MANAGEMENT
AND COST
ACCOUNTING
SIXTH EDITION
COLIN DRURY
Management and Cost Accounting, 6th edition, ISBN 1-84480-028-8
© 2004 Colin Drury
Part Three:
Information for decision-making
Chapter Fourteen:
Capital investment decisions 2
Management and Cost Accounting, 6th edition, ISBN 1-84480-028-8
© 2000 Colin Drury
© 2004 Colin Drury
14.1a
Capital investments with unequal lives
•
Machines A and B are two mutually exclusive machines A ’s life =3 years
and B’s life =2 years
•
Can we base the decision on the NPV or IRR ’s of each machine? (Only
if the task for which they are required ceases at the end of the project
lives).
•
What if the task for which the machines are required is for many years
(say >6 years)?
We are faced with a replacement chain problem and as long as the
common denominator for the project lives is less than the task life we can
use either the lowest common multiple method or the equivalent annual
cash flow method.
•
Lowest common denominator method:
Lowest common multiple =6 years (2 replacements of machine A and 3
of B)
Management and Cost Accounting, 6th edition, ISBN 1-84480-028-8
© 2000 Colin Drury
© 2004 Colin Drury
14.1b
Management and Cost Accounting, 6th edition, ISBN 1-84480-028-8
© 2000 Colin Drury
© 2004 Colin Drury
14.2a
• Equivalent annual cost (cash flow) method:
1.The costs are made comparable by converting the cash flows to an
equivalent annual cost (EAC).
2. EAC = PV of costs /Annuity factor for n years at R%
3. EAC for A = £1 796.8/2.4869 (Based on years 0 –3) or
£3 146.8/4.3553 (Based on years 0 –6)
= £722.5 for both time periods
4 EAC for B =£705.7 (calculated as above)
5. The cash flow stream of A is equivalent in PV terms to an annual
cash outflow of £722.5 (£705.7 for B). Therefore choose B
Management and Cost Accounting, 6th edition, ISBN 1-84480-028-8
© 2000 Colin Drury
© 2004 Colin Drury
14.2b
• Assume the task life < lowest common denominator
Task life = 10 years
Machine X life = 6 years
Machine Y life = 8 years
Lowest common multiple is 24 years
Suggest use a 10 year horizon with each machine being
replaced once and incorporate an estimate of machine
realisable values at the end of year 10.
Management and Cost Accounting, 6th edition, ISBN 1-84480-028-8
© 2000 Colin Drury
© 2004 Colin Drury
14.3a
Single period capital rationing
1. Refers to a situation where investment funds are restricted and it is
not possible to accept all positive NPV projects.
2. Where capital rationing exists, ranking in terms of NPVs will normally
result in an incorrect allocation of scarce capital.
3. The correct approach is to rank by profitability index (PI):
PI =
PV
Investment outlay
Management and Cost Accounting, 6th edition, ISBN 1-84480-028-8
© 2000 Colin Drury
© 2004 Colin Drury
14.3b
4.
Example
Project
I0
£
A
25 000
B
100 000
C
50 000
D
100 000
E
125 000
F
25 000
G
50 000
NPV
PV
£
32 500
108 250
75 750
123 500
133 500
30 000
59 000
NPV
£
7 500
8 250
25 750
23 500
8 500
5 000
9 000
PI
1.30
1.08
1.51
1.23
1.07
1.20
1.18
PI
ranking ranking
6
5
1
2
4
7
3
2
6
1
3
7
4
5
Funds available for investment are restricted to £200 000.
5. NPV ranking leads to acceptance of C,D and G (NPV = £58 250).
PI ranking leads to acceptance of C,A,D and F (NPV = £61 750).
Management and Cost Accounting, 6th edition, ISBN 1-84480-028-8
© 2000 Colin Drury
© 2004 Colin Drury
14.4a
Taxation and investment decisions
1. Taxation legislation specifies that net cash inflows of companies are
subject to taxes,and capital allowances (writing down allowances)
are available on capital expenditure.
