INVESTMENT APPRAISAL
OVERVIEW
Objective
„
To introduce profit based measures of investment appraisal and discounted
cash flow methods of investment appraisal.
NON DCF TECHNIQUES
„ Purpose of investment appraisal
„ Accounting rate of return
„ Payback period
REVISION OF DISCOUNTING
TECHNIQUES
„ Discount factors
„ Change of interest rates
„ Non-annual cash flows
NPV AND IRR
„ Net present value calculation
„ The meaning of net present value
„ Internal rate of return calculation (IRR)
RELEVANT CASH FLOWS
TAXATION
„ Effect of tax on investment appraisal
„ Tax calculation
INFLATION
„ Real and money (or nominal) discount rates
„ Current and money cash flows
„ Discounting with inflation
0201
INVESTMENT APPRAISAL
1
NON DCF METHODS OF INVESTMENT APPRAISAL
1.1
Purpose of investment appraisal
The purpose of investment appraisal techniques is to determine whether or not a
medium to long term investment project gives an adequate financial return. This return
can be measured in a variety of ways but the most common are either by measuring the
profitability of the investment or the cash flows from the investment.
Profits can be distorted by selection of different accounting policies and by inflation
and therefore on the whole measures based on cash flows are to be preferred.
1.2
Accounting rate of return
The accounting rate of return (ARR) of a project is calculated either as:
Average annual profit
100
Initial investment
OR
Average annual profit
100
Average investment
where the average annual profit is the accounting profit after deducting accounting
items such as depreciation.
Advantages
Disadvantages
Easy to understand
Uses profit not cash flow
% result easy to interpret
Choice of formula to use
Similar to ROCE used to appraise
divisions and companies
Ignores the time value of money
1.3
Payback period
This is the number of years before the cash flows from a project repay the initial
investment in the project:
=
Project investment
Annual cash flow
0202
INVESTMENT APPRAISAL
Advantages
Disadvantages
Easy to understand
Ignores timing of cash flows within
the payback period
Uses cash flows not profits
Ignores cash flows after the end of the
payback period
Appears to take account of risk
by using more certain earlier
cash flows
Ignores the time value of money
2
REVISION OF DISCOUNTING TECHNIQUES
2.1
Discount factors
„
Annual cash flow
1
n
 discount factor
(1 i)
Annual discount factors are given for interest rates from 1% to 20% for up to 15 years
in the first of the two PV tables given in the exam.
„
Annuities
Annuities are equal annual cash flows each year for a number of years.
The first cash flow is assumed to start at T1
£ per annum at i% for n years has a value given by:


 1
1
1
1 
= £x × 
+
+
+ 

2
3
(1 + i)
(1 + i)
(1 + i) n 
(1 + i)

= £x ×

1
1 


i  (1 + i) n 
1
1 
1 - (1 + r) -n
1
=
annuity
factor
OR


i  (1 + i) n 
r



Annuity factors calculated for interest rates of 1% to 20% for up to 15 years are given
in the second table printed in the examine, Annuity Table.
In some instances the annuity will not start until some period after time 1.
The tables cannot be used directly here as they assume that the first cash flow is at
time 1.
0203
INVESTMENT APPRAISAL
Two methods are possible.
Illustration
Suppose that an equal annual amount £x is to be received for each of 10 years starting
at time 3 with interest rates of 10% per annum.
The discounts factor to be applied to £x to find the present value is:
Method 1
10 year 10% annuity factor
6.145
=
×
2 year 10% discount factor
×
0.826

