Investment Appraisal – Asset Replacement Decisions, EAC, Lease vs. Buy, Capital Rationing, Profitability Index, Non-Divisible Projects

1. STRATEGIC FINANCIAL
MANAGEMENT
INVESTMENT APPRAISAL – ASSET REPLACEMENT DECISIONS, EAC, LEASE
VS. BUY, CAPITAL RATIONING, PROFITABILITY INDEX, NON-DIVISIBLE
PROJECTS
Dayana Mastura Baharudin

2. Asset Replacement Decisions
• Asset replacement cycle – DCF technique can be
useful in asset replacement decisions to assess how
frequently a non-current asset that is in continual
use in a business (eg delivery vehicles) should be
replaced
• If an asset is replaced less frequently, then it has a
longer replacement cycle (the length of time
between an asset being purchased and the asset
being replaced)

3. Shorter
replacement
cycle
Assets replaced frequently
Lower operating costs as operations
using new machinery
Higher residual value when the asset
is disposed of
Increased capital expenditure as the
asset is being bought more
frequently

4. Longer
replacement
cycle
Asset not replaced frequently
Reduced capital expenditure since the
asset is being bought less frequently
But as the assets gets older, it may cost
more to operate as operations using old
machinery may not be smooth
Residual value / scrap value will be
lower

5. Ideal replacement cycle
WILL MINIMIZE THE
COSTS PER YEAR
OVER THE
REPLACEMENT CYCLE
THIS IS CALCULATED
AS THE;
EQUIVALENT ANNUAL
COST (EAC)

6. EQUIVALENT
ANNUAL COST
(EAC)
EAC = NPV
OF COSTS
OVER THE
REPLACEME
NT CYCLE /
ANNUITY
FACTOR FOR
THE LIFE OF
THE ASSET

7. Equivalent Annual Cost
(definition)
Expresses the present value of the costs of an asset
replacement cycle as a cost per year

8. Example – Asset Replacement
Year 1 Year 2 Year 3
$ $ $
Purchase cost: $25,000
Running costs (cash
expenses)
(7,500) (11,000) (12,500)
Resale value (end of
year)
15,000 10,000 7,500
• A company uses machinery which has the above costs and resale values over its three-year life (per machine)
• The organization’s cost of capital is 10%
• Required: Identify how frequently the asset should be replaced.

9. Solution – Asset Replacement (Replace every
year)
Year Discount factor Cash Flow PV @ 10%
$ $ $
0 1.00 (25,000) (25,000)
1 0.909 (7,500) (6,818)
15,000 13,635
2 0.826
3 0.751
PV of cost over one
replacement cycle
(18,183)

10. Solution – Asset Replacement (Replace every
2 years)
Year Discount factor Cash Flow PV @ 10%
$ $ $
0 1.00 (25,000) (25,000)
1 0.909 (7,500) (6,818)
2 0.826 (11,000) (9,086)
10,000 8,260
3 0.751
PV of cost over one
replacement cycle
(32,644)

11. Solution – Asset Replacement (Replace every
3 years)
Year Discount factor Cash Flow PV @ 10%
$ $ $
0 1.00 (25,000) (25,000)
1 0.909 (7,500) (6,818)
2 0.826 (11,000) (9,086)
3 0.751 (12,500) (9,388)
7,500 5,633
PV of cost over one
replacement cycle
(44,659)

12. Solution – EAC
(replacement
every year)
EAC = (18,183) /
0.909 = (20,003)
0.909 is the
discount factor for
10% for year 1

13. Solution – EAC
(replacement
every 2 years)
EAC = (32,644) / 1.736 = (18,804)
0.909 is the discount factor for 10% for
Year 1
0.826 is the discount factor for 10% for
Year 2
The annuity factor (cumulative discount
factor) for 2 years = 0.909 + 0.826 =
1.736

14. Solution – EAC
(replacement
every 3 years)
EAC = (44,659) / 2.487 = (17,957)
0.909 is the discount factor for 10% for Year 1
0.826 is the discount factor for 10% for Year 2
0.751 is the discount factor for 10% for year 3
The annuity factor (cumulative discount factor)
for 3 years = 0.909 + 0.826 + 0.751 = 2.487

15. EAC – Optimum
Replacement
Policy
The optimum replacement policy is the one with
the lowest EAC which is every 3 years at 17,957

