# CAPITAL BUDGETING part 2

```CAPITAL BUDGETING
DISCOUNTED PAYBACK
o Refers to the length of time required for the present value of an investment’s cash flows
(discounted at the investment’s cost of capital) to recover a project’s cost.
You have invested in a project that costs P20,000. The estimated annual cash inflows are P5,000.
Assuming a cost of capital of 10%, what is the discounted payback period?
You have invested in a project that costs P10,000. The estimated annual cash inflows for Years 1 to 3
are P5,000, P4,000, and P3,000, respectively. Assuming a cost of capital of 10%, what is the
discounted payback period?
o It helps control the risks associated with the uncertainty of future cash flows.
o It helps minimize the impact of an investment on a firm’s liquidity problems.
o It helps control the risk of obsolescence.
o It helps control the effect of the investment on performance measures.
o It considers the time value of money.
o Easy to calculate and understand.
o Ignores salvage value.
o No concrete decision criteria to indicate if an investment increases the firm value.
o Does not consider the cash flows occurring after the payback period, consequently
ignoring a project’s total profitability
DISCOUNTED PAYBACK
If projects are independent
Accept all the projects that fit into the firm’s “acceptable” criteria. Otherwise, reject.
If projects are mutually exclusive
Accept the project with the shortest discounted payback period and that which fits into the
firm’s “acceptable” criteria. Otherwise, reject.
If projects are mutually inclusive
Accept the primary and the subsequent secondary projects connected to the former if they
fit into the firm’s “acceptable” criteria. Otherwise, reject the projects.
DISCOUNTED PAYBACK BAILOUT
The length of time it would take to recover an investment considering discounted accumulated cash
returns and terminal (salvage) value
A machine costs P100,000. Annual cash inflows relating to the machine is estimated to be P25,000.
Salvage values at the end of 7 years are 60k, 50k, 40k, 30k, 20k, 10k, and zero. Assume that cost of capital
is 10%. Compute for the payback bailout period. Compute for the discounted payback bailout period.
DISCOUNTED PAYBACK BAILOUT
A machine costs P100,000. Annual cash inflows relating to the machine is estimated to be P25,000.
Salvage values at the end of 7 years are 60k, 50k, 40k, 30k, 20k, 10k, and zero. Assume that cost of capital
is 10%. Compute for the payback bailout period. Compute for the discounted payback bailout period.
DISCOUNTED PAYBACK BAILOUT
If projects are independent
Accept all the projects that fit into the firm’s “acceptable” criteria. Otherwise, reject.
If projects are mutually exclusive
Accept the project with the shortest discounted payback bailout period and that which fits
into the firm’s “acceptable” criteria. Otherwise, reject.
If projects are mutually inclusive
Accept the primary and the subsequent secondary projects connected to the former if they
fit into the firm’s “acceptable” criteria. Otherwise, reject the projects
DISCOUNTED PAYBACK BAILOUT
o It helps control the risks associated with the uncertainty of future cash flows.
o It helps minimize the impact of an investment on a firm’s liquidity problems.
o It helps control the risk of obsolescence.
o It helps control the effect of the investment on performance measures.
o Considers salvage value and time value of money.
o No concrete decision criteria to indicate if an investment increases the firm value.
o Does not consider the cash flows occurring after the payback bailout period, consequently
ignoring a project’s total profitability.
PROFITABILITY INDEX
➢ Also known as profit investment ratio, present value index, value investment ratio, benefit-cost
rate, or desirability index.
➢ Refers to the ratio of discounted benefits over discounted costs.
➢ PI = PV of future cash flows / Initial investment
PROFITABILITY INDEX
If projects are independent
Accept all the projects whose Profitability Index &gt; or at least = 1. Otherwise, reject.
If projects are mutually exclusive
Accept the project with the highest Profitability Index, provided that the PI &gt; or at least = 1.
Otherwise, reject. If a necessity, accept the project with the highest PI.