2 year 10% annuity factor

1.736
5.076
OR
Method 2
12 year 10% annuity factor
6.814
=
5.078 (difference due to rounding of discount factor in tables)
A further alternative is that an annuity may begin at Time 0, ie now. This simply
means that there is an additional cash flow at Time 0 which will always have a discount
factor of 1. Therefore 1 should be added to the annuity factor taken from the annuity
tables.
„
Perpetuities
Equal annual cash flows for ever.
1
 perpetuity factor
i
0204
INVESTMENT APPRAISAL
2.2
Change of interest rates
Normally for discounting purposes the annual interest rate is assumed to be constant
each year. However it is possible for interest rates to change in which case discount
factors must be calculated from first principles.
Illustration
Interest rates for year 1 are anticipated to be 10% and to be 11% in year 2.
Discount factor for Time 1 cash flow =
=
Discount factor for Time 2 cash flow =
=
2.3
1
1.10
0.909
1
1.10 
1.11
0.819
Non-annual cash flows
DCF questions normally assume that cash flows occur at each year end however this
may not always be the case. If cash flows occur at anything other than annual time
periods then a matching non-annual interest rate must be calculated using the following
formula:
1+r
where
=
n
1 R
r
=
periodic interest rate
R
=
annual interest rate
n
=
number of periods per annum
Example 1
A cash flow is to occur in 3 months time and the annual interest rate is 10%.
What discount factor should be applied to this cash flow?
0205
INVESTMENT APPRAISAL
3
NPV AND IRR
3.1
Net present value calculation
The net present value (NPV) of a project is the net of the total of the present values of
all of the cash inflows and outflows of the project.
There can be a large number of different types of cash flows to tabulate and some care
should be taken with the layout of the NPV calculation.
Illustration
A company invests £10,000 today in a machine. It expects to earn £7,000 per year for 2
years as a result.
Calculate the NPV of the investment at an interest rate of 15%.
Layout 1
Time
Narrative
0
1–2
Machine
Project income
Cash
flow
£
(10,000)
7,000
Net present value
15%
Discount
factor/
annuity
factor
Present
value
£
1
(10,000)
1.626 11,382
———
1,382
———
OR
Layout 2
Machine
Income
15% factor
Present value
Time 0
(10,000)
———
(10,000)
1
———
(10,000)
Time 1
Time 2
7,000
———
7,000
0.870
———
6,090
7,000
———
7,000
0.756
———
5,292
NPV
= 1,382
———
In most longer questions with a number of cash flows the format in (b) is preferable as
discounting calculations need only be done once for each point in time.
Layout 1 is appropriate where cash flows include a number of annuities or perpetuities,
or the project is to run for seven or more years.
0206
INVESTMENT APPRAISAL
3.2
The meaning of net present value
The investment appraisal rule is that an investment is worthwhile if it produces a
positive NPV at the appropriate discount rate. This decision rule stems from our
assumption that the corporate objective is to maximise shareholders wealth. A positive
NPV is the amount by which the shareholders wealth will increase if the project is
accepted. Therefore if there is a choice of projects that with the highest NPV should be
chosen as this will maximise the wealth of the shareholders.
3.3
Internal rate of return calculation (IRR)
IRR is the discount rate which makes the NPV of the project equal zero.
NPV
POSITIVE
NPV
ZERO
NPV
DISCOUNT RATE
r1%
r2%
NEGATIVE
NPV
IRR (between
r1r2%)
The investment appraisal rule is to accept all projects with an IRR greater than the
company’s required discount rate.
IRR is estimated using the method of linear interpretation.
0207
INVESTMENT APPRAISAL
NPV
NPV1
DISCOUNT RATE
r1
r2
NPV2
Method
(1)
Calculate the project’s NPV at two discount rates r1 and r2, (aim to get one
positive and one negative NPV)
(2)
Estimate IRR using the equation
NPV 1
(r 2  r1)
NPV1 NPV 2
IRR =
r1 +
where
r1 and r2 are the two discount rates
and
NPV1 and NPV2 their corresponding net present values
0208
INVESTMENT APPRAISAL
Where cash flows are annuities interest tables can be used to estimate the IRR.
Illustration
Initial investment
Annuity for 10 years
£400,000
£80,000
What is the IRR?
Set out the NPV calculation and set it equal to zero.
Time
0
1  10
Cash flow Annuity factor
PV
(400,000)
1
(400,000)
80,000
5 (bal fig)
400,000
NPV