16. Lease vs Buy
Lessor – A
lessor received
lease payments
Lessee – A
lessee makes
lease payments

17. Type of Leases:
Leases that
minimize risk to
the lessee
Short-term leases are rental agreements between a
lessor and a lessee that are structured so that the
lessor retains most of the risks of ownership
The lessor is responsible for servicing and maintaining
the leased equipment
The risk of ownership is also minimized for the lessee
because if there is a change in technology then the
lessee can exit from the rental agreement at the end
of the lease term and is not tied to using the assets
that are technologically out of date

18. Leases that
are purely a
source of
finance
Some leases are long-term arrangement that transfer the
risks and rewards of ownership of an asset to the lessee.
These are arrangements between the lessee and the
lessor for most or all of the asset’s expected useful life
The lessee is responsible for the upkeep, servicing and
maintenance of the asset
This can be a cheaper source of finance than a bank loan
if the lessor buys a large quantity of assets (eg aircraft)
and obtains bulk purchase discounts as a result; some of
the savings from such discounts can be shared with the
lessee in the form of lower rental payments.

19. Benefits of
leasing – to
the lessee
A firm that cannot get a bank loan tu
fund a purchase of an asset due to
unfavourable financial background (eg
lack of assets as backup or lack of cash
flow or even low profitability)
If a company has obtained many loans
before then it will be difficult for them
to obtain more bank loans in the future
(highly leveraged) – bank views them as
a risky customer

20. Example – Lease vs Buy
B Co has decided to invest in a new machine which has a ten-year life and no residual value.
The machine can either be:
Purchased now for $50,000 with a bank loan; pr
It can be leased for ten years with lease rental payments of $8,000 per annum payable at the
end of each year
The cost of capital to be applied is 9% and taxation should be ignored.
Required: Compare the cost of the two financing options

21. Solution – Lease vs Buy (PV of Leasing Costs)
Present value of leasing costs ;
Cash is paid in time periods 1-10
PV = Annuity factor at 9% for 10 years x $8,000
= 6.418 x $8,000 = $51,344

22. Solution – Lease
vs Buy (PV of
Purchase with a
Loan)
This is simply the amount of the loan,
ie. $50,000
If the machine was purchased now, ot
would cost $50,000 (the cost of a bank
loan is simply the amount borrowed)
The purchase with a loan is therefore
the least-cost financing option

25. Capital Rationing Techniques
Capital Rationing
Divisible Projects –
Profitability Index
Non-divisible projects –
NPV of the affordable
combination of projects

26. Types of
Projects
Divisible projects – Projects
that can be scaled down and
done in parts
Non-divisible projects –
Projects that must be
undertaken completely or
not at all

27. Example – Profitability Index
Project Investment
required
PV of cash
inflows
NPV Profitability
Index (PI)
Ranking as
per NPV
Ranking as
per PI
$ $ $ $ $ $
W (10,000) 11,240 1,240 1.12 3 1
X (20,000) 20,991 991 1.05 4 4
Y (30,000) 32,230 2,230 1.07 2 3
Z (40,000) 43,801 3,801 1.10 1 2
Hard Times Co is considering four projects W,X,Y and Z as above.
Required:
Calculate the NPV from investing in the optimal combination of projects if only $60,000 was available
for capital investment

28. Profitability
Index
formulae
Profitability Index = Present
value of cash inflows / Initial
cash outflow

29. Solution – Profitability Index (Capital
rationing of $60,000)
Project Priority Outlay Workings
$ $
W 1 10,000
Z 2 40,000
Y (balance)
TOTAL
3 10,000
60,000
(1/3 of $30,000)

30. Solution – Profitability Index (Total NPV)
Project NPV Workings
$ $
W 1,240
Z 3,801
Y (balance) 743 (1/3 x $2,230)
TOTAL 5,784
By choosing projects according to the Profitability Index, the resulting NPV (if only $60,000
Is available) is $5,784.

31. Example – Non-divisible projects
Project Investment required PV of inflows at 20%
$000 $000
P 40 56.5
Q 50 67
R 30 48.8
SF Co has capital of $95,000 available for investment in the forthcoming period.
The directors decide to consider projects P,Q and R only. The wish to invest only in whole projects.
Required:
Which combination of projects will produce the highest NPV at a cost of capital of 20%

32. Solution – Non-Divisible Projects
Projects Required Investment PV of inflows NPV from projects
$000 $000
P and Q 90 (40 + 50) 123.50 (56.5 + 67) 33.5 (123.5 – 90)
P and R 70 (40 + 30) 105.3 (56.5 + 48.8) 35.3 (105.3 – 70)
Q and R 80 (50 + 30) 115.8 (67 + 48.8) 35.8 (115.8 – 80)
The highest NPV will be achieved by undertaking projects Q and R