If projects are mutually inclusive
Accept if the primary project and all related secondary projects lead to an overall PI &gt; or =
1. Otherwise, reject the projects.
PROFITABILITY INDEX
o Considers all cash flows and time value of money.
o Tells whether a project will increase or decrease a firm’s value.
o Not in peso amount – does not give a direct measure as to the project’s contribution to
the increase in firm value.
o It does not consider the size of the project when evaluating projects and may be
incorrect when evaluating mutually exclusive projects.
PROFITABILITY INDEX
A company invests in a project that costs P5 million. P2 million is expected to be generated for the next 3
years, and P1 million subsequently. The project is expected to last for 5 years. Assuming a cost of capital of
10%, what is the profitability index?
NET PRESENT VALUE
• The difference between the PV of cash inflows and outflows associated with a project and it
measures the profitability of an investment.
Calculate the NPV of a project which requires an initial investment of P243,000 and is expected to
generate cash inflows of P50,000 each month for 12 months. Assume that the cost of capital is 12%.
An initial investment of machinery of P8,320,000 is expected to generate cash inflows of P3,411,000,
P4,070,000, P5,824,000, and P2,065,000 at the end of each of the next four years. At the end of the fourth
year, the machine will be sold for P900,000. If discount rate is 18%, what is the NPV?
You have a choice between 2 mutually exclusive investments. If you require a 15% return, which
investment should you choose?
NET PRESENT VALUE
If projects are independent
Accept all the projects with + NPV. Otherwise, reject. If NPV is positive, it means that that
(1) initial investment has been recovered, (2) the required rate of return has been
recovered, and (3) a return in excess of (1) and (2) has been received.
If projects are mutually exclusive
Accept the project with the highest + NPV. If the project is a necessity, then accept the
project with the highest NPV.
If projects are mutually inclusive
Accept if the primary project and all related secondary projects lead to an overall + NPV.
Otherwise, reject.
Profitability Index vs. NPV
• Independent Projects
There would not be a conflict between PI and NPV because they yield same accept/reject
rules. This is because PI can be greater than 1 only when NPV is positive.
• Mutually Exclusive Projects
There may be a conflict between PI and NPV because the size of the project does not
matter for PI but it matters for NPV.
Conflict: Profitability Index vs. NPV
Project X
Project Y
PV of cash inflows
200,000
100,000
Initial investment
100,000
40,000
PI
NPV
In case of conflict, the NPV method must be followed (except under capital rationing) because the NPV
reflects the net increase in the firm’s wealth.
INTERNAL RATE OF RETURN
➢ The interest rate that sets the present value of a project’s cash inflows equal to the present value of
the project’s cost. It is the interest rate that forces the NPV to be zero, so PV of inflows = PV of
outflows.
Internal Rate of Return
R1
R2
NPV1
NPV2
=
=
=
R1
+
NPV1 x (R2 - R1)
(NPV1 - NPV2)
Lower discount rate
Higher discount rate
Higher Net Present Value (derived from R1)
Lower Net Present Value (derived from R2)
Find the IRR of an investment having initial cash outflow of P213,000. The annual cash inflows for 6 years
is expected to be P40,000.
If WACC is 4%, will you accept this project?
Find the IRR of an investment having initial cash outflow of P213,000. The cash inflows for Years 1 to 4 is
expected to be P65,200, P98,000, P73,100, and P55,400 respectively.
If WACC is 10%, will you accept this project?
INTERNAL RATE OF RETURN
If projects are independent
Accept all the projects whose IRR &gt; or at least = WACC. If IRR &gt; than WACC, NPV is
positive.
If projects are mutually exclusive
Accept the project with the highest IRR, provided that the IRR &gt; or at least = WACC. If it is
a necessity, accept the project with the highest IRR.
