Week 1: investment decision rules
Corporate finance is how corporates look at financial decision, this is useful if you have a financial
position, if you are dealing with other corporations & if you’re curious how world around you works.
H7: Investment decision rules
There are four different methods of making investments decisions, these are further discussed below.
NPV and Stand-Alone projects
In asset pricing you learned how to calculate PV of financial instruments, PV is:
C
- Perpetuity: PV =
r
C
- Constant growth Perpetuity: PV =
r−g
1
- Annuity: PV =C × ¿
r
The present value of a potential (currently not existing) is:
C
- Perpetuity: NPV =−I+
r
1
- Annuity: PV =−I +C × ¿
r
Important things to notice when applying the NPV rule:
- Take-it-or-leave-it decision Yes/No execute the project
- Single, stand-alone project project is looked at isolated
- Ability to undertake other projects not affected no constraints or exclusiveness
- The NPV depends on the discount rate (cost of capital) NPV changes with discount rate
NPV Investment Rule: When making an investment decision, take the alternative with the highest
NPV. Choosing this alternative is equivalent to receiving its NPV in cash today.
The internal Rate of Return Rule
IRR is like an average return on the investment. IRR Investment rule: Take any investment where the
IRR exceeds the cost of capital and turn down any investment whose IRR is less than the cost of
capital. IRR mostly gives same result as NPV, but not in all situations. The IRR works for stand-alone
projects if all the project’s negative cash flows precede its positive cash flows.
They now give a IRR Rule example, where they set NPV to 0 and numerically solve IRR.
There are 3 pitfalls of IRR:
- Pitfall 1: Delayed investments when benefits of investment occur before costs, the NPV is
an increasing function of the discount rate.
- Pitfall 2: Multiple IRRs the graph has a U-form
- Pitfall 3: Nonexistent IRR No IRR exists because NPV is positive for all values of discount
rate. Thus the IRR rule cannot be used.
IRR rule provides the correct decision only if the project has a positive NPV for every discount rate
below the IRR. So Discount < IRR.
The payback rule
Payback period is amount of time it takes to recover (pay back) the initial investment. If payback
period is less than pre-specified time than you accept the project.
- Advantages of payback period: It’s simple
1
, - Disadvantages: incorrect, ignores projects cost of capital and time value of money, ignores
cashflows after payback period and relies on ad hoc decision criterion (payback period length)
When the above rules conflict, NPV decision rule should be followed.
Choosing between projects
If you have mutually exclusive projects, with the NPV Rule select the project with the highest NPV
and with the IRR Rule select the project with the highest IRR (IRR may lead to mistakes!)
NPV and Mutually exclusive projects
Starts with an example of 4 different NPV calculations (using growth perpetuity). Then you choose the
one with highest NPV. If you tried to use the IRR you would’ve been misled, this can be due:
- Difference in Scale rather have 500% on $1 or 20% on $1 million
- Difference in Timing lower yearly return can be more profitable if earned over more years.
- Difference in Risk The higher cost of capital means a higher IRR is necessary to make
project attractive.
Using Incremental IRR to compare alternatives
Incremental IRR investment: Apply the IRR rule to the difference between the cash flows of the two
mutually exclusive alternatives (the increment to the cash flows of one investment over the other)
An example is used when a firm has two options: minor and major overhaul. You first calculate the
two IRR’s of the options by using excel. Then you want to now which project is the best, but because
the projects have different scales, we cannot compare their IRRs directly. To compute incremental
IRR of switching from minor to major overhaul, we calculate the cash flows by doing: major overhaul
amount – minor overhaul amount. Then you calculate the incremental IRR (same as normal IRR) with
excel. The incremental IRR is higher than the cost of capital, so switching to major overhaul is good.
This incremental IRR determines the crossover point or discount rate at which the optimal decision
changes.
Shortcomings of incremental IRR rule are:
- Incremental IRR may not exist
- Multiple Incremental IRR could exist
- The fact that the IRR exceeds cost of capital for both projects doesn’t imply that either of the
projects has a positive NPV.
