The document discusses investment appraisal methods like net present value (NPV) and internal rate of return (IRR). It provides examples to calculate NPV and IRR for a project to determine if it should be accepted. NPV compares the present value of cash inflows to outflows, with a positive NPV meaning the project should be accepted. IRR is the discount rate that results in an NPV of zero. Both are superior to simpler methods like payback period. While NPV is more accurate, IRR is easier for non-financial managers to understand and use to evaluate projects.

1. INVESTMENT APPRAISAL – NPV & IRR
Dayana Mastura Baharudin
STRATEGIC
FINANCIAL
MANAGEMENT

2. Investment Appraisal: Net Present Value (NPV)
The NPV method uses the concept of discounting and recognizes the time value of money

4. Net Present
Value
This method compares the present
value (PV) of all cash inflows from
a project with the present value of
all the cash outflows
NPV = PV of all cash inflows – PV of
all cash outflows
NPV = represents the change in
wealth of the investor as a result
of investing in the project

6. Net Present
Value
NPV positive = Return from
investment’s cash inflows in excess of
cost of capital (YES, proceed with the
project)
NPV negative = Return from
investment’s cash inflows below cost of
capital (NO, do not proceed with the
project)
NPV Zero = Return from investment’s
cash inflows same as cost of capital
(means you can just cover the cost
without making any profit, it could be
worth undertaking the project)

8. Example -
NPV
• LTH manufactures product X which it sells for $5
per unit. Variable costs of production are currently
$3 per unit. Sales of product X are estimated to be
75,000 units per annum.
• A new machine is available which would cost
$90,000 but which could be used to make product
X for a variable cost of only $2.50 per unit. Fixed
costs, however, would increase by $7,500 per
annum as a direct result of purchasing the
machine.
• The machine would have an expected life of four
years and a disposal value of $10,000.
• LTH expects to earn at least 12% per annum from
its investments.
• Required:
• Using NPV analysis, determine if LTH should
acquire the machine?

9. Solution -
NPV
• Savings are 75,000 units x ($3 - $2.50) = $ 37,500 per
annum
• This is because $3 is the variable cost under current
production
• $2.50 is the the variable cost if new machinery was to be
used
• Additional cost are $7,500 per annum
• Machine depreciation is (90,000 – 10,000)/4 years =
$20,000 per annum (depreciation is not a cash flow)
• Net cash savings = $37,500 - $7,500 = $30,000 per annum
• Relevant cash flow for Year 1 = 30,000, Year 2 = 30,000,
Year 3 = 30,000 and Year 4 = 30,000 + 10,000 = 40,000.
• It is assumed that the machine will be sold in year 4 after
its useful life at $10,000

10. Solution - NPV
Discount factor = 12%
Year 0 (initial outlay or year of purchase of new machine) = discount factor is 1.0
Year 1 = discount factor = [ 1 / (1 + 0.12) ] = 0.893
Year 2 = discount factor = [ 1/(1+0.12) x (1+0.12)] = 0.797
Year 3 = discount factor = [1/(1+0.12)x(1+0.12)x(1+0.12)] =0.712
Year 4 = discount factor = [1/(1+0.12)x(1+0.12)x(1+0.12)x(1+0.12)]= 0.636

11. Solution - NPV
Year 0 1 2 3 4
Cash flow ($) (90,000) 30,000 30,000 30,000 40,000
Discount
factor
1.0 0.893 0.797 0.712 0.636
Present value
($)
(90,000) 26,790 23,910 21,360 25,440
The net present value = (90,000) + 26,790 + 23,910 + 21,360 + 25,440 = 7500
NPV is $7,500
The NPV is positive and so the project is expected to earn more than 12% per annum and is therefore
Acceptable to proceed with the purchase of this new machinery at $90,000

12. Internal Rate of Return (IRR)
A discounted cash flow technique that calculates the percentage return
given by a project.
If this return is used to discount a project’s cash flows, it would deliver an
NPV of Zero.
The IRR calculates the exact return which a project is expected to
achieve; in other words, the rate which if used as a discount factor would
deliver an NPV of Zero

13. Recap – Positive NPV
At 12% discount factor, the NPV is positive at $7,500
Now we need to identify a discount factor which
will result in a negative NPV through trial and error.
We shall try the discount factor of 16%

14. NPV with discount factor of 16% based on the
previous example
Year 0 1 2 3 4
Cash flow ($) (90,000) 30,000 30,000 30,000 40,000
Discount
factor
1.0 0.862 0.7432 0.6406 0.5522
Present value
($)
(90,000) 25,860 22,296 19,218 22,088
The net present value = (90,000) + 25,860 + 22,296 + 19,218 + 22,088 = -538
NPV is -$538
The NPV is negative and so the project is expected to earn less than 16% per annum and is therefore
Not acceptable to proceed with the purchase of this new machinery at $90,000 with the discount
factor of 16%

15. Interpolation
• If a question provides two project NPVs which are mutually exclusive, then
these can be used to estimate the internal rate of return of a project.
• Mutually exclusive is a statistical term describing two or more events that
cannot happen simultaneously.
• This approach is called interpolation.
• IRR = a% + [NPVa / NPVa – NPVb] (b% - a%)
• a% = 12%
• b% = 16%
• NPVa = 7,500
• NPVb = -538
• IRR = 12 + [7,500 / 7,500 + 538] (16 - 12) = 15.7%

17. NPV compared to IRR
Both NPV and IRR are
superior methods for
appraisaing investments
compared to the simpler
techniques like Payback
period and Accounting Rate
of Return;
Both NPV and IRR are
Discounted Cash Flow (DCF)
methods as they account
for the time value of money
unlike Payback and ARR
NPV and IRR focus on
relevant cash flows unlike
ARR
NPV and IRR looks at the
cash flows over the whole
life of the project unlike
Payback

18. Advantage of
IRR over NPV
this concept is easy for non-financial
managers to understand and for
financial managers to calculate
because it does not require the
calculation of a cost of capital.
IRR gives the percentage return of a
project;

19. Advantage of NPV over IRR
When comparing projects of different sizes;
As IRR is a percentage measure it can lead to incorrect choices
being made when choosing between mutually exclusive
projects.
Mutually exclusive is a statistical term describing two or more
events that cannot happen simultaneously.

20. Conclusion
There is a general
consensus that NPV is the
superior technique from a
technical viepoint.
However, IRR is still
extremely useful for
explaining the appraisal of
an investment to non-
financial managers
This is why both NPV and
IRR are both widely used
This is not to say that NPV
is perfect;
Like any financial
technique, there is the
danger that the non-
financial benefits of an
investment are ignored;
Or that the financial
estimates are inaccurate