in mind that they are based on Balance Sheet figures and
are therefore representative of only one particular moment in time. It would be useful to monitor the trends
in these ratios over time. It would also be useful to prepare a cash flow forecast in order to gain a better
understanding of the likely liquidity position of the business in the future. The bank overdraft is the major
form of short-term finance and the continuing support of the bank is likely to be of critical importance to
the company.
(b) The operating cash cycle of a business represents the time period between the outlay of cash on the pur-
chase of stocks and the receipt of cash from trade debtors. In the case of a wholesale business it can be cal-
culated as follows:
Average holding period for settlement period for settlement
period for creditors
The operating cash cycle is important because the longer this period is, the greater the financing
requirements of the business and the greater the risks involved.
(c) The operating cash cycle is:
debtors Averagestocks Average
0.6:1
£163,000
£285,000
Acid-test ratio
Current assets 1less stocks2
Creditors due for repayment within one year
1.1:1
£306,000
£285,000
Current ratio
Current assets
Creditors due for repayment within one year
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706 Appendix B Solutions to selected questions
No. of days
149
130
279
Less:
(153)
126
(d) The operating cash cycle of the company seems to be quite long. It may be reduced by a reduction in the
stocks, improving the collection period from debtors, extending further the average settlement period for
creditors or some combination of these measures. The stockholding period and average settlement period for
debtors seems high and might be reduced without difficulty. As the average settlement period of creditors
appears to be high, it may be difficult to extend this further without incurring problems for the company.
£145,000
1£341,000>£3602
Average settlement
period for creditors
Average level of creditors
Average daily purchases
£163,000
1£452,000>3602
Average settlement
period for debtors
Average level of debtors
Average daily sales
1£125,000 £143,0002>2
1£323,000>3602
Average period stocks are held
Average value of stocks held
Average daily cost of sales
CHAPTER 14
1 Formula for the cost of cash discounts:
2 The Baumol cash management model assumes cash is drawn down at an even rate and, at some point, is
replenished to its original balance. The Miller – Orr model assumes that short-term cash movements cannot
be predicted since they meander in a random fashion.
3 Hunslett Express Company
Discount%
1100 Discount%2
365
1Final date Discount period2
Average level of debtors – current policy
1,534
Average levels of debtors – proposed policy
329
876
1,205
Reduction in debtors under new policy 329
Financing cost savings 43
Bad debt savings 20
Administration cost savings 12
75
Cost of cash discounts
(80)
Estimated cost of scheme (5)
The net cost of the proposed scheme is £5,000.
50% £8 m 2%
113% £329,0002
50% 80>365 £8 m
50% 30>365 £8 m
70>365 £8 m
1£000s2
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Appendix B Solutions to selected questions 707
4
Salford Engineers Ltd
(a) The optimum stockholding level is a trade-off between the cost of holding stocks and the cost of not hold-
ing stock.
Stockholding costs include:
(i) Storage costs. Where stock is valuable these costs can be large.
(ii) Financing costs. Excessive stock requires unnecessary and expensive working capital.
(iii) Insurance costs against theft or damage.
(iv) Obsolescence costs. Stock held for long periods of time may become obsolete through new products
coming to the market.
Costs of holding too little stock include:
(i) Loss of customer goodwill and business through not being able to supply goods on time.
(ii) Production stoppages. A ‘stockout’ can mean costly and harmful disruptions to the production
process.
(iii) Lost flexibility. Shortage of stock makes it difficult for a firm to respond to unexpected demand or to
extended production runs.
(b) In investigating the reasons for large stock levels for Salford Engineering, the following action should be
taken:
(i) Examine the stock re-order levels for each stock line.
(ii) Examine how the optimum stock level is determined. Is any technique for assessing the optimum
level employed?
(iii) Are stock requirements carefully budgeted?
(iv) Are ratios used (e.g. stock turnover) to monitor stock levels in total and by stock lines?
(v) Are stock records reliable and adequate?
