ACCA paper f9 financial management study materials F9FM session06 d08

SESSION 06 – APPLICATIONS OF DCF

OVERVIEW
Objective
To apply discounted cash flow techniques to specific areas.

DCF
APPLICATIONS

CAPITAL
RATIONING
Definition
Methods

ASSET
REPLACEMENT
DECISIONS
The issue
Limitations of replacement
analysis

LEASE v BUY
The issue
Decision-making
The investment decision
The financing decision
The final decision

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SESSION 06 – APPLICATIONS OF DCF

1

CAPITAL RATIONING

1.1

Definition

A situation where there is not enough finance available to undertake all
available positive NPV projects.

Hard capital rationing – where the capital markets impose limits on the amount of
finance available e.g. due to high perceived risk of the company.
Soft rationing – where the company itself sets internal limits on finance availability e.g.
to encourage divisions to compete for funds.
Single-period capital rationing – where capital is in short supply in only one period.
Multi-period – where capital is rationed in two or more periods.

1.2

Methods

1.2.1

Divisible projects

A divisible project is where the company can undertake between 0-100% of the project infinite divisibility. However a project cannot be repeated.
Calculate a “profitability index” for each project = NPV/Initial Investment

Rank projects according to their index
Allocate funds to the most effective projects in order to maximise NPV.

Example 1
Projects
NPV
Cash flow at t0

A
$000
100
(50)

Cash is rationed to $50,000 at t0
Projects are divisible.

Required:
Determine the optimal investment plan.

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B
$000
(50)
(10)

C
$000
84
(10)

D
$000
45
(15)


SESSION 06 – APPLICATIONS OF DCF

Solution

1.2.2

Non-divisible projects

A non-divisible/indivisible project must be done 100% or not at all.
Do not calculate a profitability index;
Simply list all possible combinations of projects
Choose combination with highest NPV.

Example 2
Detail as for example 1 but assume that projects are non-divisible.

Solution

1.2.3

Mutually-exclusive projects

Mutually exclusive projects is where two or more particular projects cannot be undertaken

at the same time e.g. because they use the same land.
Divide projects into groups; with one of the mutually-exclusive projects in each group.
Calculate the highest NPV available from each group (assume projects are divisible
unless told otherwise)
Choose the group with the highest NPV
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SESSION 06 – APPLICATIONS OF DCF

Example 3
As for example 1 but C and D are mutually exclusive.

Solution

1.2.4

Multi-period capital rationing

If finance is limited in several periods then a linear programming model would have to
be set up and solved in order to find the optimal investment strategy.
This is outside of the scope of the syllabus

2

ASSET REPLACEMENT DECISIONS

2.1

The issue

Assume that the company has already decided it requires a particular non-current asset.
A secondary decision is about how often to replace the asset.
For example how often should the company replace its fleet of motor vehicles or its
computer equipment?
This is referred to as an asset replacement decision.

Method:
1

Calculate the NPV of each possible replacement cycle.

2

Calculate the Annual Equivalent Cost (AEC) of each cycle
AEC = NPV/Annuity factor

3

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Choose the cycle with the lowest AEC.


SESSION 06 – APPLICATIONS OF DCF

Example 4
A machine costs $20,000.

Year 1
Year 2

Running costs
5,000
5,500

Scrap proceeds
16,000
13,000

Company’s cost of capital = 10%

Required:
Should the machine be replaced every one or every two years?

Solution

2.2

Limitations of replacement analysis
Changing technology e.g. it may be advisable to replace IT equipment more often than
suggested by the above analysis.
Asset requirements may change over time.
Non-financial factors e.g. employees may be more satisfied if their company cars are
replaced more often.

