ACCA F9 Financial Management - 2010 - Study text - Emile Woolf Publishing
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Chapter 10: DCF: risk and uncertainty
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Other methods of risk and uncertainty analysis
Risk modelling: simulation modelling
Risk-adjusted discount rates
Adjusted payback
Dscounted payback period
4 Other methods of risk and uncertainty analysis
4.1 Risk modelling: simulation modelling
The risk in an investment can be assessed by constructing a ‘model’ for the
investment, and then considering possible variations in the possible outcomes.
For capital investment appraisal, a risk model might be constructed using a
spreadsheet.
Having constructed the model, the risk in the investment can be assessed by testing
different scenarios, such as delays in achieving the benefits from an investment, and
combinations of variations in costs and benefits.
Simulation modelling
A complex risk model can be used to assess the range of possible outcomes from the
investment, and to construct a probability distribution of possible outcomes, for
statistical analysis. One such type of risk model is a Monte Carlo simulation model.
With a Monte Carlo simulation model, probabilities are estimated for the different
values that might occur for all the uncertain variables in the model. Random
numbers are assigned to these values.
For example:
Units per
year
Probability
Random
numbers
Cost
Probability
Random
numbers
3,000 0.15 00 – 14 $3.00 0.20 00 – 19
4,000 0.20 15
–
34
$3.50
0.50
20
–
69
5,000 0.30 35
–
64
$4.00
0.30
70
–
99
6,000 0.25 65
–
89
7,000 0.10 90
–
99
With a complex model, a large number of different variables could be given various
possible values, with associated probabilities and random number allocations.
The model is then used to produce a large number of possible outcomes and NPVs
for the project. For each possible outcome, random values are given to each of the
uncertain variables by generating random numbers and deciding the value in
accordance with the random number generated.
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If the model produces hundreds, possibly thousands, of different possible NPVs,
each calculated using different values for the variables according to the random
numbers generated, the different outcomes can be analysed into a probability
distribution with a mean and a standard deviation.
In many cases, the probability distribution will show the characteristics of a normal
statistical distribution.
Where a normal distribution is produced, the mean and standard deviation can be
used to analyse the possible outcomes from the project in some detail. For example,
the probability of a negative NPV can be calculated, or the minimum expected NPV
at the 95% or the 99% confidence level.
Advantages of simulation
The model can include all the possible values for each variable and their
associated probabilities
Simulation can be very useful for the analysis of large and complex investment
projects.
Disadvantages of simulation
Constructing a reliable simulation model can be complex, time-consuming and
expensive. The benefits might not be worth the time and cost.
The probability estimates for each of the variables may be highly subjective and
unreliable. This will affect the reliability of the risk assessment and probability
distribution derived from the model.
4.2 Risk-adjusted discount rates
Risk-adjusted discount rates might be used to evaluate projects with different risk
characteristics. The broad principle is to increase the minimum required return (in
other words, increase the discount rate or cost of capital) to compensate for the
higher risk involved.
4.3 Adjusted payback
The minimum required payback period may be reduced in a particularly risky
environment. Payback may be a good indicator of the liquidity of a project. Projects
Chapter 10: DCF: risk and uncertainty
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which pay back quickly avoid the risk of trying to produce accurate revenue and
cost projections far into the future.
In a fast-changing business environment it may also be important to generate
liquidity in order to have funds to invest in new projects as new business
opportunities continue to arise and to adopt new technology as soon as it becomes
available.
4.4 Discounted payback period
Instead of using the ordinary payback to decide whether a project is acceptable,
discounted payback might be used as an alternative. A maximum discounted
payback period is established and projects should not be undertaken unless they
pay back within this time.
A consequence of applying a discounted payback rule (and the same applies to
ordinary payback) is that projects are unlikely to be accepted if they rely on cash
profits in the long-term future to make a suitable financial return. Since longer-term
estimates of cash flows are usually more unreliable than estimates in the shorter-
term, using discounted payback as a criterion for project selection will result in the
rejection of risky projects.
A discounted payback period is calculated in the same way as the ‘ordinary’
payback period, with the exception that the cash flows of the project are converted
to their present value. The discounted payback period is the number of years before
the cumulative NPV of the project reaches $0.
Year
Annualcash
flow
$
0 (200,000)
1 (40,000)
2 30,000
3 120,000
4 150,000
5 100,000
6 50,000
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The discounted payback period is calculated as follows.