CHAPTER 15
1 Cost of extra trade discount of 3 per cent , i.e. on an invoice of face value of Over the
extra 30 days during which you delay payment, you are paying a cost of roughly:
More accurately, the annual rate is
2 (a) Option 1: The net cost of a full-year loan.
Interest
Less interest received on surplus funds
Q1:
Compounded for Qs 2–4:
Q4:
Option 2: The cost of a fluctuating overdraft.
Total £56,000
Q4:£200,000 3.5% £7,000
Q3:£500,000 3.5% £17,500
Q2:£500,000 3.5% £17,500
Q1:£400,000 3.5% £14,000
Quarterly interest rate 14%>4 3.5%
£51,878
1£6,00021£500,000 £200,0002 2%
1£2,1222 £2,00011.022
3
1£500,000 £400,0002 2% £2,000
£60,000£500,000 12%
11 £30>£9702
12.167
1 11.03092
12.167
1 1.448 1 0.448,
i.e. 44.8%
3.09 12.167 37.6%
1£30>extra finance2 365>30 1£30>£9702 12.167
£1,000.
£30
credit lost
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708 Appendix B Solutions to selected questions
Even without any interest charges on accumulated quarterly overdraft interest, the loan is the cheaper
option. However, the overdraft offers possible access to lower interest rates. (Equally, they could rise!).
( monthly overdraft rate
(b) An average annual interest rate of 13% on the overdraft (3.25% per month) is the break-even rate.
3 Cost of early This corresponds to an effective annual interest
cost of roughly:
More accurately, the annual rate is:
4 £85,000
£25,500
£110,500
7 Amalgamated Effluents plc
The evaluation should be conducted in three stages.
(i) Is the project inherently worthwhile? The basic project must first be evaluated assuming no change in
financing, i.e. using the equity cost of capital. Assuming the outlay can be set against year zero profit, cash
flows are:
Cash flows (marked by ) (£m)
01234
Operating cash inflow 0.200 0.200 0.200 0.200
Equipment cost (0.500) 0.050
WDA 0.125 0.094 0.070 0.053 0.108
WDV 0.375 0.281 0.211 0.158 0.050
Taxable income (0.125) 0.106 0.130 0.147 0.092
Tax impact @ 30% 0.038 (0.032) (0.039) (0.044) (0.028)
Net cash flows (0.462) 0.168 0.161 0.156 0.172
PV @ 10% (0.462) 0.153 0.133 0.117 0.117
The hence the project is worthwhile.
(ii) Should the equipment be leased or purchased? The relevant discount rate is the post-tax cost of bor-
rowing, i.e.
The respective cash flow implications of leasing and outright purchase are:
The PV of the rental
The PV of the tax i.e.
Hence PV of leasing i.e.
Purchase via bank loan:
The relevant cash flows are those connected with the purchase itself rather than the operation of the proj-
ect, i.e. the outlay less tax savings and the residual value.
1£0.1742.costs 0.248 0.074 0.174,
£74,000savings 0.24810.302 0.074,
stream 0.0701PVIFA
5>4
2 0.07013.5462 0.248
7%11 30%2 5%
NPV 0.58, i.e. £58,000,
*
*
*
*
Required monthly payment £110,500>14 122 £2,302.
Total required payments
Total interest cost 17.5% £85,000 42
Net amount borrowed 1£100,000 £15,0002
11.0232
3
1 1.0706 1 0.0706,
i.e. 7.06%
1£4,500>£195,5002 12>4 6.9%
discounting 1£200,000 £195,5002 £4,500.
I 0.0324, rounded to 0.0325,
i.e. 3.25%, or 13%p.a.2
I 3£51,878>£1,600,000 4
£51,878 I 3£400,000 £500,000 £500,000 £200,0004
Let I average
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Appendix B Solutions to selected questions 709
Cash flows (marked by *) (£m)
01234
Outlay (0.500) 0.050
WDA 0.125 0.094 0.070 0.053 0.108
Tax savings @ 30% 0.041 0.031 0.023 0.017 0.036
Net cash flows (0.459) 0.031 0.023 0.017 0.036
PV @ 5% (0.459) 0.030 0.021 0.015 0.030
PV of cash i.e.