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SESSION 06 – APPLICATIONS OF DCF

3

LEASE v BUY

3.1

The issue
Should the company acquire an asset through:
A straight purchase i.e. borrowing to buy, or
A lease.
There are two main types of lease:
Operating lease; where the asset is simply rented for a relatively short part of its
useful economic life;
Financial/capital lease; where the asset is leased for most of its life.
Although the distinction between operating and finance lease is important in financial
reporting, it is not so relevant in financial management.
The important issue for financial management is the cash flows created by a lease, as
compared to a straight purchase of the asset.

3.2

Decision-making
TWO DECISIONS

INVESTMENT DECISION

FINANCING DECISION

Does the asset give operational benefits?

Is it cheaper to buy or lease?

Focus on the NPV of the operating cash
flows

Focus on the relative beefits of
WDA’s from buying and the tax
relief on the lease payments.

Discount these cash flows using a rate
which reflects operating risk of
investment e.g average cost of capital

Discount these cash flows using
after-tax cost of borrowing

Commentary
The issue here is stripping financing cash flows from operating cash flows and
using separate discount rates for each.
Examination questions may focus merely on the financing decisions.

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SESSION 06 – APPLICATIONS OF DCF

3.3

The investment decision

Discount the cash flows from using the asset (sales, materials, labour, overheads, tax on net
cash flows, etc) at the firm’s weighted average cost of capital (WACC).

3.4

The financing decision

Discount the cash flows specific to each financing option at the after-tax cost of debt. The
assumption is that shareholders view borrowing and leasing as equivalent in terms of
financial risk, so the after-tax cost of debt is an appropriate discount rate for both options.
The preferred financing option will be that with the lowest NPV of cost.
The relevant cash flows for each possible method of financing are as follows.
Buy asset

–

Purchase cost, tax saving on WDA’s, scrap
proceeds

Lease asset (operating
or finance lease)

–

Lease payments, tax saving on lease payments

Under UK tax law all lease payments are tax allowable deductions – both for finance leases
and operating leases.

3.5

The final decision

If the NPV of the cost of the best finance source is less than the NPV of the operating cash
flows, then the project should be undertaken.

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SESSION 06 – APPLICATIONS OF DCF

Example 5
New project
Asset costs $200,000 on the first day of a new accounting period.
Scrap value $25,000 on the last day of the next accounting period.
Operating inflows $150,000 for two years.
Tax at 33% and paid one year in arrears.
Weighted average cost of capital 10%.
Capital allowances at 25% reducing balance.
Finance options:
(1)

borrowing at a post-tax cost of 7%;

(2)

lease for $92,500 per year in advance for two years (lease payments
are tax allowable).

Required:

(a)
(b)
(c)

Determine the operational benefit of the project.
Determine how the project should be financed.
Decide whether the project is worthwhile.

Solution
(a) Operational value

Time

Cash flow
$

Narrative

DF @ 10%

PV
$
________

Present value
∴

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________

SESSION 06 – APPLICATIONS OF DCF

(b) Financing decision
(1) Borrow and buy flows
Time

Cash flow
$

Narrative

DF @ 7%

PV
$

________
________
(W)

WDA’s
Time
$

Tax effect
at 33%
$

Time

(2) Leasing flows
Time

Cash flow
$

Narrative

DF @ 7%

PV
$
________

PV of leasing

________

(c) Final decision
PV of operating flows
PV of cheaper finance
NPV

$
________
________

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SESSION 06 – APPLICATIONS OF DCF

Key points
With capital rationing it is essential to identify the nature of the projects
i.e. divisible or non-divisible, mutually exclusive or not.
With asset replacement decisions, the key is the use of Annual Equivalent
Cost to compare cycles of different lengths.
With lease vs. buy decisions, the key is to separate the financing decision
from the investment decision and analyse each at a discount rate reflecting
the risk of the cash flows. Also remember all lease payments are tax
deductible expenses in the UK.

FOCUS
You should now be able to:
distinguish between hard and soft capital rationing;
apply profitability index techniques for single period divisible projects;
use DCF to analyse asset replacement decisions;
apply DCF methods to projects involving lease or buy problems.