If projects are mutually inclusive
Accept if the primary project and all related secondary projects’ overall IRR &gt; or at least =
WACC.
o Tells whether an investment increases value or not.
o It contains information regarding a project’s safety margin.
o Considers all cash flows and the time value of money.
o It is more appealing to business managers because it provides a basis (rate of return)
for decision making, rather than just a peso amount.
o Unrealistic assumption of using IRR as the reinvestment rate whereas using WACC
would have been more realistic.
o IRR cannot rank mutually exclusive projects properly all the time. IRR can only rank
independent projects properly, if signs do not change. Sometimes decision rule for IRR
can conflict with NPV, in which case, IRR is erroneous.
o Multiple IRR problems They cannot properly rank mutually exclusive projects all the
time.
NPV vs IRR
o Assumption of cash flow reinvestment
o Different lives, sizes, risk factors, timing of cash flows
CROSSOVER POINT
• Crossover Rate or Fisher rate is the cost of capital at which the NPV profiles of 2 projects cross,
and thus, at which the projects’ NPVs are equal.
• If projects are independent, the NPV and IRR always lead to the same accept/reject decisions.
• If projects are mutually exclusive:
o If r &gt; crossover point, the two methods lead to the same decision and there is no
conflict.
o If r &lt; crossover point, the two methods lead to different accept/reject decisions.
REINVESTMENT RATE ASSUMPTIONS
• NPV method assumes CFs are reinvested at r, the opportunity cost of capital.
• IRR method assumes CFs are reinvested at IRR.
Assuming CFs are reinvested at the opportunity cost of capital is more realistic, because:
• If a firm has a reasonably good access to capital markets, it can raise all the capital it
needs at the going rate (WACC).
• Since the firm can obtain capital at the going rate (WACC), if it has investment
opportunities with positive NPVs, it should take them on and finance them at the going
rate (WACC).
• If the firm uses internally generated cash flows from past projects rather than external
capital, it will save the going rate (WACC).
Thus, NPV method is the best. NPV method should be used to choose between mutually exclusive
projects.
ANOTHER PROBLEM FOR USING IRR
• Multiple IRR – the situation where a project has 2 or more IRRs
• A non-normal cash flow occurs when a project calls for a large cash outflow sometime during or at
the end of its life.
• Project P has cash flows (in 000s): CF0 = -\$800, CF1 = \$5,000, and CF2 = -\$5,000. Find Project P’s
NPV and IRR.
• NPV = -\$386.78 IRR = ? Try using 25% and try using 400%
• You typically encounter Multiple IRR problems when any of your cash flows change signs more
than once. (Non-normal Cash Flows)
MODIFIED INTERNAL RATE OF RETURN
MIRR (Modified Internal Rate of Return) is the discount rate that causes the PV of a project’s terminal
value (TV) to equal the PV of costs. TV is found by compounding inflows at WACC.
Where:
FVCF – the future value of positive cash flows discounted at the reinvestment rate
PVCF – the present value of negative cash flows discounted at the financing rate
n – the number of periods
•
•
•
•
MIRR assumes cash flows are reinvested at the WACC.
MIRR correctly assumes reinvestment at opportunity cost = WACC.
MIRR also avoids the problem of multiple IRRs.
Managers like rate of return comparisons, and MIRR is better for this than IRR.
Compute for the MIRR of Projects L and S
Project L
Project S
0
-100
-100
1
10
70
2
60
50
3
80
20
If WACC is 10%, which project(s) would you accept if the projects are independent? What if they are
mutually exclusive?
MODIFIED INTERNAL RATE OF RETURN
Compute for the MIRR of Projects A and B
If WACC is 10%, which project(s) would you accept if the projects are independent? What if they are
mutually exclusive?
MODIFIED INTERNAL RATE OF RETURN
Independent
Accept Projects if MIRR &gt; or at least = to WACC
Mutually Exclusive
Accept the Project with the higher MIRR, provided that the MIRR must be greater than
WACC.
NPV vs MIRR CONFLICT
Size
Life
Verdict
Equal
Same
NPV and MIRR same conclusion
Equal
Different
NPV and MIRR same conclusion
Different
Same/Different
NPV and MIRR may conflict
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