Year
Annualcash
flow
Discount
factorat10%
PVofcash
flow
Cumulative
NPV
$$ $
0 (200,000) 1.000 (200,000) (200,000)
1 (40,000) 0.909 (36,360) (236,360)
2 30,000 0.826 24,780 (211,580)
3 120,000 0.751 90,120 (121,460)
4 150,000 0.683 102,450 (19,010)
5 100,000 0.621 62,100 43,090
6 50,000 0.564 28,200 71,290
–
–––––––
NPV
+71,290
–
–––––––
The discounted payback period is Year 5, and we can estimate it in years and
months as:
4 years + (19,010/62,100) × 12 months
= 4 years 4 months.
The discounted period for a capital investment is always longer than the ‘ordinary’
non-discounted payback period.
One criticism of the discounted payback method of project evaluation is the same as
for the non-discounted payback method. It ignores the expected cash flows from the
project after the payback period has been reached.
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Paper F9
Financial management
CHAPTER
11
Capital investment appraisal:
further aspects
Contents
1 Theleaseversusbuydecision
2 Assetreplacementdecisions
3 Capitalrationingdecisions
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The lease versus buy decision
The nature of the lease versus buy decision
Making a lease versus buy decision
The acquisition decision
The financing decision
1 The lease versus buy decision
1.1 The nature of the lease versus buy decision
Occasionally, a company might be faced with a decision about whether or not to
acquire a new non-current asset, and if the asset is acquired, whether the acquisition
should be financed with a bank loan or by means of a finance lease arrangement. In
capital investment appraisal, this is usually referred to as a ‘lease versus buy’
decision.
The lease versus buy decision involves:
deciding whether or not to acquire the asset, and
if the decision is to acquire it, whether to borrow the money to buy the asset or
whether to obtain the asset under a finance lease arrangement.
1.2 Making a lease versus buy decision
If you are required to advise on a lease versus buy decision, the decision should be
considered in two separate stages.
The acquisition decision (or investment decision). The first step is to decide
whether or not the asset should be acquired. This decision is based on the
assumption that the asset will be purchased.
The financing decision. The second stage is to make a financing decision.
− If the decision is not to acquire the asset, this second stage is unnecessary.
− If the decision is to acquire the asset, this stage of the decision is to select the
preferred method of financing the acquisition – in other words, whether to
buy the asset for cash (financed by a bank loan) or whether to lease it under a
finance lease arrangement.
1.3 The acquisition decision
The acquisition decision should be reached using the normal NPV method of
investment appraisal. If the project has a positive Net Present Value, the
recommendation will be to acquire the asset.
Chapter 11: Capital investment appraisal: further aspects
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The following guidelines should be followed:
The purchase cost of the asset should be a cash outflow of the project. Typically
this will be a Year 0 cash outflow, which is the purchase cost of the asset. If the
purchase would be financed by a bank loan, ignore the bank loan for the
purpose of the acquisition decision (and do not treat the bank loan as a year 0
cash inflow).
The cash flows in the acquisition decision should include the expected benefits
and costs from the project, such as extra cash revenues and cash expenses each
year, and working capital requirements. If the asset would have a residual value
at the end of its life if purchased, include the residual value as a cash flow of the
project in the final year.
The tax cash flows should be considered in full. These consist of the tax effect on
tax of higher or lower annual cash profits, and also the effect on cash flows of
tax-allowable depreciation (capital allowances).
The cost of capital should be the company’s normal (after-tax) cost of capital.
1.4 The financing decision
If the decision in stage 1 is that the asset should be acquired, the next stage – the
financing decision – is to decide on the best method of financing for the asset.
Since the asset will be acquired, no matter what financing method is chosen, all the
cash flows that will occur anyway, whatever the financing method, can now be
ignored because they are not relevant to the financing decision.
The only relevant cash flows are the cash flows relating to the financing methods.
The PV of a bank loan to purchase the asset
If the asset is financed with a bank loan if purchased, the cash flows for the bank
loan should be discounted to a PV of cost at the after-tax cost of borrowing.
However if we discount the cash flows of a loan (allowing for interest payments and
the tax relief on interest payments) at the after-tax cost of capital, the present value
of cost is always equal to the amount of the loan.
In other words, the PV of the cost of a loan to purchase the asset with a bank loan is
the purchase cost of the asset (= the amount of the loan). This assumes that the
discount rate is the after-tax cost of borrowing.
The PV of the option to purchase the asset with a loan is reduced by the reduction in
tax payments that will occur by claiming capital allowances on the asset. The net PV
of cost is therefore the amount of the loan minus the PV of the tax benefits from
capital allowances.
The PV of other financing alternatives
The financing cash flows of the alternative financing method should now be
discounted at the same cost of capital (the after-tax cost of the borrowing).