- When individual projects have different cost of capital, it is not obvious which cost of capital
the incremental IRR should be compared to.
Project selection with resource constraints
The profitability index can be used to identify the optimal combination of projects to undertake.
Value Created NPV
- profitability index= =
Resource Consumed Resource Consumed
Conditions for reliable usage of the Profitability Index:
- Using it exhaust the resource
- There is only one resource constraint
H14: Fundamentals of Capital Budgeting
Capital budgeting lists the investments that a company plans to undertake and analyses alternative
investments and decide which one to accept.
Forecasting project consequences
2
,Projects have consequences on revenues and costs. The ultimate goal is to determine the effect on free
cash flows, then we can calculate NPV like we learned.
Determining Free Cash Flow and NPV
The incremental effect of a project on a firm’s available cash is its free cash flow. The incremental
cash flows are the cash flows of the firm with the project minus the cash flows of the firm without the
project. These forecast must also take into account: Capital expenditure and depreciation, taxes and
opportunity costs of existing resources. The interest expenses are ignored for now.
Capital expenditures are the actual cash outflows when an asset is purchased and Depreciation is a
non-cash expense. Straight-line depreciation: asset’s costs (less any expected salvage value) is
divided equally over its life. Taxes are also relevant because a investment of a project (investment in
R&D) can reduce taxable income and this should be credited to the project.
- Incremental earnings forecast = Sales – COGS = Gross Profit – S,G&A costs – R&D costs –
Depreciation = EBIT – income tax = unlevered net income
Indirect effects
A project also has indirect effects:
- Opportunity costs value a resource could have provided in its best alternative
- Sunk costs cost that already have been paid (not in incremental earnings forecast)
- Project externalities synergies & cannibalization
In capital budgeting decision, interest expense is typically not included, the rationale is that the project
should be judged on its own, not on how it will be financed.
Calculating FCF from earnings
Earnings and cash flows are not the same. After calculating the unlevered net income we need to make
adjustments:
- Add the depreciation
- Reduce Capital expenditures
- Reduce increase in Net Working Capital
Most product require an investment in net working capital:
-
net working capital =current assets−current liabilities=cash+inventory +receivables− payables
Increase in net working capital is defined as:
- ∆ NWC t=NWC t −NWCt −1
Example of increase in net working capital: cash set aside, inventories of raw materials and product
Calculating Free Cash Flow and NPV
The formula for calculating the Free Cash Flow is as following:
-
Unleverd Net Income
Free Cash Flow=⏞
( Revenues−Costs−Depreciation ) × ( 1−τ c ) + Depreciation−CapEx−∆ NWC
FCF t
- PV ( FCF t )= t
( 1+ r)
3
, Reminder: the cost of capital for a project is the expected return that investors could earn on their best
alternative investment (with similar risk and maturity)
Further adjustments to Free Cash Flow
First of all we have this adjustments to free cash flow:
- Non-cash items (patents)
- Timing of cash flows
- Accelerated depreciation
- Liquidation or salvage value
- Terminal or continuous value
- Tax carryforward
Also with further adjustments to Free Cash Flows you have the capital gain and book value:
- after tax cash flow ¿ asset sale=sale price−( τ c × Capital Gain )
- Capital Gain=Sale Price−Book Value
- Book Value=Purchase Price− Accumulated Depreciation
Also with further adjustment to free cash flow you have the terminal or continuation value. This
amount represents the market value of the free cash flow from the project at all future dates:
FCF 1 FCF 2 FCF N Vn
- V 0= + + …+ +
1+r wacc (1+r wacc)2 N
( 1+r wacc ) (1+r wacc )
N
- V N=
FCF N +1
=
(1+ g FCF
r wacc −gFCF r wacc−g FCF )
× FCF N
Sensitivity and Scenario Analysis
Sensitivity analysis show how the NPV varies with a change in one of the assumptions, holding all of
the other assumptions constant. This reveals which assumptions are critical. Scenario analysis
considers the effect on the NPV of simultaneously changing multiple assumptions
4
Corporate finance is how corporates look at financial decision, this is useful if you have a financial
position, if you are dealing with other corporations & if you’re curious how world around you works.
