1. Warden Co plans to buy a new machine.

The cost of the

machine, payable immediately, is $800,000 and the machine
has an expected life of five years. Additional investment in
working capital of $90,000 will be required at the start of the
first year of operation.

At the end of five years, the machine will be sold for scrap, with
the scrap value expected to be 5% of the initial purchase cost of
the machine. The machine will not be replaced.

Production and sales from the new machine are expected to be

100,000 units per year. Each unit can be sold for $16 per unit and
will incur variable costs of $11 per unit. Incremental fixed costs
arising from the operation of the machine will be $160,000 per
year.

Warden Co has an after-tax cost of capital of 11% which it uses

as a discount rate in investment appraisal. The company pays
profit tax one year in arrears at an annual rate of 30% per year.
Capital allowances and inflation should be ignored.

Required:

Calculate the net present value of investing in the new machine

and advise whether the investment is financially acceptable.

Calculate the internal rate of return of investing in the new

machine and advise whether the investment is financially
acceptable.

(i) Explain briefly the meaning of the term ‘sensitivity analysis’ in

the context of investment appraisal;

(ii) Calculate the sensitivity of the investment in the new machine

to a change in selling price and to a change in discount rate, and
comment on your findings.

Ans: Refer Excel Sheet

2. Discuss the nature and causes of the problem of capital
rationing in the context of investment appraisal, and explain how
this problem can be overcome in reaching the optimal investment
decision for a company.

Ans:

In real-world capital investment decisions, companies are limited

in the funds that are available for investment. However, the basis
for investment decisions should still be to maximise the wealth of
shareholders. The NPV decision rule calls for a company to invest
in all projects with a positive net present value, but this is
theoretically possible only in a perfect capital market, i.e. a capital
market where there is no limit on the finance available.

Since investment funds are limited in the real world, it is not

possible in the real world for a company to invest in all projects
with a positive NPV.

The reasons why investment funds are limited in the real world
are either external to the company (hard capital rationing) or
internal to the company (soft capital rationing).

Several reasons have been suggested for hard capital rationing,

such as that investors may feel that a company is too risky to
invest in, with its credit rating being seen as too low for the
amount of investment it needs. Perhaps capital markets may be
depressed, so that there is a general unwillingness by investors to
provide funds for capital investment.

Capital may be in short supply due to ‘crowding-out’ as a result of

high government borrowing, for example in order to finance a
Keynsian injection of funds into the circular flow of income so as
to encourage or assist recovery from an economic recession.
Soft capital rationing may be due to reluctance by a company to
raise finance. For example, the amount of funds needed may be
small in relation to the costs of raising the finance: or the
company may wish to avoid dilution of control or earnings per
share by issuing new equity; or the company may wish to avoid a
commitment to paying fixed interest because it believes future
economic conditions may put its profitability under pressure.

Alternatively, the company may limit the funds available for capital
investment in order to encourage competition between potential
investment projects, so that only robust investment projects are
accepted. This is the ‘internal capital market’ reason for soft
capital rationing.

If a company cannot invest in all projects with a positive NPV, it

must ensure that it generates the maximum return per dollar
invested. With single-period capital rationing, where investment
funds are limited in the first year only, divisible investment
projects can be ranked in order of desirability using the
profitability index. This can be defined either as the NPV divided
by the initial investment, or as the present value of future cash
flows divided by the initial investment.

The optimal investment decision for a company is then to invest in

the projects in turn, moving from highest profitability index
downwards, until all the funds have been exhausted. This may
require partial investment in the last desirable project selected,
which is possible with divisible investment projects.