=

For the NPV to be zero the annuity factor for 10 years must be 5. Reading off from the
annuity factor row for 10 year a discount factor of 5.019 is found at an interest rate of
15%. Therefore the estimated IRR is 15%.
4
RELEVANT CASH FLOWS
When calculating either a NPV or an IRR it is important that only relevant cash flows
are included in the calculations.
The costs and revenues to be included are only those that can affect the decision to be
made or are affected by it. In general terms this means only future incremental cash
flows.
Specifically included are:
„
all opportunity costs and revenues
Specifically excluded are:
„
„
„
„
„
„
non-cash flows (eg depreciation)
sunk costs
historic costs
book values
unavoidable costs
finance costs
0209
INVESTMENT APPRAISAL
5
TAXATION
5.1
Effect of tax on investment appraisal
Taxation has two effects in investment appraisal
NEGATIVE
EFFECT
POSITIVE
EFFECT
Tax charged
on net
cash flows
Tax relief given
on assets
purchased
WRITING DOWN
ALLOWANCES
„
„
Inland Revenue (UK tax authority)’s version of
depreciation
Assumptions unless otherwise stated
 Given at 25% reducing balance
 No WDA in year of sale. Balancing
allowance/charge given instead
 Sufficient profits available to utilise all tax
benefits in full, at once
Other assumptions
„
Tax payments occur one year after the related cash flow
„
Corporation tax paid at 33% (say)
„
Tax rate is constant (unlikely in practice)
„
Working capital flows have no tax effects
0210
INVESTMENT APPRAISAL
5.2
Tax calculation
Method
Step 1
Set up table for cash flows(for one
year more than the life of the
project)
↓
Step 2
(a)
T1
T2
TRADING REVENUE
x
x
TRADING COSTS
(x)
(x)
NET TRADING
REVENUE
x
x
T3
Slot in trading revenues and
costs
↓
(b)
T0
Total columns for net trading
revenues
↓
(c)
Calculate tax payable on net
trading revenues and slot in
with one year time delay if
appropriate
↓
Step 3
Put in capital outlay and capital
receipts
Tax @ 33%
INVESTMENT
(x)
(x)
(x)
SCRAP PROCEEDS
x
↓
Step 4
Calculate tax saving on WDAs as a
separate working and slot in
WDA TAX SAVINGS
x
x
(x)
x
x
(x)
DISCOUNT
FACTOR i%
x
x
x
x
PRESENT VALUE
x
x
x
x
↓
Step 5
Total columns for net cash flows
and discount
0211
INVESTMENT APPRAISAL
Example 2
(1)
A company buys an asset for £10,000 at the beginning of an accounting
period (1 January 19X1) to undertake a two year project.
(2)
Net trading revenues at T1 and T2 are £5,000.
(3)
The company sells the asset on the last day of the second year for £6,000.
(4)
Corporation tax = 33%. Writing down allowance = 25%.
Calculate the net cash flows for the project.
0212
INVESTMENT APPRAISAL
6
INFLATION
DCF takes account of the time value of money NOT inflation. Therefore we need to
take account of the effects of inflation separately when appraising projects.
6.1
Real and money (or nominal) discount rates
„
Real rate of interest reflects the rate of interest that would be required in the
absence of inflation.
„
Money (or nominal) rate of interest reflects the real rate of interest adjusted
for the effect of general inflation (measured by the RPI).
Illustration
Say you invest £100 today for one year. In the absence of inflation you require a return
of 5%. The RPI is expected to change by 10% over the coming year.
In one year, in the absence of inflation, you require
£100 × 1.05 = £105
To maintain the purchasing power of your investment, ie to cover inflation you require
£105 × 1.1 = £115.50
You therefore require a money return of
„
15.50
= 15.5% over the year.
100
Money rates, real rates and general inflation (RPI) are linked by the
following.
(1 + m) = (1 + r) (1 + i)
m
r
i
=
=
=
money rate
real rate
general inflation
So in our illustration above
(1 + m) = (1.05) (1.1)
= 1.155
m = 15.5%
6.2
Current and money cash flows
„
Current cash flows are cash flows expressed in today’s terms which will be
affected by inflation in the future and have not yet been adjusted.
„
Money (or nominal) cash flows are cash flows where any inflationary effects
have already been taken into account.
0213
INVESTMENT APPRAISAL
6.3
Discounting with inflation
Money method



