3 Capital investment appraisal
3.1 interest and discount
(1) Future value: F=P(1+r)n , the beginning is o year, the future value is at the end of n year; if you are required to calculate the value at the beginning of (n+1) year, it is also the value at the end of n year.
(2) Present value: P=F/(1+r)n, the same principle applied as future value, the beginning of (n+1) year, is equal to the end of n year.
(3) Annuity. Future value at end of year: n=A {[(1+r) n-1]/r}. Based on the assumption that the first annuity is invested at the end of the first time period, and the last annuity is invested at the very end of the final time period.
Present value of an annuity: P= A/rｘ[1-1/(1+r)n ]
Remember the two formulas, in case the time horizon is out of the range in the annuity table.
Present value of perpetuity=A/r
(4) Special condition for annuity
for example: calculate the discount factor at 10%, year 2-5.
First step: calculate the discount factor at 10%, year 1-5 3.791
Second step: calculate the discount factor at 10%, year 1 (0.909)
Then: the discount factor at 10%, year 2-5 2.882
Another method:
Year 2-5 amounts to 4years, discount factor at 10%, year 1-4 3.170
Discounted to the beginning, discount factor at 10%, year 1 ｘ0.909
Then: the discount factor at 10%, year 2-5 2.882
This is useful for calculating the tax, generally they are 1 year in arrear.
(5) Annual percentage rate (APR)
This is used when the payment is made on month or quarter basis.
For example: nominal rate: 8%, paid every six months,
APR=(1+4%) 2-1=8.16%, also named effective rate.
(6) Inflation
(1+N)=(1+R)(1+I)
3.2 method of capital expenditure appraisal
3.2.1 ROCE or ARR
(1)Most common formula: ROCE=EBIT(after depreciation)/ initial capital costs
(2) pros and cons for ROCE:
pros:•simplicity: based on profits and asset, it is easily understood and visible to shareholders.
•link with other accounting measures: managers and accountants are familiar; manager’s performance is evaluated and rewarded by similar terms.
Cons:•fail to take account of the project life or time value of money.
•it will vary with specific accounting policies.
•no definite investment signal.
3.2.2 Payback
(1) Payback period= Initial payment/Annual cash inflow, payback is not always an exact number of years
(2) pros and cons for payback:
pros:•simplicity.
•Rapidly-changing technology. If new plan is likely to be obsolete, a quick pay back is essential.
•improving investment condition. If investment conditions are expected to improve in the near future, attention should direct to those projects which will release funds soonest.
•favoring projects with a quick return, for rapid company growth, minimizing risk and maximizing liquidity.
•cash flow. Avoid the distortion made by different accounting policy.
cons:•ignore the project return after the payback period.
•ignore the time value of money.
•no objective measure.
•project profitability is ignored.
3.2.3 NPV
(1) basic assumptions:
•cash outlay occurs in year 0 (now).
•cash flows occurs at the end of the year.
•if a cash flow occurs at the beginning of a year, it is assumed to occur at the end
of the previous year.
(2) Pros and cons for NPV.
Pros:•take account of time value of money.
•use cash flow not profit.
Cons:•NPV assumes firms pursue the objective of maximizing the wealth of their shareholders, this is questionable given the wider range of stakeholders who might have conflicting interests to those of the shareholders.
•NPV is not easy to apply, such as the factor of risk.
•NPV assumes that cash surplus can be reinvested at the discount rate, it is in doubt that any other project is available which has at least a zero NPV.
•NPV assumes cash flow arising at periods ends and can not cope with the mid-term cash flows.
•NPV is not widely used in small business environment, evidence showed.
•NPV doesn’t consider profit, as far as projects with long time horizons and large initial investment and very delayed cash flows are concerned, accounting measures maybe preferable.
•NPV only account for the time value of money, in some case distant horizons are less important than near horizons.
•NPV doesn’t account non-financial information.
3.2.4 IRR
(1) Basic principle: IRR is the cost of capital at which the NPV is zero, if the
expected IRR is higher than a target rate of return, the project is financially worth undertaking.
(2)Selection between IRR and NPV: when a choice has to be made between mutually exclusive projects, in such case the NPV should be selected, because higher NPV can maximize shareholder wealth.