H7: Investment decision rules
There are four different methods of making investments decisions, these are further discussed below.
NPV and Stand-Alone projects
In asset pricing you learned how to calculate PV of financial instruments, PV is:
C
- Perpetuity: PV =
r
C
- Constant growth Perpetuity: PV =
r−g
1
- Annuity: PV =C × ¿
r
The present value of a potential (currently not existing) is:
C
- Perpetuity: NPV =−I+
r
1
- Annuity: PV =−I +C × ¿
r
Important things to notice when applying the NPV rule:
- Take-it-or-leave-it decision Yes/No execute the project
- Single, stand-alone project project is looked at isolated
- Ability to undertake other projects not affected no constraints or exclusiveness
- The NPV depends on the discount rate (cost of capital) NPV changes with discount rate
NPV Investment Rule: When making an investment decision, take the alternative with the highest
NPV. Choosing this alternative is equivalent to receiving its NPV in cash today.
The internal Rate of Return Rule
IRR is like an average return on the investment. IRR Investment rule: Take any investment where the
IRR exceeds the cost of capital and turn down any investment whose IRR is less than the cost of
capital. IRR mostly gives same result as NPV, but not in all situations. The IRR works for stand-alone
projects if all the project’s negative cash flows precede its positive cash flows.
They now give a IRR Rule example, where they set NPV to 0 and numerically solve IRR.
There are 3 pitfalls of IRR:
- Pitfall 1: Delayed investments when benefits of investment occur before costs, the NPV is
an increasing function of the discount rate.
- Pitfall 2: Multiple IRRs the graph has a U-form
- Pitfall 3: Nonexistent IRR No IRR exists because NPV is positive for all values of discount
rate. Thus the IRR rule cannot be used.
IRR rule provides the correct decision only if the project has a positive NPV for every discount rate
below the IRR. So Discount < IRR.
The payback rule
Payback period is amount of time it takes to recover (pay back) the initial investment. If payback
period is less than pre-specified time than you accept the project.
- Advantages of payback period: It’s simple
1
, - Disadvantages: incorrect, ignores projects cost of capital and time value of money, ignores
cashflows after payback period and relies on ad hoc decision criterion (payback period length)
When the above rules conflict, NPV decision rule should be followed.
Choosing between projects
If you have mutually exclusive projects, with the NPV Rule select the project with the highest NPV
and with the IRR Rule select the project with the highest IRR (IRR may lead to mistakes!)
NPV and Mutually exclusive projects
Starts with an example of 4 different NPV calculations (using growth perpetuity). Then you choose the
one with highest NPV. If you tried to use the IRR you would’ve been misled, this can be due:
- Difference in Scale rather have 500% on $1 or 20% on $1 million
- Difference in Timing lower yearly return can be more profitable if earned over more years.
- Difference in Risk The higher cost of capital means a higher IRR is necessary to make
project attractive.
Using Incremental IRR to compare alternatives
Incremental IRR investment: Apply the IRR rule to the difference between the cash flows of the two
mutually exclusive alternatives (the increment to the cash flows of one investment over the other)
An example is used when a firm has two options: minor and major overhaul. You first calculate the
two IRR’s of the options by using excel. Then you want to now which project is the best, but because
the projects have different scales, we cannot compare their IRRs directly. To compute incremental
IRR of switching from minor to major overhaul, we calculate the cash flows by doing: major overhaul
amount – minor overhaul amount. Then you calculate the incremental IRR (same as normal IRR) with
excel. The incremental IRR is higher than the cost of capital, so switching to major overhaul is good.
This incremental IRR determines the crossover point or discount rate at which the optimal decision
changes.
Shortcomings of incremental IRR rule are:
- Incremental IRR may not exist
- Multiple Incremental IRR could exist
- The fact that the IRR exceeds cost of capital for both projects doesn’t imply that either of the
projects has a positive NPV.
