UGBS 048
BUSINESS FINANCE
Investment evaluation techniques
Hadija N. Nyante, PhD
hnyante@ug.edu.gh
College of Education
Dept. of Distance Education
Session Overview
• This course introduces the student to the
methods used to assess the profitability
and viability of investment projects. This
session covers such techniques including
Net Present Value (NPV), Internal Rate of
Return (IRR), Payback Period, and
Profitability Index.
Session Objectives
On successful completion of this session, students
would be able to:
Discuss the various investment evaluation
techniques, including their advantages and
disadvantages.
Apply these techniques to the evaluation of projects.
Interpret the results of the application of these
techniques in accordance with their respective
decision rules.
Understand the importance of net present value.
Reading List
• Read Recommended Text –
• Fundamentals of Corporate Finance by Brealey, Myres,
Marcus, Maynes, and Mitra
• Foundations of Corporate Finance by Ross, Westerfield, and
Jordan
• University of Ghana Finance Reader
• Securities Markets and Investments: A Ghanaian Primer by
Mensah, S.
• Other Finance text books available to students
Session outline
Net Present Value
The Payback Rule
The Discounted Payback Rule
The Accounting Rate of Return
The Internal Rate of Return
The Practice of Capital Budgeting
Summary and Conclusions
Net Present Value (NPV)
• Net present value (NPV) is the difference between an
investment’s market value (in today’s cedis) and its cost
(also in today’s cedis).
• An investment is worth undertaking if it creates value
for its owners.
• Value is created by identifying an investment that is
worth more in the marketplace than it costs to acquire.
• NPV provides a measure of how much value is created
by undertaking an investment.
NPV
• Recall that the important elements in making financial
decisions are:
– the cash flows
– the timing of the cash flows and
– the risk of the cash flows.
• Estimation of these elements are important in the
calculation of the NPV.
Steps in calculating NPV:
• The first step is to estimate the expected future cash
flows.
• The second step is to estimate the required return
for projects of this risk level.
• The third step is to find the present value of the cash
flows and subtract the initial investment.
NPV Illustrated
0 1 2
Initial outlay Revenues 1000 Revenues 2000
(GHC1100) Expenses 500 Expenses 1000
Cash flow 500 Cash flow 1000
– GHC1100.00
1
GHC500 x
1.10
+454.55
1
GHC1000 x
1.102
+826.45
+GHC181.00 NPV
When should an investment be
accepted, using NPV?
• An investment should be accepted if the NPV is
positive and rejected if it is negative.
• NPV is a direct measure of how well the
investment meets the goal of financial
management—to increase owners’ wealth.
• A positive NPV means that the investment is
expected to add value to the firm.
Payback Period
• Payback period is the amount of time required for an
investment to generate cash flows to recover its initial cost.
• Steps in estimating the payback period are:
– Estimate the cash flows.
– Accumulate the future cash flows until they equal the initial
investment.
– Work out how long this takes to happen.
• An investment is acceptable if its calculated payback is less
than some prescribed number of years.
Payback Period Illustrated
Initial investment = –GHC1000
Year Cash flow
1 GHC200
2 400
3 600
Accumulated
Year Cash flow
1 GHC200
2 600
3 1200
Payback period = 2 + 400/600 = 2 2/3 years
Evaluation of Payback Period
• Advantages:
– Easy to understand.
– Adjusts for uncertainty of later cash flows.
– Biased towards liquidity.
• Disadvantages:
– Time value of money and risk ignored.
– Ignores cash flows beyond the cut-off date.
– Biased against long-term and new projects.
– Arbitrary determination of acceptable payback period.
Discounted Payback Period
• Discounting payback period is the length of time required
for an investment’s discounted cash flows to equal its
initial cost.
• Takes into account the time value of money.
• More difficult to calculate.
• An investment is acceptable if its discounted payback is
less than some prescribed number of years.
Example—Discounted Payback
Initial investment = —GHC1000
R = 10%
PV of
Year Cash flow Cash flow
1 GHC200 GHC182
2 400 331
3 700 526
4 300 205
Example—Discounted Payback
(continued)
Accumulated
Year discounted cash flow
1 GHC182
2 513
3 1039
4 1244
Discounted payback period is just under
three years.
Ordinary and Discounted Payback
Initial investment = –GHC300
R = 12.5%
Cash Flow Accumulated Cash Flow
Year Non-Discounted Discounted Non-discounted Discounted
1 GHC100 GHC100 GHC 89
2 GHC89 200 168
3 100 79 300 238
4 100 70 400 300
5 100 62 500 355
100 55
• What is the ordinary payback period?
• What is the discounted payback period?
Evaluation of Discounted Payback
• Disadvantages
• Advantages
- May reject positive NPV
- Includes time value of investments
money
- Arbitrary determination
- Easy to understand of acceptable payback
- Does not accept negative period
estimated NPV investments - Ignores cash flows beyond
- Biased towards liquidity the cut-off date
- Biased against long-term
and new products
Accounting Rate of Return (ARR)
• An investment’s average net income divided by its
average book value.
average net profit
ARR
average book value
• A project is accepted if ARR > target average
accounting return.