3.2.5 Expected value
(1) Definition: computed by multiplying the value of each possible outcome by the probability of that outcome, and summing the results.
(2) Pros and cons:
Pros: •more sophisticated than single value forecasts by recognize that there are several possible outcomes.
•enable the probability of the different outcomes to be quantified.
•leads directly to a simple optimizing decision rule.
•calculation are relatively simple.
•ideally suited to the sort of problem which is repetitive and involves only small outlays of money.
Cons: •the whole forecasting procedures is complicated.
•only indicates the average payoff if the project is repeated many times.
•no indication of possible outcomes about the expected value. The more widely spread out the possible results are, the more risky the investment is usually seen to be, EV ignores this.
•ignores the investors’ attitude to risk. Some investors are more likely to take risks than others.
3.3 Highlights in NPV calculation
3.3.1 Incorporating taxation into NPV appraisals:
(1) Basic assumption of taxation:
•taxable profits are the net project cash flows;
•where are tax loss arises from the project, there are sufficient taxable profits else where to allow the loss to reduce any relevant tax payment;
•the first capital allowance is immediate, with the first benefit one year later, and there are balancing adjustments on the disposal of all assets.
•in general, tax payment is one year in arrear.
(2) Capital allowance:
1. Basic rules:
•usually calculated on a reducing balance basis, the reduction in taxation is the capital allowance multiplied by the tax rate.
•at the end of project or the asset is eventually disposed of, there is a balancing allowance or a balancing charge.
•capital allowance themselves are not cash flows and so should not be included in the NPV analysis.
2. A case
A project is 4 years life, machine costing $20,000, disposal value is $5,000, tax allowance on the machine are 25% pa reducing balance, tax rate is 30%, calculate the tax saved.
Solution:
Year written down value($) capital allowance($) tax saved($)
0 20,000 5,000 0
1 15,000 3,750 1,500
2 11,250 2,813 1,125
3 8,437 2,109 844
4 5,000 1,328(w1) 633
5 398
Total tax saved 4,500
w1=8,437-2,109-5,000=$1,328
(3) Discount factor, pay attention to the discount factor is before or after tax, if
the discount factor is after tax, the cash flow should also be after tax; if the
cash flow is after tax, the discount factor should also be after tax.
(4) Always keep in mind the decrease in cost will lead to an increase in tax, the increase in cost will lead to an decrease in tax, they are combined together.
3.3.2 Inflation
(1). Two impacts of inflation on NPV appraisal:
•the discount rate given may include an allowance for a general rate of inflation;
•the cash flows may be subject to inflation, possibly at different rates for
different flows.
(2) money discount rate.
A case
Real discount rate is 10%, inflation rate is 5%, nominal discount rate=
(1+10%)ｘ(1+5%)=1+15.5%
Recommendation: you can discount money cash flows at money discount rates or real cash flow at real discount rates, the former is recommended for its simplicity.
(3) calculation of inflation on cash flow
A case
Inflation for wage costs is 10% for the next five years, now is 1,000
Year 1: 1,000ｘ(1+10%)= 1,100
Year 2: 1,000ｘ(1+10%)2=1,210
Year 3: 1,000ｘ(1+10%)3 =1,331
Year 4: 1,000ｘ(1+10%)4 =1,464
Year 5: 1,000ｘ(1+10%)5 =1,610
3.3.3 Working capital and residual value
Remember that working capital should be input at the beginning of the project
and will be back at the end of the project at the same amount except inflation
is introduced;
Residual value should be regarded as a cash inflow.
3.3.4 Other factors should be taken into consideration when NPV is applied:
•sensitivity analysis or simulating analysis to assess the risk project faced.
•the accuracy of cash flow estimate.
•the inflation rate, cash flow is in real term or nominal term.
•alternative uses for this investment to gain more NPV.
•chance of change in tax rate.
•after the investment term, the cash flow.
•any additional investment needed?
•strategy of the company, does it fit the strategy of the company.
•other non-financial consideration. Political risk,
•Ethical consideration.
* cause pollution, do damage to the environment.
* experiment on animal.
* human rights.
* local corruption.
* trading in drugs of arms.
* wage below ordinary level, the condition of working environment.
3.4 Sensitivity analysis and simulation
pros and cons