- When individual projects have different cost of capital, it is not obvious which cost of capital
the incremental IRR should be compared to.
Project selection with resource constraints
The profitability index can be used to identify the optimal combination of projects to undertake.
Value Created NPV
- profitability index= =
Resource Consumed Resource Consumed
Conditions for reliable usage of the Profitability Index:
- Using it exhaust the resource
- There is only one resource constraint
H14: Fundamentals of Capital Budgeting
Capital budgeting lists the investments that a company plans to undertake and analyses alternative
investments and decide which one to accept.
Forecasting project consequences
2
,Projects have consequences on revenues and costs. The ultimate goal is to determine the effect on free
cash flows, then we can calculate NPV like we learned.
Determining Free Cash Flow and NPV
The incremental effect of a project on a firm’s available cash is its free cash flow. The incremental
cash flows are the cash flows of the firm with the project minus the cash flows of the firm without the
project. These forecast must also take into account: Capital expenditure and depreciation, taxes and
opportunity costs of existing resources. The interest expenses are ignored for now.
Capital expenditures are the actual cash outflows when an asset is purchased and Depreciation is a
non-cash expense. Straight-line depreciation: asset’s costs (less any expected salvage value) is
divided equally over its life. Taxes are also relevant because a investment of a project (investment in
R&D) can reduce taxable income and this should be credited to the project.
- Incremental earnings forecast = Sales – COGS = Gross Profit – S,G&A costs – R&D costs –
Depreciation = EBIT – income tax = unlevered net income
Indirect effects
A project also has indirect effects:
- Opportunity costs value a resource could have provided in its best alternative
- Sunk costs cost that already have been paid (not in incremental earnings forecast)
- Project externalities synergies & cannibalization
In capital budgeting decision, interest expense is typically not included, the rationale is that the project
should be judged on its own, not on how it will be financed.
Calculating FCF from earnings
Earnings and cash flows are not the same. After calculating the unlevered net income we need to make
adjustments:
- Add the depreciation
- Reduce Capital expenditures
- Reduce increase in Net Working Capital
Most product require an investment in net working capital:
-
net working capital =current assets−current liabilities=cash+inventory +receivables− payables
Increase in net working capital is defined as:
- ∆ NWC t=NWC t −NWCt −1
Example of increase in net working capital: cash set aside, inventories of raw materials and product
Calculating Free Cash Flow and NPV
The formula for calculating the Free Cash Flow is as following:
-
Unleverd Net Income
Free Cash Flow=⏞
( Revenues−Costs−Depreciation ) × ( 1−τ c ) + Depreciation−CapEx−∆ NWC
FCF t
- PV ( FCF t )= t
( 1+ r)
3
, Reminder: the cost of capital for a project is the expected return that investors could earn on their best
alternative investment (with similar risk and maturity)
Further adjustments to Free Cash Flow
First of all we have this adjustments to free cash flow:
- Non-cash items (patents)
- Timing of cash flows
- Accelerated depreciation
- Liquidation or salvage value
- Terminal or continuous value
- Tax carryforward
Also with further adjustments to Free Cash Flows you have the capital gain and book value:
- after tax cash flow ¿ asset sale=sale price−( τ c × Capital Gain )
- Capital Gain=Sale Price−Book Value
- Book Value=Purchase Price− Accumulated Depreciation
Also with further adjustment to free cash flow you have the terminal or continuation value. This
amount represents the market value of the free cash flow from the project at all future dates:
FCF 1 FCF 2 FCF N Vn
- V 0= + + …+ +
1+r wacc (1+r wacc)2 N
( 1+r wacc ) (1+r wacc )
N
- V N=
FCF N +1
=
(1+ g FCF
r wacc −gFCF r wacc−g FCF )
× FCF N
Sensitivity and Scenario Analysis
Sensitivity analysis show how the NPV varies with a change in one of the assumptions, holding all of
the other assumptions constant. This reveals which assumptions are critical. Scenario analysis
considers the effect on the NPV of simultaneously changing multiple assumptions
4