Where investment projects are not divisible, the total NPV of

various combinations of projects must be compared, within the
limit of the investment funds available, in order to select the
combination of projects with the highest NPV. This will be the
optimum investment decision. Surplus funds may be left over, but
since the highest-NPV combination has been selected, the
amount of surplus funds is irrelevant to the selection of the
optimal investment schedule. Investing these surplus funds in a
bank or in the money market would have an NPV of zero
3. Explain the meaning of the term ‘cash operating cycle’ and
discuss the relationship between the cash operating cycle
and the level of investment in working capital. Your answer
should include a discussion of relevant working capital policy
and the nature of business operations.
The cash operating cycle is the average length of time
between paying trade payables and receiving cash from
trade receivables. It is the sum of the average inventory
holding period, the average production period and the
average trade receivables credit period, less the average
trade payables credit period. Using working capital ratios,
the cash operating cycle is the sum of the inventory turnover
period and the accounts receivable days, less the accounts
payable days.
The relationship between the cash operating cycle and the
level of investment in working capital is that an increase in
the length of the cash operating cycle will increase the level
of investment in working capital. The length of the cash
operating cycle depends on working capital policy in relation
to the level of investment in working capital, and on the
nature of the business operations of a company.
Working capital policy
Companies with the same business operations may have
different levels of investment in working capital as a result of
adopting different working capital policies. An aggressive
policy uses lower levels of inventory and trade receivables
than a conservative policy, and so will lead to a shorter cash
operating cycle.
A conservative policy on the level of investment in working
capital, in contrast, with higher levels of inventory and trade
receivables, will lead to a longer cash operating cycle. The
higher cost of the longer cash operating cycle will lead to a
decrease in profitability while also decreasing risk, for
example the risk of running out of inventory.
Nature of business operations
Companies with different business operations will have
different cash operating cycles. There may be little need for
inventory, for example, in a company supplying business
services, while a company selling consumer goods may have
very high levels of inventory. Some companies may operate
primarily with cash sales, especially if they sell direct to the
consumer, while other companies may have substantial
levels of trade receivables as a result of offering trade credit
to other companies.
 4. Extracts from the recent financial statements of
Bold Co are given below.
$000
turnover 21300
cost of sales 16400
-------
gross profit 4900
-------
$000 $000
non-current assets 3000
current assets
inventory 4500
trade receivables 3500
-------
8000
-------
total assets 11000
-------
current liabilities
trade payables 3000
overdraft 3000
-------
6000
equity
ordinary shares 1000
reserves 1000
-------
2000
non-current liabilities
bonds 3000
-------
11000
-------
A factor has offered to manage the trade receivables of Bold Co
in a servicing and factor-financing agreement. The factor expects
to reduce the average trade receivables period of Bold Co from its
current level to 35 days; to reduce bad debts from 0·9% of
turnover to 0·6% of turnover; and to save Bold Co $40,000 per
year in administration costs.

The factor would also make an advance to Bold Co of 80% of the

revised book value of trade receivables. The interest rate on the
advance would be 2% higher than the 7% that Bold Co currently
pays on its overdraft.

The factor would charge a fee of 0·75% of turnover on a with-

recourse basis, or a fee of 1·25% of turnover on a non-recourse
basis. Assume that there are 365 working days in each year and
that all sales and supplies are on credit.

Required:

Calculate the cash operating cycle of Bold Co. (Ignore the factor’s
offer in this part of the question).

Ans

Inventory days = 365 x 4,500/16,400 = 100 days

Trade receivables days = 365 x 3,500/21,300 = 60 days
Trade payables days = 365 x 3,000/16,400 = 67 days
Cash operating cycle = 100 + 60 – 67 = 93 days

(c) Calculate the value of the factor’s offer:

(i) on a with-recourse basis;

(ii) on a non-recourse basis.

ANS: Refer Excel sheet

(d) Comment on the financial acceptability of the factor’s offer and

discuss the possible benefits to Bold Co of factoring its trade
receivables.
ANS

The factor’s offer is financially acceptable on a with-recourse

basis, giving a net benefit of $13,497. On a non-recourse basis,
the factor’s offer is not financially acceptable, giving a net loss of
$93,003, if the elimination of bad debts is ignored.

The difference between the two factor fees ($106,500 or 0·5% of

sales), which represents insurance against the risk of bad debts,
is less than the remaining bad debts ($127,800 or 0·6% of sales),
which will be eliminated under non-recourse factoring.

When this elimination of bad debts is considered, the non-

recourse offer from the factor is financially more attractive than
the with-recourse offer.
 5. Recent financial information relating to Close Co, a stock
market listed company, is as follows.

$m
profit after tax (earnings) 66.6
dividends 40.0
statement of financial position information
$m $m
non current assets 595
current assets 125
-------
total assets 720
-------
current liabilities 70
equity
ordinary shares ($1 nominal) 80
reserves 410
-------
490
non current liabilities
6% bank loan 40
8% bonds ($100 nominal) 120
-------
160
-------
720
-------
Financial analysts have forecast that the dividends of Close
Co will grow in the future at a rate of 4% per year. This is
slightly less than the forecast growth rate of the profit after
tax (earnings) of the company, which is 5% per year.
The finance director of Close Co thinks that, considering the
risk associated with expected earnings growth, an earnings
yield of 11% per year can be used for valuation purposes.
 Close Co has a cost of equity of 10% per year and a before-
tax cost of debt of 7% per year. The 8% bonds will be
redeemed at nominal value in six years’ time. Close Co pays
tax at an annual rate of 30% per year and the ex-dividend
share price of the company is $8·50 per share.
Required:

Calculate the value of Close Co using the net asset value

method

ANS:
Net asset valuation
In the absence of any information about realizable values
and replacement costs, net asset value is on a book value
basis. It is the sum of non-current assets and net current
assets, less long-term debt, i.e. 595 + 125 – 70 – 160 = $490
million.

