Compute IRR and NPV in Microsoft Excel
1.IRR Function
Description:
The Microsoft Excel IRR function returns the internal rate of return for a series of cash flows. The cash
flows must occur at regular intervals, but do not have to be the same amounts for each interval.
Syntax
The syntax for the IRR function in Microsoft Excel is:
IRR(range, [estimated_irr] )
Parameters or Arguments
range
A range of cells that represent the series of cash flows.
estimated_irr
Optional. It is your guess at the internal rate of return. If this parameter is omitted, it
assumes an estimated_irr of 0.1 or 10%
Example (as Worksheet Function)
Let's look at some Excel IRR function examples and explore how to use the IRR function as a
worksheet function in Microsoft Excel:
Based on the Excel spreadsheet above:
This first example returns an internal rate of return of 28%. It assumes that you start a
business at a cost of $7,500. You net the following income for the first four years: $3,000,
$5,000, $1,200, and $4,000.
This next example returns an internal rate of return of 5%. It assumes that you start a
business at a cost of $10,000. You net the following income for the first three years: $3,400,
$6,500, and $1,000.
=IRR(B1:B4)
Result: 5%
2.NPV Function
Description
The Microsoft Excel NPV function returns the net present value of an investment.
Syntax
The syntax for the NPV function in Microsoft Excel is:
NPV( discount_rate, value1, [value2, ... value_n] )
Parameters or Arguments
discount_rate
The discount rate for the period.
value1, value2, ... value_n
The future payments and income for the investment (ie: cash flows). There can be up
to 29 values entered.
Note
Microsoft Excel's NPV function does not account for the intial cash outlay, or may account for
it improperly depending on the version of Excel. However, there is a workaround.
This workaround requires that you NOT include the initial investment in the future
payments/income for the investment (ie: value1, value2, ... value_n), but instead, you need to
subtract from the result of the NPV function, the amount of the initial investment.
The workaround formula is also different depending on whether the cash flows occur at the
end of the period (EOP) or at the beginning of the period (BOP).
If the cash flows occur at the end of the period (EOP), you would use the following formula:
=NPV( discount_rate, value1, value2, ... value_n ) - Initial Investment
If the cash flows occur at the beginning of the period (BOP), ou would use the following
formula:
=NPV( discount_rate, value2, ... value_n ) - Initial Investment + value1
Example (as Worksheet Function)
Let's look at some NPV examples and explore how to use the NPV function as a worksheet
function in Microsoft Excel:
This first example returns a net present value of $3,457.19. It assumes that you pay $7,500
as an initial investment . You then receive the following in ...
Compute IRR and NPV in Microsoft Excel 1.IRR Function .docx
1. Compute IRR and NPV in Microsoft Excel
1.IRR Function
Description:
The Microsoft Excel IRR function returns the internal rate of
return for a series of cash flows. The cash
flows must occur at regular intervals, but do not have to be the
same amounts for each interval.
Syntax
The syntax for the IRR function in Microsoft Excel is:
IRR(range, [estimated_irr] )
Parameters or Arguments
range
A range of cells that represent the series of cash flows.
estimated_irr
Optional. It is your guess at the internal rate of return. If this
parameter is omitted, it
assumes an estimated_irr of 0.1 or 10%
Example (as Worksheet Function)
Let's look at some Excel IRR function examples and explore
2. how to use the IRR function as a
worksheet function in Microsoft Excel:
Based on the Excel spreadsheet above:
This first example returns an internal rate of return of 28%. It
assumes that you start a
business at a cost of $7,500. You net the following income for
the first four years: $3,000,
$5,000, $1,200, and $4,000.
This next example returns an internal rate of return of 5%. It
assumes that you start a
business at a cost of $10,000. You net the following income for
the first three years: $3,400,
$6,500, and $1,000.
=IRR(B1:B4)
Result: 5%
2.NPV Function
Description
The Microsoft Excel NPV function returns the net present value
of an investment.
Syntax
3. The syntax for the NPV function in Microsoft Excel is:
NPV( discount_rate, value1, [value2, ... value_n] )
Parameters or Arguments
discount_rate
The discount rate for the period.
value1, value2, ... value_n
The future payments and income for the investment (ie: cash
flows). There can be up
to 29 values entered.
Note
Microsoft Excel's NPV function does not account for the intial
cash outlay, or may account for
it improperly depending on the version of Excel. However, there
is a workaround.
This workaround requires that you NOT include the initial
investment in the future
payments/income for the investment (ie: value1, value2, ...
value_n), but instead, you need to
subtract from the result of the NPV function, the amount of the
initial investment.
The workaround formula is also different depending on whether
the cash flows occur at the
end of the period (EOP) or at the beginning of the period
(BOP).