Hence, leasing is the preferable (least-cost) method of financing ( compared to ), i.e.
the lease has a net advantage of
(iii) The third stage in the evaluation is now a formality – the optimal decision is to acquire the equipment
using lease finance.
£0.189 m.
£0.363 m£0.174 m
1£0.363 m2flow 10.3632,
*
*
CHAPTER 16
1 (i) Pence
3 old shares prior to rights issue at 320p 960
1 new share at 200
4 shares worth 1,160
1 share therefore worth 1,160/4 290
(ii) Value of the rights is the difference between the offer price and the ex-rights price:
for every new share issued.
2 Proposed preference share issue
(a) Benefits to the company:
– Dividends are only paid if funds are available.
– No asset security required as with some loans.
– Lower risk than for ordinary share capital, giving a cheaper source of finance.
– Suitable when a company does not want to increase the number of ordinary shares but is concerned that
its gearing is already high.
Drawbacks to the company:
– Cost of preference shares is usually higher than for debentures because the risks are greater.
– No tax relief on the dividends (unlike loan interest).
(b) Benefits to the investor:
– Should produce a higher yield than fixed-interest securities.
– Lower risk than ordinary shares.
– Redeemable preference shares provide a means of liquidating the investment where markets are thin or
non-existent.
Drawbacks to the investor:
– Unable to participate fully in the profits.
– Not usually secured.
– No guaranteed dividend.
Many of the drawbacks can be overcome where preference shares are cumulative, participating,
redeemable and convertible into equity if desired.
4 (a) Burnsall needs additional finance to fund both working and fixed capital needs. As sales are expected to
increase by 20 per cent, and since working capital needs are expected to rise in line with sales, the pre-
dicted working capital needs will be 20 per cent above the existing working capital level, i.e.
£32.4 m, increase of £5.4 m.
1.2 3£16 m £23 m £6 m £18 m4
1.2 3stock debtors cash trade creditors4
1290p 200p2 90p
£2
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710 Appendix B Solutions to selected questions
Together with the additional capital expenditures of the total funding
This funding requirement can be met partly by internal finance and partly by new external capital. The
internal finance available will derive from depreciation provisions and retained earnings, after account-
ing for anticipated liabilities, such as taxation, that is, from cash flow.
Note that the profit margin on sales of before interest and tax was 16 per cent
in 1994–95. If depreciation of for 1994–95 is added back, this yields a ‘cash flow margin’ of 21 per
cent (ignoring movements in current assets/liabilities).
Using the same margin, and making a simple operating cash flow projection based on the accounts and
other information provided:
Inflows £m
Sales in 1995– 120.00
Cost of sales before depreciation @ 79% (94.80)
Operating cash flow 25.20
Outflows
Tax liability for 1994–95 (5.00)
Interest payments: (2.40)
Dividends: (5.50)
(12.90)
Net internal finance generated 10.30
Funding requirements (25.40)
Net additional external finance required (13.10)
(b) (i) Some new equipment could be leased, via a long-term capital lease. Tax relief is available on rental
payments, lowering the effective cost of using the equipment. Lessors may ‘tailor’ a leasing package
to suit Burnsall’s specific needs regarding timing of payments and provision of ancillary services.
Alternatively, good quality property assets at present owned by Burnsall could be sold to a financial
institution and their continued use secured via a leaseback arrangement, although this arrangement
involves losing any capital appreciation of the assets.
(ii) If Burnsall’s assets are of sufficient quality, i.e. easily saleable, it may be possible to raise a mortgage
secured on them. This enables retention of ownership.
(iii) Burnsall could make a debenture issue, interest on which would be tax-allowable. The present level of
gearing (long-term debt-to-equity) is relatively low at Burnsall has no short-term
debt apart from trade creditors and the Inland Revenue, and its interest cover is healthy with profit
before tax and interest divided by interest times. It
is likely that Burnsall could make a sizeable debt issue without unnerving the market. Any new deben-
ture would be subordinate to the existing long-term debt and probably carry a higher interest rate.