(a) Calculate the value of Close Co using the dividend growth

model

ANS: Dividend growth model

Total dividends of $40 million are expected to grow at 4% per

year and Close Co has a cost of equity of 10%.

Value of company = (40m x 1·04)/(0·1 – 0·04) = $693 million

(b) Discuss the weaknesses of the dividend growth model as a

way of valuing a company and its shares.

ANS:

The future dividend growth rate

The DGM is based on the assumption that the future dividend

growth rate is constant, but experience shows that a constant
dividend growth rate is, in reality, very rare. This may be seen as
less of a problem if the future dividend growth rate is regarded as
an average growth rate.

Estimating the future dividend growth rate is very difficult in

practice and the DGM is very sensitive to small changes in this
key variable. It is common practice to estimate the future dividend
growth rate by calculating the historical dividend growth, but the
assumption that the future will reflect the past is an easy one to
challenge.

The cost of equity

The DGM assumes that the future cost of equity is constant, when
in reality it changes quite frequently. The cost of equity can be
calculated using the capital asset pricing model, but this model
usually employs historical information, which may not reflect
accurately expectations about the future.

Zero dividends

It is sometimes claimed that the DGM cannot be used when no

dividends are paid, but this depends on whether dividends are
expected in the future. If dividends are forecast to be paid from a
future date, the dividend growth model can be applied at that
point to calculate a share price, which can then be discounted to
give the current ex dividend share price.

Only in the case where no dividends are paid and no dividends

are expected to be paid will the DGM have no application.

Calculate the value of Close Co using the earnings yield

method

Earnings yield method

Profit after tax (earnings) is $66·6 million and the finance director
of Close Co thinks that an earnings yield of 11% per year can be
used for valuation purposes.
Ignoring growth, value of company = 66·6m/0·11 = $606 million

Alternatively, profit after tax (earnings) is expected to grow at an

annual rate of 5% per year and earnings growth can be
incorporated into the earnings yield method using the growth
model.

Value of company = (66·6m x 1·05)/(0·11 – 0·05) = $1,166 million

Calculate the weighted average after-tax cost of capital of

Close Co using market values where appropriate.