Example—ARR
Year
1 2 3
Sales 440 240 160
Expenses 220 120 80
Gross profit 220 120 80
Depreciation 80 80 80
Taxable income 140 40 0
Taxes (30%) 42 12 0
Net profit 98 28 0
Assume initial investment = GHC240
ARR CONT’D
• Average net profit = 98 + 28 + 0 = GHC42
3
• Average book value =
initial investment + salvage value =
2
= 240 + 0 = GHC120
2
ARR CONT’D
• ARR = AVERAGE PROFIT
AVERAGE BOOK VALUE
= GHC42
GHC 120
• = 35%
Evaluation of ARR
• Advantages:
– Easy to calculate and understand.
– Accounting information almost always available.
• Disadvantages:
– The measure is not a ‘true’ reflection of return.
– Time value is ignored.
– Arbitrary determination of target average return.
– Uses profit and book value instead of cash flow and market
value.
Internal Rate of Return (IRR)
• IRR is the discount rate that equates the present value of
the future cash flows with the initial cost.
• A project is accepted if:
IRR > the required rate of return
• The IRR on an investment is the required return that results
in a zero NPV when it is used as the discount rate.
Example 1—IRR
Year Cash flow
Initial investment = –GHC200
1 GHC 50
2 100
3 150
n Find the IRR such that NPV = 0
50 100 150
0 = –200 + + +
(1+IRR)1 (1+IRR)2 (1+IRR)3
50 100 150
200 = + +
(1+IRR)1 (1+IRR)2 (1+IRR)3
Example 1—IRR (continued)
Trial and Error
Discount rates NPV
0% GHC100
5% 68
10% 41
15% 18
20% –2
IRR is just under 20%—about 19.44%
Example 2—NPV Profile
Net present value
120 Year Cash flow
0 – GHC275
100 1 100
2 100
80 3 100
4 100
60
40
20
– 20
– 40 Discount rate
2% 6% 10% 14% 18% 22%
IRR
Advantages of IRR
• Popular in practice.
• Does not require a discount rate.
• The IRR appears to provide a simple way of
communicating information about a proposal.
Problems with IRR
• Multiple rates of return
– Occurs if more than one discount rate makes the NPV of an
investment zero.
– This will happen when there is more than one negative cash
flow (non-conventional cash flows).
• Mutually exclusive investment decisions
– Project is not independent mutually exclusive investments.
Highest IRR does not indicate the best project.
Multiple Rates of Return
Assume you are considering a project for
which the cash flows are as follows:
Year Cash flows
0 –GHC60
1 155
2 –100
Multiple Rates of Return
n To find the IRR on this project
NPV is calculated at various rates:
at 10%: NPV = -GHC1.74
at 20%: NPV = - 0.28
NPV crosses
at 30%: NPV = 0.06
zero
at 40%: NPV = - 0.31
n Two questions:
u 1. What is going on here?
u 2. How many IRRs can there be?
IRR and Non-conventional Cash Flows
• When the cash flows change sign more than once,
there is more than one IRR.
• When you solve for IRR you are solving for the root
of an equation and when you cross the x axis more
than once, there will be more than one return that
solves the equation.
• If you have more than one IRR, you cannot use any of
them to make your decision.
Present Value Index (PVI)
• The present value index is the present value of an
investment’s future cash flows divided by its initial cost.
PV of inflows
PVI
Initial cost
• The PVI is also known as the benefit/cost ratio.
• Accept a project with a PVI > 1.0.
Net Present Value Index (NPVI)
• The net present value index is the net present value of
the future cash flows divided by the initial investment.
NPV of inflows
NPVI
Initial cost
• The NPVI differs from the PVI by a scale of one.
• The ranking problems associated with the PVI are also
applicable to the NPVI.
Example—PVI
Assume you have the following information on Project X:
Initial investment = –GHC1100 Required return = 10%
Annual cash revenues and expenses are as follows:
Year Revenues Expenses
1 GHC1000 GHC500
2 2000 1000
Example—PVI (continued)
500 1 000
NPV 1100
1.10 1.102
$181
181 1100
PVI
1100
1.1645
181
NPVI
1100
0.1645
Evaluation of PVI and NPVI
• Advantages
• Disadvantages
- Closely related to NPV,
generally leading to - May lead to
identical decisions. incorrect decisions
- Easy to understand. in comparisons of
- May be useful when mutually-exclusive
available investment investments.
funds are limited.
Capital Budgeting in Practice
• We should consider several investment criteria when
making decisions.
• NPV and IRR are the most commonly used primary
investment criteria.
• Payback is a commonly used secondary investment
criteria.
Summary and Conclusions
• Six criteria used to evaluate proposed investments are:
– Net present value (NPV)
– Payback period
– Discounted payback period
– Accounting rate of return (ARR)
– Internal rate of return (IRR)
– Present value index (PVI)
• Financial managers act in the best interests of
shareholders by identifying and undertaking positive NPV
investments.
• The other investment criteria provide additional
information about whether a project truly has a positive
NPV.