adjust individual cash flows for specific inflation to
convert to money cash flows
discount using money rate
This is the simplest technique. Use wherever possible.
Real method



remove the effects of general inflation from money cash
flows
discount using real rate
achieves the same result as money method
Example 3
A project has the following anticipated cash flows in current terms/at today’s prices (ie
before allowing for inflationary increases).
t0
£000
(750)
t1
£000
330
t2
£000
242
t3
£000
532
The cost of capital has been calculated to include an allowance for inflation at 15.5%.
The rate of inflation is expected to remain constant at 5%.
Calculate the NPV of the project in terms of the following.
Real discount rates
and cash flows
Money discount rates
and cash flows
0214
INVESTMENT APPRAISAL
FOCUS
You should now be able to
„
appraise a project using a variety of profit based and cash flow based
methods
„
understand the benefit and importance of the net present value method
„
calculate net present values and internal rates of return by identifying relevant
cash flows, tax implications and the impact of price level changes.
0215
INVESTMENT APPRAISAL
EXAMPLE SOLUTIONS
Solution 1
1+r =
1 R
n
R = 10%
n = 4 (3 month periods per annum)
1+r =
4
1.10
1 + r = 1.0241
 3 month interest rate is 2.41%
Discount factor for a cash flow in 3 months time
=
1
1.0241
= 0.976
Solution 2
1
2
3
4
5
T0
Net trading revenue
Tax at 33%
Asset
Scrap proceeds
T1
5,000
T3
(1,650)
(6,000)
825
———
10,175
495
———
(1,155)
(10,000)
Tax savings on WDAs (W)
Net cash flow
T2
5,000
(1,650)
———
(10,000)
———
5,000
0216
INVESTMENT APPRAISAL
WORKING
Tax computation
IN
YEAR 1
„
„
„
Asset purchases 1 Jan 19X1
First WDA will be set off
against profits earned in
year 1 (T0  T1)
First tax relief at T2
T0
T1
Investment in asset
WDA @ 25%
T2
Proceeds
Balancing allowance
„
„
Asset sold 31 Dec 19X1
No WDA in year of sale
(T1  T2)
£
10,000
(2,500)
———
7,500
(6,000)
———
(1,500)
0217
Tax relief at
33%
Timing
825
T2
495
T3
INVESTMENT APPRAISAL
Solution 3
(a)
Real discount rates and cash flows
Discount rate as per the question of 15.5% includes investor’s/lender’s inflation
expectation of 5%.
Hence “real” discount rate, r, is given by
1 + m
1 + i
1+r
=
where
m
= money interest rate
i
= rate of inflation
Substituting
1+r
=
1  0.155
1  0.05
= 1.10
and
r is once again 0.10 or 10%.
Discounting the cash flows as per the question.
Year
Cash flow
PV factor
@ 10%
£
(750)
330
242
532
0
1
2
3
1.000
0.909
0.826
0.751
Net present value
(b)
Present
value
£
(750)
300
200
400
——
150
——
Money discount rates and cash flows
The discount rate as per the question of 15.5% is the money discount rate. Cash flows,
however, need to be increased by 5% compound each year from year 0 to allow for
inflation.
Year
Real cash
flow
(i)
0
1
2
3
£
(750)
330
242
532
Inflation
factor
Money*
cash flow
(ii)
(iii)
1
1 + 0.05
(1 + 0.05)2
(1 + 0.05)3
£
(750)
346
267
616
Net present value
0218
Discount
factor
Present
value
(iv) = (ii) × (iii) @ 15.5%
1.000
0.866
0.750
0.649
£
(750)
300
200
400
——
150
——