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SESSION 06 – APPLICATIONS OF DCF

EXAMPLE SOLUTIONS
Solution 1 — Divisible projects
Projects
NPV

Cash flow at t0

A
$000
100
(50)

B
$000
(50)
(10)

C
$000
84
(10)

D
$000
45
(15)

NPV
Investment

100
50

( 50 )
10

84
10

45
15

Cost benefit ratio

=2

Reject

= 8.4

=3

1

2

Rank

3

Plan:

CASH
___

NPV
___

AVAILABLE
C

50
(10)
___

84

D

40
(15)
___

45

50% A

25
(25)
___

50
_____

–

$179
_____

Solution 2 — Non-divisible
Combinations

NPV
$000
100
129

A only
C+D
... Choose C + D.

Solution 3 — Mutually exclusive

NPV
$

A
100
50
___

Group 1
$000
B
(50)

10
___

A
100
50
___

Group 2
$000
B
(50)
10
___

C
84
10
___

D
45
15
___

Index

2
___

(5)
___

8.4
___

2
___

(5)
___

3
___

Rank

2

Reject

1

2

Reject

1

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SESSION 06 – APPLICATIONS OF DCF

Plan

NPV

Accept C

84

Accept 0.8 A

80
___

Capital
50
(10)
___
(40)
___

NPV
Accept D

45

Accept 0.7 A

70
___

164
___

Capital
50
(15)
___
(35)
___

115
___

... Accept C and 0.8A.

Solution 4 — Machine replacement
Replace every year
Time
0
1
1

Purchase
Running costs
Scrap proceeds

Cash flow
(20,000)
(5,000)
16,000

Discount factor
1
0.909
0.909
NPV =

Annual equivalent cost =

PV
(20,000)
(4,545)
14,544
______
(10,001)
______

10,001
NPV
= $11,002
=
1 year
0.909
annuity factor

Now repeat the above procedure, assuming the machine is replaced every two years.

Time

0
1
2
2

Narrative

Purchase
Running costs
Running costs
Scrap proceeds

Cash flow
@ 10%
(20,000)
(5,000)
(5,500)
13,000

Discount factor
value
1
0.909
0.826
0.826

18 ,350
18 ,350

Annual equivalent =
=
= $10 ,570
2 year 10% AF 1.736
Conclusion. Replace every two years.

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Present

(20,000)
(4,545)
(4,543)
10,738
______

NPV = (18,350)


SESSION 06 – APPLICATIONS OF DCF

Solution 5 — Lease or Buy
(a) Operational value

Time

Cash flow
$
150,000
(49,500)

1–2
2–3

Narrative

DF @ 10%

Project returns
Tax on above

1.736
1.578

Present value

PV
$
260,400
(78,111)
_______

182,289
_______

(b) Financing decision
(1) Borrow and buy flows
Time

Cash flow

$
(200,000)
25,000
16,500
41,250

0
2
2
3

Narrative

DF @ 7%

Purchase cost
Sale proceeds
(W)
(W)

1
0.873
0.873
0.816

PV
$
(200,000)
21,825
14,405

33,660
________

(130,110)
________
(W)

WDA’s
Time

0
1

2

Purchase
WDA at 25%

$
200,000
(50,000)
________

WDV b/f
Sale

150,000
25,000
________

Balancing allowance

125,000
________

Tax effect
at 33%
$

Time

16,500

2

41,250

3

(2) Leasing flows
Time

0–1
2–3

Cash flow
$
(92,500)
30,525

Narrative

Lease payments
Tax relief thereon

PV of leasing flows

DF @ 7%

1.935
0.873 + 0.816
= 1.689

PV
$
(178,988)
51,557

________
(127,431)
________

Conclusion: The cheapest method of finance is to lease.

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SESSION 06 – APPLICATIONS OF DCF

(c) Final decision

PV of operating flows
PV of leasing flows (cheaper finance – see (b))

$
182,289
(127,431)
________

NPV

54,858
________

The asset should be acquired using a lease.

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