Example
I0 = £100 000, cash inflows
Estimated sale proceeds
Capital allowances
Corporate tax rate
= £50 000 for four years
= Tax WDV at end of year 4
= 25% on a reducing balance basis
= 35%
Management and Cost Accounting, 6th edition, ISBN 1-84480-028-8
© 2000 Colin Drury
© 2004 Colin Drury
14.4b
2.Calculation of capital allowances
Year
Annual
WDAs
£
WDV
0
1
2
3
4
0
25 000 (25% × 100 000)
18 750 (25% × 75 000)
14 063 (25% × 56 250)
10 547 (25% × 42 187)
100 000
75 000
56250
42187
31 640
Management and Cost Accounting, 6th edition, ISBN 1-84480-028-8
© 2000 Colin Drury
© 2004 Colin Drury
14.4c
3. Calculation of incremental taxes arising from the project:
Incremental profits
WDAs
Taxable profits
Taxes at 35%
Year
1
£
50 000
25 000
25 000
8 750
Year
2
£
50 000
18 750
31 250
10 937
Year
3
£
50 000
14 063
35 937
12 578
Year
4
£
50 000
10 547
39 453
13 809
Management and Cost Accounting, 6th edition, ISBN 1-84480-028-8
© 2000 Colin Drury
© 2004 Colin Drury
14.5
Taxation and investment decisions
4. If the estimated sale proceeds exceeded the WDV (say, £45 000)
there would also be an additional balancing charge of £13 360 (£45
000 – £31 640) to deduct from the WDAs in year 4 (taxable profits
would equal £52 813).
5. If the estimated sale proceeds were less than the WDV (say £25 000)
there would be an additional balancing allowance of £6 640 (£31 640
–£25 000) to add to the WDAs in year 4.
Management and Cost Accounting, 6th edition, ISBN 1-84480-028-8
© 2000 Colin Drury
© 2004 Colin Drury
14.6a
Dealing with inflation
• Inflation affects both future cash flows and interest rates
(i.e.RRR /discount rate)
Impact on Cash Flows
• Assume no inflation and estimated cash flows of £100 at time 1 and you can
buy a basket of goods for £1 at time 0
Therefore your cash flow has the potential of buying 100 baskets at time 0 or
time 1.
• Assume now estimated inflation is 10%
Estimated cash flows at time 1 = £110
The cash flows have increased but your purchasing power is unchanged (You
still have the potential to purchase 100 baskets i.e.£110 /£1.10)
Management and Cost Accounting, 6th edition, ISBN 1-84480-028-8
© 2000 Colin Drury
© 2004 Colin Drury
14.6b
•
Cash flows can be expressed in monetary units at the time they are
received (i.e.nominal cash flows = £110 at time 1)
or
they can be expressed in today ’s (time zero) purchasing power (i.e.real
cash flows =£110 /£1.10 = £100)
therefore £110 nominal cash flows is equivalent to £100 in real cash flows.
•
Nominal CF ’s
= Real CF ’s ×(1 + inflation rate)n
= £100 (1.10)1 =£110
•
Real CF ’s
=
Nominal CF ’s
(1 +inflation rate)n
= £110 /1.101=£100
REAL CASH FLOWS ARE WHAT THE CASH FLOWS WOULD BE IN A WORLD
OF NO INFLATION
Management and Cost Accounting, 6th edition, ISBN 1-84480-028-8
© 2000 Colin Drury
© 2004 Colin Drury
14.7
Impact of inflation on interest rates (also discount rates)
• Assume the interest rate is 2% in a world of no inflation therefore you require
£102 for an investment of £100 (provides purchasing power to purchase 102
baskets)
• Now assume the anticipated rate of inflation is 10%. You require a NOMINAL
return of 12.2% to maintain your purchasing power (£112.20 /£1.10 =102
baskets)
• REAL RATE OF INTEREST RATE = WHAT THE INTEREST RATE WOULD BE
IN A WORLD OF NO INFLATION
1 +Nominal rate
1 +Real rate
= (1 +Real rate)× (1 +Est.inflation rate)
= (1 +0.02)× (1 +0.10) = 1.122 =12.2%
= (1 +Nominal rate)/(1 +Est.inflation rate)
= (1 +0.122)/(1 +0.10)=1.02 =2%
• Approximations may suffice 2%real rate +10% inflation rate =12%approximation
• Note that interest rates and RRR ’s on securities are derived from current
financial market data (.they will already be expressed in nominal terms)
Management and Cost Accounting, 6th edition, ISBN 1-84480-028-8
© 2000 Colin Drury
© 2004 Colin Drury
14.8a
Investment appraisal and inflation
• Two correct approaches:
1. Discount nominal cash flows at a nominal discount rate
2. Discount real cash flows at the real discount ate
Example
A company is appraising a project with an investment outlay of £200,000
with estimated annual cash inflows of £100,000 per annum for years 1, 2
and 3.The cost of capital is 9% and the expected rate of inflation is zero.