(iv) An alternative to a debt issue is a rights issue of ordinary shares. Because rights issues are made at
a discount to the existing market price, they result in lower EPS and thus market price, although if
existing shareholders take up their allocations, neither their wealth nor control is diluted. If the mar-
ket approves of the intended use of funds, a capital gain may ensue, although the company and its
advisers must carefully manage the issue regarding the declared reasons and its timing in order to
avoid unsettling the market.
(v) Burnsall could approach a venture capitalist such as 3i, which specialises in extending development
capital to small-to-medium-sized firms. However, 3i may require an equity stake, and possibly insist
on placing an appointee on the Board to monitor its interests.
(vi) Burnsall could utilise official sources of aid, such as a regional development agency depending on
its location, or perhaps the European Investment Bank.
£20 m4 6.6charges 316% £100 m4>312%
£20 m>£120 m 16%,
1.1 £5 m
12% £20 m
96 1£10 10 m2 20%
£5 m
1£10 10 m units2£100 m
£20 m2 £25.4 m.
requirement 1£5.4 m £20 m,
CHAPTER 17
1 With a residual dividend policy:
Tom has issued 10 million shares with par value 50p each, giving total book value of million. Total divi-
dends are Hence, capex 1£10 m £2 m2 £8 m.120p 10 m2 £2 m.
£5
Dividends 3Distributable Earnings Capital Expenditure4
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Appendix B Solutions to selected questions 711
2
As all projects are indivisible, only whole projects with per cent can be selected, i.e. with
total expenditure of million. As this infringes the capital availability constraint of million, Dick is
restricted to only with joint outlay of million, leaving million as a residual dividend.
3 According to Lintner’s target adjustment theory, companies only partially adjust their dividends in line with
earnings changes. The change in dividend will be half of the difference between current EPS and the last div-
idend, i.e.
so that the new
4
Per share, this is (cum dividend).
The ex-dividend share price is reduced by the dividend per share of 10.5p, i.e.
5 (a) The price per share is given by:
where is next year’s dividend, is the shareholder’s required return and g is the expected rate of
growth in dividends.
The growth rate can be found from the expression:
where g is the past (compound) growth rate.
or
From the present value tables, whence:
(b) With at just 5.0p, using managerial expectations for the investment:
(c) To break even, share price must not fall below i.e.
Solving for g, we find marginally above the assessment of the more pessimistic managers.g 12.3%,
£1.34
5.0p
116% g2
£1.34,
P
o
5.0p
116% 14% 2
5.0p
0.02
£2.50
D
1
P
o
7.3p11.12
116% 10% 2
8.03p
0.06
£1.34
g 10%,
1
11 g2
4
0.6849
11 g2
4
7.3p
5.0p
1.46
5.0p11 g2
4
7.3p
k
e
D
1
P
o
D
1
1k
e
g2
£1.40.
1£1.505 £0.1052£1.505
1£150.5 m>100 m2 £1.505
1£140 m £10.5 m2 £150.5 m
Value cum dividend 1£21 m>15%2 £10.5 m
3£30 m £2 m £2 m £9 m4 £21 m
Net 1i.e. post-tax2 cash flow 3Pre-tax profit depreciation replacement investment tax4
i.e. 1£10.5 m>100 m2 10.5p per share
150% £21 m2 £10.5 m Dividend
£21 m 1£30 £9 m2 Profit after tax
Tamas¿ tax charge 1
30% £30 m2 £9 m
dividend 1£1.0 £0.252 £1.25.