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The preferred financing method is the one with the lower (or lowest) PV of cost.
Financing costs for a finance lease
The main financing cash flows that will need to be taken into account are as follows:
The lease payments, which are a financing cost
Tax relief on the lease payments, which reduce the financing cost.
Example
Crimson is considering a project requiring a new machine. The machine costs $3
million and it would have a useful life of three years and no residual value at the
end of that time.
The machine will produce cash operating surpluses of $1.6 million each year. Tax
allowable depreciation is 15% on a straight-line basis. Tax is 30% on operating cash
flows and is payable one year in arrears.
Crimson has an after-tax cost of capital of 20%.
It is considering either borrowing from the bank at the pre-tax interest rate of 14%
and buying the asset outright, or leasing it at a cost of $1.3 million each year for
three years, with the lease payments payable in advance at the beginning of each
year.
Required
Evaluate the project. Should the asset be acquired, and if so which financing method
should be used?
Answer
Stage 1: The acquisition decision (investment decision)
Year 0 1 2 3 4
$000 $000 $000 $000 $000
Machinecost (3,000)
Taxreliefonmachine135 135 135 495
Operatingcashflows1,600 1,600 1,600
Taxonoperatingcashflows(480) (480) (480)
–
–––––––
–
–––––––
–
––––––– –––––––– ––––––––
Netcashflows (3,000) 1,735 1,255 1,255 15
–
–––––––
–
–––––––
–
––––––– –––––––– ––––––––
Discountfactorat20% 1.000 0.833 0.694 0.579 0.482
PVat20% (3,000) 1,445 871 727 7
NPV(in$000) +50
–
–––––––
Acquisition decision
The NPV is positive; therefore the machine should be acquired.
Chapter 11: Capital investment appraisal: further aspects
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Workings
The tax-allowable depreciation is 15% × $3,000,000 = $450,000 each year for years 1 –
3.
The total amount of tax allowable depreciation is therefore 3 × $450,000 = $1,350,000.
There will be a balancing allowance of $1,650,000 ($3,000,000 – $1,350,000) at the end
of Year 3.
It is assumed that the first tax allowance for depreciation would be claimed early in
Year 1, i.e. in Year 0, resulting in a tax saving (one year later) at the end of Year 1.
The savings in tax payments will therefore be (one year in arrears):
For Years 1 – 3: $450,000 × 30% = $135,000.
For Year 4: $1,650,000 × 30% = $495,000.
Stage 2: The financing decision
There are two financing options: to buy the asset with a bank loan or to obtain the
asset under a finance lease arrangement. The cash flows of these financing options
should be converted into a PV of cost using the after-tax cost of borrowing.
The PV of the option to purchase the asset is a cost of $3,000,000 (the purchase cost
of the asset and the amount of the loan), if the cash flows are discounted at the after-
tax cost of borrowing. This is different from the company’s after-tax cost of capital.
The after-tax cost of borrowing is 14% × (1 – 30%) = 9.8%.
The discount factors at a cost of capital of 9.8% are:
Year
1 1/(1.098)= 0.911
2 1/(1.098)
2
= 0.829
3 1/(1.098)
3
= 0.755
4 1/(1.098)
4
= 0.688
(Note: Instead of using a cost of capital of 9.8%, it would be acceptable in an
examination to round this figure to 10% and use discount factors from the discount
tables.)
PV of leasing cost
Year 0 1 2 3
$000 $000 $000 $000
Leasepayments (1,300) (1,300) (1,300)
Taxreliefonpayments(30%)390 390 390
–
–––––––
–
–––––––
–
––––––– ––––––––
Netcashflows (1,300) (910) (910) 390
–
–––––––
–
–––––––
–
––––––– ––––––––
Discountfactorat9.8% 1.000 0.911 0.829 0.755
PVat9.8% (1,300) (829) (754) 294
PVofleasingcost (2,589)
–
–––––––
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PV of cost of purchasing
Year 0 1 2 3 4
$000 $000 $000 $000 $000
Machinecost (3,000)
Taxreliefonmachine135 135 135 495
–
––––––
–
––––––
–
––––––
–
–––––– –––
–
–––
Netcashflows (3,000) 135 135 135 495
–
––––––
–
––––––
–
––––––
–
–––––– –––––––
Discountfactorat9.8% 1 0.911 0.829 0.755 0.688
PVat9.8% (3,000) 123 112 102 341
PVofcostofpurchasing (2,322)
–
––––––
Financing decision
As the lease finance option is more expensive than the option to purchase cost,
Crimson should purchase the asset and finance the purchase with a bank loan at
14%.