NPV =100 /(1.09)+100 /(1.09)2+100 /(1.09)3– 200 = 53.1
NOW ASSUME ANTICIPATED RATE OF INFLATION =10%
Management and Cost Accounting, 6th edition, ISBN 1-84480-028-8
© 2000 Colin Drury
© 2004 Colin Drury
14.8b
1. Discount nominal cash flows at the nominal discount rate
NPV = 100 (1.10)
(1.09)(1.10)
+
100 (1.10)2 + 100 (1.10)3
(1.09)2(1.10)2
(1.09)3(1.10)3
- 200 = 53.1
Management and Cost Accounting, 6th edition, ISBN 1-84480-028-8
© 2000 Colin Drury
© 2004 Colin Drury
14.8c
2. Discount real cash flows at the real discount rate
NPV =100 /(1.09)+100 /(1.09)2+100 /(1.09)3–200 =53.1
• We have assumed that current price cash flows are equivalent to real cash flows
but this only applies if all company cash flows are subject to the general rate of
inflation.
WHAT IF THE CASH FLOWS ARE SUBJECT TO A SPECIFIC RATE OF
INFLATION OF 8% AND THE GENERAL RATE FOR THE ECONOMY IS 10%?
We must calculate real cash flows as follows:
Year 1 =100 (1.08)/1.10; Year 2 =100 (1.08)2/(1.10)2
In these circumstances it is easier to discount nominal cash flows at a nominal
discount rate.
Management and Cost Accounting, 6th edition, ISBN 1-84480-028-8
© 2000 Colin Drury
© 2004 Colin Drury
14.9a
Calculating risk adjusted discount rates
1. The returns which shareholders require from investing in risky securities
= Risk free rate + Risk premium.
2. The greater the risk, the greater the return required by investors.
3. The market portfolio is used as a benchmark for determining risk/return
relationships.The risk of an investment relative to the market portfolio is
measured by beta:
• An investment with identical risk to the market portfolio will have a beta of 1.
• An investment half as risky as the market portfolio will have a beta of 0.5.
• An investment twice as risky as the market portfolio will have a beta of 2.
Management and Cost Accounting, 6th edition, ISBN 1-84480-028-8
© 2000 Colin Drury
© 2004 Colin Drury
14.9b
4. The return that shareholders require (i.e.the opportunity cost of an investment)
is:
Risk free rate + (Risk premium × Beta) = CAPM formula
5. The past average risk premium of 8% (defined as the return on the market
portfolio less the risk free rate) is normally used. If the risk free rate is 4% then
the following returns will be required:
• Security A (Beta of 1) = 4%+(8%×1) = 12%
• Security B (Beta of 0.5) = 4%+(8%×0.5) = 8%
• Security C (Beta of 2) = 4%+(8%×2) = 20%
6. Note the risk premium = (Return on the market – risk free rate)
Management and Cost Accounting, 6th edition, ISBN 1-84480-028-8
© 2000 Colin Drury
© 2004 Colin Drury
14.10
The capital asset pricing model
Required return on a security = Rf +(Rm –Rf) × Beta
Management and Cost Accounting, 6th edition, ISBN 1-84480-028-8
© 2000 Colin Drury
© 2004 Colin Drury
14.11
Weighted average cost of capital (WACC)
1. The CAPM is used to calculate the cost of equity finance.
2. Most firms use a combination of debt and equity finance and both sources of
finance should be taken into account when calculating the discount rate.
3. Where combinations of debt and equity are used, the WACC is used to discount
project cash flows.