0.5 £0.5 £0.25
0.5 30.5 1£3.02 £14
Dividend change 0.5 30.5 EPS
t
Div
t 1
4
£2£7B C,
£9£14
B C E,IRR 7 20
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712 Appendix B Solutions to selected questions
(d) Until 1990, Galahad pursued a policy of distributing 40–50 per cent of profit after tax as dividend. Each
year, it has offered a steady dividend increase, even in 1989, when its earnings actually fell. This was pre-
sumably out of reluctance to lower the dividend, fearing an adverse market reaction, and reflecting a
belief that the earnings shortfall was a temporary phenomenon. In 1990 it offered a 12 per cent dividend
increase, the highest percentage increase in the time series, possibly to compensate shareholders for the
relatively small increase (only 8 per cent) in 1989. It would appear that Galahad has either already built
up a clientèle of investors whose interests it is trying to safeguard, or that it is trying to do so.
The proposed dividend cut to 5.0p per share would represent a sharply increased dividend cover of 3.5,
on the assumption that EPS also grows at 10 per cent p.a. Such a sharp rise in the dividend safety margin
is likely to be construed by the market as implying that Galahad’s managers expect earnings to be
depressed in the future, especially as it follows a year of record dividend increase. Such an abrupt change
in dividend policy is thus likely to offend its clientèle of shareholders at best, and at worst, to alarm the
market as to the reliability of future earnings.
In an efficient capital market, with homogeneous investor expectations, the share price would increase
by the amount calculated in (b), at least, if the market agreed with the managers’ views about the attrac-
tions of the projected expenditure. However, in view of the information content of dividends, Galahad’s
board will have to be very confident of its ability to persuade the market of the inherent desirability of
the proposed investment programme. This may well be a difficult task, especially given the stated doubts
of some of its managers. The board will have to explain why they feel internal financing is preferable to
raising capital externally, either by a rights issue, or by raising further debt finance. While the level of
indebtedness of Galahad is not given, the implication is that it is unacceptably high, so as to obviate the
issue of additional borrowing instruments. If this is the case, then it seems doubly risky to propose a div-
idend cut, as it may signal fears regarding Galahad’s ability to service a high level of debt.
If the dividend cut is greeted adversely, then the ability of the shareholder clientèle to home-make div-
idends will be impaired, since, apart from the transactions costs involved, there will perhaps be no capi-
tal gain to realise. Any significant selling to convert capital into income will further depress share price.
If the investment programme is truly worthwhile, Galahad’s managers perhaps should not shrink from
offering a rights issue, since, despite the costs of such issues, shareholders will eventually reap the bene-
fits in the form of higher future earnings and dividends. However, this might suggest a short-term reduc-
tion in share price, which may penalise short-term investors, but who still have the option of protecting
their interests by selling their rights.
CHAPTER 18
1
2
Market value of
(i)
(ii)
(iii) cost of debt is the solution R to:
Solution value for R 10.3%
£90
£8
11 R2
£8
11 R2
2
p
£8 £100
11 R2
6
cost of debt £811 30%2>£90 1£5.6>£902 6.2%
cost of debt 38% £1004>£90 1£8>£902 8.9%
debt £100 1£45 m>£50 m2 £90
Total Liabilities>Total Assets 1£300 m>£800 m2 37.5%
Income Gearing 11>4.82 100 21%
Interest Cover 1£120 m>£25 m2 4.8 times.
Net Debt>Equity 1£190 m>£500 m2 38%
Net Debt 1£200 m £50 m2
1£20 m £40 m2 £190 m.
Total Debt>Equity 1£200 m £50 m2>£500 m 50%
LTD>1LTD Equity2 £200 m>1£200 m £500 m2 28%
LTD>Equity 1£200 m>£500 m2 40%
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Appendix B Solutions to selected questions 713
(iv) The cost of debt is the solution R to:
Solution value for
3 (a)
Current Structure – £200 m equity.
Tax @ 30% (1.5) (15) (45)
PAT 3.5 35 105
ROE 1.8% 17.5% 52.5%
Programme (i) – debt/ equity.
Interest @ 8% (3.2) (3.2) (3.2)
Taxable profit 1.8 46.8 146.8
Tax @ 30% (0.5) (14.0) (44.0)
PAT 1.26 32.8 102.8
ROE 0.8% 20.5% 64.3%
Programme (ii) – debt/£120 m equity.
