Since the internal rate of return of the investment (16%) is greater than the cost of capital of Warden Co, the investment is
financially acceptable.
Examiner’s note: although the value of the calculated IRR will depend on the two discount rates used in linear interpolation,
other discount rate choices should produce values close to 16%.
(c) Sensitivity analysis indicates which project variable is the key or critical variable, i.e. the variable where the smallest relative
change makes the net present value (NPV) zero. Sensitivity analysis can show where management should focus attention in
order to make an investment project successful, or where underlying assumptions should be checked for robustness.
The sensitivity of an investment project to a change in a given project variable can be calculated as the ratio of the NPV to
the present value (PV) of the project variable. This gives directly the relative change in the variable needed to make the NPV
of the project zero.
Selling price sensitivity
The PV of sales revenue = 100,000 x 16 x 3696 = $5,913,600
The tax liability associated with sales revenue needs be considered, as the NPV is on an after-tax basis.
Tax liability arising from sales revenue = 100,000 x 16 x 03 = $480,000 per year
The PV of the tax liability without lagging = 480,000 x 3696 = $1,774,080
(Alternatively, PV of tax liability without lagging = 5,913,600 x 03 = $1,774,080)
Lagging by one year, PV of tax liability = 1,774,080 x 0901 = $1,598,446
After-tax PV of sales revenue = 5,913,600 1,598,446 = $4,315,154
Sensitivity = 100 x 103,000/4,315,154 = 24%
Discount rate sensitivity
Increase in discount rate needed to make NPV zero = 16 11 = 5%
Relative change in discount rate needed to make NPV zero = 100 x 5/11 = 45%
Of the two variables, the key or critical variable is selling price, since the investment is more sensitive to a change in this
variable (24%) than it is to a change in discount rate (45%).
(d) 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.
122 (a) 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.
(d) 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 05% of sales), which represents insurance against the risk of bad debts,
is less than the remaining bad debts ($127,800 or 06% 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.
13There are a number of benefits of factoring that could be discussed, as follows.
The expertise of the factor
It is possible the factor can improve the efficiency of the receivables management of Bold Co due to its expertise in the areas
of credit analysis, credit control and receivables collection. This would lead to a lower level of bad debts, as indicated by the
factor’s offer.
Insurance against bad debts
Non-recourse factoring offers protection from bad debts, although the factor’s fee will include the cost of this insurance
element, as indicated by the difference between the factor’s fees.
Factor finance
A factor will advance up to 80% of the value of invoices raised, allowing a company quicker access to cash from sales than
would be possible if it had to wait for accounts receivable to be settled. Bold Co could pay trade payables promptly, perhaps
benefiting from early settlement discounts.
Lower administration costs
Since administration of trade receivables would be taken over by the factor, administration costs of the company would
decrease over time, although some incremental short-term costs, such as redundancy costs, might be incurred.
3 (a) Net asset valuation
In the absence of any information about realisable 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.
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 104)/(01 004) = $693 million
Earnings yield method
Profit after tax (earnings) is $666 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 = 666m/011 = $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 = (666m x 105)/(011 005) = $1,166 million
Examiner’s note: full credit would be gained whether or not growth is incorporated in the earnings yield method.
(b) The dividend growth model (DGM) is used widely in valuing ordinary shares and hence in valuing companies, but there are
a number of weaknesses associated with its use.
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.
(c) Market value of equity
Close Co has 80 million shares in issue and each share is worth $850 per share.
The market value of equity is therefore 80 x 850 = $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.
14Present value of future interest = (8 x 4767) = $3814
Present value of future principal payment = (100 x 0666) = $6660
Ex interest bond value = 3814 + 6660 = $10474 per bond
Market value of bonds = 120m x (10474/100) = $1257 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 03) = 7 x 07 = 49% 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 03) = 6 x 07 = 42% per year
Calculation of weighted average after-tax cost of capital (WACC)
Total value of company = 680m + 1257m + 40m = $8457m
After-tax WACC = ((680m x 10) + (1257m x 49) + (40 x 42))/8457 = 90 % per year
Examiner’s note: the after-tax cost of debt of the 8% bonds could have been calculated using linear interpolation, although
the result would be close to 49%.
(d) 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.
4 (a) Theoretical ex rights price
Rights issue price = 750 x 08 = $600 per share
Number of shares issued = $90m/600 = 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 750) + (1 x 600))/5 = $720 per share
Alternatively, theoretical ex rights price = ((60m x 750) + (15m x 600))/75m = $720 per share, where 75 million is the
number of shares after the rights issue.
(b) Financial acceptability to shareholders of buying back bonds
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 $11250 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 (100/11250) = $80 million
Interest saved by redeeming bonds = 80m x 008 = $64 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 64m) = $454 million
Revised profit after tax (earnings) = 454m x 07 = $3178 million
Revised earnings per share = 100 x (3178m/75m) = 4237 cents per share
15Current earnings per share = 100 x (27m/60m) = 45 cents per share
Current price/earnings ratio = 750/45 = 167 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 = 167 x 4237 = 708 cents or $708 per share
This share price is less than the theoretical ex rights price per share ($720) 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 (720/4237), 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) Current interest coverage ratio = 49m/10m = 49 times
Revised interest coverage ratio = 49m/(10m 64m) = 49m/36m = 136 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) = 205%
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 205%, and by the significant increase in the interest coverage ratio from 49 times to 136 times.
Examiner’s note: full credit would be given to a revised gearing calculation (196%) that omits the loss due to buying back
bonds at a premium to nominal value.
(d) 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.
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