ANS
Market value of equity
Close Co has 80 million shares in issue and each share is worth $8·50
per share.
The market value of equity is therefore 80 x 8·50 = $680 million
Cost of equity
This is given as 10% per year.
Market value of 8% bonds
The market value of each bond will be the present value of the
expected future cash flows (interest and principal) that arise from
owning the bond. Annual interest is 8% per year and the bonds will be
redeemed at their nominal value of $100 per bond in six years’ time.
The before-tax cost of debt is given as 7% per year and this is used as
a discount rate.
Present value of future interest = (8 x 4·767) = $38·14
Present value of future principal payment = (100 x 0·666) = $66·60
Ex interest bond value = 38·14 + 66·60 = $104·74 per bond
Market value of bonds = 120m x (104·74/100) = $125·7 million
After-tax cost of debt of 8% bonds
The before-tax cost of debt of the bonds is given as 7% per year.
After-tax cost of debt of bonds = 7 x (1 – 0·3) = 7 x 0·7 = 4·9% per
year
Value of the 6% bank loan
The bank loan has no market value and so its book value of $40
million is used in calculating the weighted average cost of capital.
After-tax cost of debt of 6% bank loan
The interest rate of the bank loan can be used as its before-tax cost of
debt.
After-tax cost of debt of bank loan = 6 x (1 – 0·3) = 6 x 0·7 = 4·2% per
year
Calculation of weighted average after-tax cost of capital (WACC)
Total value of company = 680m + 125·7m + 40m = $845·7m
After-tax WACC = ((680m x 10) + (125·7m x 4·9) + (40 x 4·2))/845·7 =
9·0 % per year
 6. Discuss the circumstances under which the weighted
average cost of capital (WACC) can be used as a discount
rate in investment appraisal. Briefly indicate alternative
approaches that could be adopted when using the WACC
is not appropriate.
ANS:
The weighted average cost of capital (WACC) is the average return
required by current providers of finance. The WACC therefore reflects
the current risk of a company’s business operations (business risk)
and way in which the company is currently financed (financial risk).
When the WACC is used as discount rate to appraise an investment
project, an assumption is being made that the project’s business risk
and financial risk are the same as those currently faced by the
investing company. If this is not the case, a marginal cost of capital or
a project-specific discount rate must be used to assess the
acceptability of an investment project.
The business risk of an investment project will be the same as current
business operations if the project is an extension of existing business
operations, and if it is small in comparison with current business
operations. If this is the case, existing providers of finance will not
change their current required rates of return. If these conditions are
not met, a project-specific discount rate should be calculated, for
example by using the capital asset pricing model.
The financial risk of an investment project will be the same as the
financial risk currently faced by a company if debt and equity are
raised in the same proportions as currently used, thus preserving the
existing capital structure.
If this is the case, the current WACC can be used to appraise a new
investment project. It may still be appropriate to use the current WACC
as a discount rate even when the incremental finance raised does not
preserve the existing capital structure, providing that the existing
capital structure is preserved on an average basis over time via
subsequent finance-raising decisions.
Where the capital structure is changed by finance raised for an
investment project, it may be appropriate to use the marginal cost of
capital rather than the WACC.
 7. Bar Co is a stock exchange listed company that is
concerned by its current level of debt finance. It plans to
make a rights issue and to use the funds raised to pay off
some of its debt. The rights issue will be at a 20% discount
to its current ex-dividend share price of $7·50 per share
and Bar Co plans to raise $90 million.
Bar Co believes that paying off some of its debt will not
affect its price/earnings ratio, which is expected to remain
constant.

income statement information

$m
turnover 472
cost of sales 423
-----
profit before interest and tax 49
interest 10
-----
profit before tax 39
tax 12
-----
profit after tax 27
-----
statement of financial position information
$m
equity
ordinary shares ($1 nominal) 60
reserves 80
-----
140
long-term liabilities
8% bonds ($100 nominal) 125
-----
265
-----
The 8% bonds are currently trading at $112·50 per $100
bond and bondholders have agreed that they will allow Bar
Co to buy back the bonds at this market value. Bar Co
pays tax at a rate of 30% per year.
 Required:
(a) Calculate the theoretical ex rights price per share of
Bar Co following the rights issue.

ANS:

Rights issue price = 7·50 x 0·8 = $6·00 per share

Number of shares issued = $90m/6·00 = 15 million shares
Number of shares currently in issue = 60 million shares
The rights issue is on a 1 for 4 basis
Theoretical ex rights price = ((4 x 7·50) + (1 x 6·00))/5 = $7·20
per share

Alternatively, theoretical ex rights price = ((60m x 7·50) + (15m

x 6·00))/75m = $7·20 per share, where 75 million is the number
of shares after the rights issue.

(b) Calculate and discuss whether using the cash raised by

the rights issue to buy back bonds is likely to be financially
acceptable to the shareholders of Bar Co, commenting in
your answer on the belief that the current price/earnings
ratio will remain constant.

ANS:

The financial acceptability to shareholders of the proposal to buy back

bonds can be assessed by calculating whether shareholder wealth is
increased or decreased as a result.
The bonds are being bought back by Bar Co at their market value of
$112·50 per bond, rather than their nominal value of $100 per bond.
The total nominal value of the bonds redeemed will therefore be less
than the $90 million spent redeeming them.
Nominal value of bonds redeemed = 90m x (100/112·50) = $80 million
Interest saved by redeeming bonds = 80m x 0·08 = $6·4 million per
year
Earnings per share will be affected by the redemption of the bonds and
the issue of new shares.
Revised profit before tax = 49m – (10m – 6·4m) = $45·4 million
Revised profit after tax (earnings) = 45·4m x 0·7 = $31·78 million
Revised earnings per share = 100 x (31·78m/75m) = 42·37 cents per
share
Current earnings per share = 100 x (27m/60m) = 45 cents per share
Current price/earnings ratio = 750/45 = 16·7 times
The revised earnings per share can be used to calculate a revised
share price if the price/earnings ratio is assumed to be constant.
Revised share price = 16·7 x 42·37 = 708 cents or $7·08 per share
This share price is less than the theoretical ex rights price per share
($7·20) and so the effect of using the rights issue funds to redeem the
bonds is to decrease shareholder wealth. From a shareholder
perspective, therefore, this use of the funds cannot be recommended.
However, this conclusion depends heavily on the assumption that the
price/earnings ratio remains constant, as this ratio was used to
calculate the revised share price from the revised earning per share. In
reality, the share price after the redemption of bonds will be set by the
capital market and it is this market-determined share price that will
determine the price/earnings ratio, rather than the price/earnings ratio
determining the share price.
Since the financial risk of Bar Co has decreased following the
redemption of bonds, the cost of equity is likely to fall and the share
price is likely to rise, leading to a higher price/earnings ratio. If the
share price increases to above the theoretical ex rights price per share,
corresponding to an increase in the price/earnings ratio to more than
17 times (720/42·37), shareholders will experience a capital gain and
so using the cash raised by the rights issue to buy back bonds will
become financially acceptable from their perspective.
 (c) Calculate and discuss the effect of using the cash
raised by the rights issue to buy back bonds on the
financial risk of Bar Co, as measured by its interest
coverage ratio and its book value debt to equity ratio.
ANS:

Current interest coverage ratio = 49m/10m = 4·9 times

Revised interest coverage ratio = 49m/(10m – 6·4m) = 49m/3·6m =
13·6 times
Current debt/equity ratio = 100 x (125m/140m) = 89%
Revised book value of bonds = 125m – 80m = $45 million
Revised book value of equity = 140m + 90m – 10m = $220 million
A loss of $10 million is deducted here because $90 million has been
spent to redeem bonds with a total nominal value (book value) of $80
million.
Revised debt/equity ratio = 100 x (45m/220m) = 20·5%
Redeeming bonds with a book value of $80m has reduced the
financial risk of Bar Co, as shown by the significant reduction in
gearing from 89% to 20·5%, and by the significant increase in the
interest coverage ratio from 4·9 times to 13·6 times.
 8. Compare and contrast the financial objectives of a stock
exchange listed company and the financial objectives of a
not-for-profit organization such as a large charity.
ANS:

A key financial objective for a stock exchange listed company is to

maximise the wealth of shareholders. This objective is usually
replaced by the objective of maximising the company’s share price,
since maximising the market value of the company represents the
maximum capital gain over a given period. The need for dividends can
be met by recognising that share prices can be seen as the sum of the
present values of future dividends.
Maximising the company’s share price is the same as maximising the
equity market value of the company, since equity market value
(market capitalisation) is equal to number of issued shares multiplied
by share price. Maximising equity market value can be achieved by
maximising net corporate cash income and the expected growth in
that income, while minimising the corporate cost of capital. Listed
companies therefore have maximising net cash income as a key
financial objective.
Not-for-profit (NFP) organisations seek to provide services to the
public and this requires cash income. Maximising net cash income is
therefore a key financial objective for NFP organisations as well as
listed companies. A large charity seeks to raise as much funds as
possible in order to achieve its charitable objectives, which are non-
financial in nature.
Both listed companies and NFP organisations need to control the use
of cash within a given financial period, and both types of organisations
therefore use budgets. Another key financial objective for both
organisations is therefore to keep spending within budget.
The objective of value for money (VFM) is often identified in
connection with NFP organisations. This objective refers to a focus on
economy, efficiency and effectiveness. These three terms can be
linked to input (economy refers to securing resources as economically
as possible), process (resources need to be employed efficiently
within the organisation) and output (the effective use of resources in
achieving the organisation’s objectives).
Described in these terms, it is clear that a listed company also seeks
to achieve value for money in its business operations. There is a
difference in emphasis, however, which merits careful consideration. A
listed company has a profit motive, and so VFM for a listed company
can be related to performance measures linked to output, e.g.
maximising the equity market value
of the company.
An NFP organisation has service-related outputs that are difficult to
measure in quantitative terms and so it focuses on performance
measures linked to input, e.g. minimising the input cost for a given
level of output.
Both listed companies and NFP organisations can use a variety of
accounting ratios in the context of financial objectives. For example,
both types of organisation may use a target return on capital
employed, or a target level of income per employee, or a target
current ratio.
Comparing and contrasting the financial objectives of a stock
exchange listed company and a not-for-profit organisation, therefore,
shows that while significant differences can be found, there is a
considerable amount of common ground in terms of financial
objectives.