Example
Cost of equity capital = 18%
Cost of debt capital = 10%
Projects financed by 50% debt and 50% equity
WACC = (0.5 × 18%)+(0.5 ×10%) = 14%
4.The WACC represents the firm ’s overall cost of capital based on the average
risk of all the firm ’s projects. If the risk of a project differs from average firm risk
the WACC of the firm will not reflect the correct risk-adjusted discount rate.
Management and Cost Accounting, 6th edition, ISBN 1-84480-028-8
© 2000 Colin Drury
© 2004 Colin Drury
14.12 and 14.13
Standard deviations and probability distributions
Use overhead as transparency
Management and Cost Accounting, 6th edition, ISBN 1-84480-028-8
© 2000 Colin Drury
© 2004 Colin Drury
14.14a
Sensitivity analysis
1. Shows how sensitive NPV is to a change in the assumptions relating
to the variables used to compute it (e.g.pessimistic, most likely or
optimistic estimates).Can also be used to indicate the extent to
which variables may change before NPV becomes negative.
Management and Cost Accounting, 6th edition, ISBN 1-84480-028-8
© 2000 Colin Drury
© 2004 Colin Drury
14.14b
Example
Year
1 (£)
Cash inflows (10 000 × £30)
VC
Net cash flows
300 000
200 000
100 000
Year
2 (£)
300 000
200 000
100 000
Year
3 (£)
300 000
200 000
100 000
I0 =£200 000, cost of capital =15%, NPV =£28 300
2. Sales volume
• NPV =0 when net cash flows are £87 600 (£200 000 / 2.283)
• Total net cash flows can decline by £12 400 p.a.before NPV becomes negative
• Total sales can fall by £37 200 p.a.(i.e.12.4%)or 1240 units
• Note net cash flows are one-third of sales.
Management and Cost Accounting, 6th edition, ISBN 1-84480-028-8
© 2000 Colin Drury
© 2004 Colin Drury
14.14c
3. Selling price
• Total sales revenue can fall to £287 600 (£300 000 – £12 400)before
NPV becomes negative =£28.76 per unit (i.e.4.1% decline)
4. Variable costs
• Can increase by £12 400 p.a.(£1.24 per unit) = 6.2% decline.
5. Initial outlay
• Can increase by £28 300 (14.15%).
Management and Cost Accounting, 6th edition, ISBN 1-84480-028-8
© 2000 Colin Drury
© 2004 Colin Drury
14.15
Sensitivity analysis (cont.)
6. Cost of capital
• IRR =23%(cost of capital can increase by 53%).
7. Highlights those variables that are most sensitive so that their estimates
can be thoroughly reviewed.
8. Limitations
• Considers variables in isolation.
• Ignores probabilities
Management and Cost Accounting, 6th edition, ISBN 1-84480-028-8
© 2000 Colin Drury
© 2004 Colin Drury
14.16
Classification of risk measurement techniques
1. CAPM approach
•
Risk is compared relative to the variability with the market portfolio.
•
Risk is divided into two categories:
(i) Specific (diversifiable) risk
(ii) Market (non-diversifiable) risk
•
CAPM assumes specific risk can be avoided and it is not rewarded.
•
CAPM assumes market rewards only non-diversifiable risk.
Management and Cost Accounting, 6th edition, ISBN 1-84480-028-8
© 2000 Colin Drury
© 2004 Colin Drury
14.16
2. Stand-alone risk measurement approach
• Does not distinguish between specific and non-diversifiable risk.
• Does not provide a basis for determining the rates of return required for
different levels of risk.
3. Corporate portfolio risk measurement approach
• Focuses on incremental total risk arising from a project.
• Recognizes that incremental risk may not be the same as the total risk of
the project.
Management and Cost Accounting, 6th edition, ISBN 1-84480-028-8
© 2000 Colin Drury
© 2004 Colin Drury
14.16
Example
SD of project X = £10 000
SD of existing projects = £60 000
SD of existing projects plus project X = £65 000
Incremental risk of project X = £5 000 (not £10 000)
• Does not distinguish between specific and non-diversifiable risk.
• Difficult practical problems in measuring risk of existing projects
Management and Cost Accounting, 6th edition, ISBN 1-84480-028-8
© 2000 Colin Drury
© 2004 Colin Drury