Interest @ 8% (6.8) (6.8) (6.8)
Taxable profit – 43.2 143.2
Tax @ 30% – (14.0) (44.0)
PAT – 30.2 100.2
ROE (1.5%) 25.2% 83.5%
(b) Risk is measured by the standard deviation of the returns on equity (ROE) around the respective expect-
ed values (EVs).
Current Capital Structure.
EV of
Outcome EV Deviation Squared
1.8 19.8 18.0 324 97.2
17.5 19.8 2.3 5.3 2.65
52.5 19.8 32.7 1069.3 213.86
Total variance 313.71
Standard i.e. 17.7%.
Programme (i)
EV of
Outcome EV Deviation Squared
0.8 23.4 22.6 510.76 153.228
20.5 23.4 2.9 8.41 4.205
64.3 23.4 40.9 1672.81 334.56
Total variance 491.993
Standard i.e. 22.2%.deviation 2491.993
22.18,
probability
ROE 10.3 0.82 10.5 20.52 10.2 64.32 23.4%
deviation 2313.71
17.7,
probability
ROE 10.3 1.82 10.5 17.52 10.2 52.52 19.8%
£80 m
£160 m£40 m
EBIT
prob. 0.3 prob. 0.5 prob. 0.2
5
50
150
£m
R 8.25%.
£90
£811 30% 2
11 R2
£5.6
11 R2
2
p
1£5.6 £1002
11 R2
6
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714 Appendix B Solutions to selected questions
Programme (ii)
EV of
Outcome EV Deviation Squared
1.5
28.9 30.4 924.16 277.248
25.2 28.9 3.7 13.69 6.845
83.5 28.9 54.6 2981.16 596.230
Total variance 880.323
Standard i.e. 29.7%
(c) Business risk, exposure to the risk of fluctuations in business activity, can be measured in different ways,
e.g. the variability in sales or in some measure of profitability. This example shows how ROE varies under
three scenarios. By abstracting from financial risk, the ROE in the all-equity case shows inherent business
risk – the ROE varies from 1.8 per cent to 52.5 per cent, with a standard deviation of 17.7 per cent.
Gearing adds a second layer of risk because it imposes an extra fixed cost, i.e. the prior interest charge
– the higher the level of gearing, the higher the financial risk. Consequently, we see that the standard
deviation of the ROE rises to 28.9 per cent under the relatively modest level of gearing, programme (i),
while programme (ii) raises it to 22.2 per cent.
4 (a) (i) Perpetual debt:
(ii) When debt is repaid in full after 5 years:
(iii) Debt repaid in equal tranches:
Year Start-year debt Interest Tax saving PV Repayment
1 100 10 3 2.73 20
2 80 8 2.4 1.98 20
3 60 6 1.8 1.35 20
4 40 4 1.2 0.82 20
5 20 2 0.6 0.37 20
Total = £7.25 m
(b) The value of the tax shield is higher:
– the higher the interest rate
– the higher the tax rate
– the higher the amount of debt
– the longer the term of the loan
– the slower that debt is repaid
– the greater the firm’s taxable capacity
5 Book value weights:
weight cost
Equity i.e. 66.7% 20%
Debt 33.3% 10% pre-tax
100%
Market value of The weights become:
Equity: £90 m>£105 m 85.7%
equity 120 m shares £4.502 £90 m.
113.3% 2.3%2 16.6%
WACC 120% 66.7% 2 110% 31 30% 4 33.3%2
£45 m
£15 m
£30 m3£10 m £20 m4
PV £3 m p.a. over 5 years @ 10% discount rate 1£3 m 3.79082 £11.37 m
1£3 m>0.12 £30 m
130% 10% £100 m2>10%
PV of Tax Savings
1T i Nominal Debt Value2
i
TiB
i
deviation 2880.323
29.7,
probability
ROE 10.3 1.52 10.5 25.22 10.2 83.52 28.9%
CFAI_Z02.QXD 10/28/05 11:53 AM Page 714