If the cash flows occur at the end of the period (EOP), you
4. would use the following formula:
=NPV( discount_rate, value1, value2, ... value_n ) - Initial
Investment
If the cash flows occur at the beginning of the period (BOP), ou
would use the following
formula:
=NPV( discount_rate, value2, ... value_n ) - Initial Investment +
value1
Example (as Worksheet Function)
Let's look at some NPV examples and explore how to use the
NPV function as a worksheet
function in Microsoft Excel:
This first example returns a net present value of $3,457.19. It
assumes that you pay $7,500
as an initial investment . You then receive the following income
for the first four years (EOP):
$3,000, $5,000, $1,200, and $4,000. An annual discount rate of
8% is used.
=NPV(8%, 3000, 5000, 1200, 4000) - 7500
This next example returns a net present value of $8,660.77. It
assumes that you pay $10,000
as an initial investment. You then receive the following income
for the first three years (BOP):
$3,400, $6,500, and $10,000. An annual discount rate of 5% is
used.
=NPV(5%, 6500, 10000) - 10000 + 3400
5. Below is the example used in Chapter 10 PPT.
Chapter 12. Cash Flow Estimation
1
6. Net Present Value analysis, IRR, and PI methods provide very
sophisticated measures of shareholder value generated by
potential capital investments.
If cash flow estimates are bad, any analytical technique for
assessing project value will lead to poor investment decisions.
Capital Budgeting and Cash Flows
2
Capital budgeting concerned with cash flows, not accounting
profit.
To evaluate a capital investment, we must know:
Incremental cash outflows of the investment (marginal cost of
investment), and
Incremental cash inflows of the investment (marginal benefit of
investment)
The timing and magnitude of cash flows and accounting profits
7. can differ dramatically.
Cash Flows Versus Accounting Profit
3
Financing costs should be excluded when evaluating a project’s
cash flow.
Ask the following: Is the project’s existence dependent on
financing?
NO!!!-- you must separate financing and investment decisions
Both interest expense from debt financing and dividend
payments to equity investors should be excluded.
Financing costs are captured in the discounting future cash
flows to present.
Financing Costs
8. 4
Land, Buildings, Equipment, etc.
Asset purchases represent negative cash flows (Accounts don’t
show purchase as a deduction from earnings-use depreciation
instead).
Shipping and installation costs should be included in the
purchase price.
Full initial cost becomes the depreciable basis.
Costs of fixed assets
9. 5
Accountants subtract depreciation from revenues to obtain net
income.
Depreciation shelters income from tax – which impacts cash
flows – so it is relevant.
Depreciation must be added to net income when estimating the
project’s cash flow.
Non-cash Charges
6
10. Working capital= Current assets – current liabilities
Usually inventory, accounts receivable, and accounts payable
Usually, working capital = Inv + AR – AP
New investment projects typically increase net working capital:
cash outflow.
Most of the increase comes from additional inventories and
receivables.
Typically an outflow at the beginning of a project and an inflow
at the end.
Changes in Net Working capital
7
Relevant
Cash flows (not accounting earnings)
Depreciation
11. Incremental cash flows
Opportunity costs: The return on the best alternative use of an
asset. Must be included. (Example: land previously owned.)
Side effects (externalities): Effects of a project on cash flows in
other parts of the firm. (E.g. cannibalism or synergy)
Taxes
Irrelevant
Sunk costs: Outlays that have already occurred.
Cash Flows
8
Opportunity Costs: Currently own land or have to purchase land
Sunk costs: Bought a cell phone, now want new I-
Phone…should original price of phone be included?
(1) Cash Flows from Operations
Operating Cash Flow = EBIT – Taxes + Depreciation
Other Methods for Computing OCF
Bottom-Up Approach
Works only when there is no interest expense
12. OCF = NI + depreciation
Top-Down Approach
OCF = Sales – Costs – Taxes
Don’t subtract non-cash deductions
Tax Shield Approach
OCF = (Sales – Costs)(1 – tc) + Depreciation* tc
Estimating Cash Flows
9
Capital Spending: Changes to fixed assets
(2) Cash Flows from Investments
Part I: Net Capital Spending
Usually up front and at the end
Remember salvage value (after tax)
Part II: Changes in Net Working Capital
Part III: Opportunity Costs
(3) Cash Flows from Side Effects
cannibalism or synergy
Estimating Cash Flows
13. 10
Speedo has decided to introduce the LZR-2. An improved
version of the LZR that Phelps and others wore.
Speedo spent 250k developing an improved “Pulse” fabric
Speedo spent 100k test marketing it with Olympic hopeful
swimmers
Test market was successful
Example: Speedo LZR-2
14. 11
Details
Speedo is assuming three years for the project. They assume
that at the end of three years the technology will be essentially
obsolete.
Cost of equipment to support the new swimsuit: $200,000
(depreciated according to MACRS 3-year life)
Increase in net working capital (mainly fabric materials):
$20,000. This will be recovered at the end of the project.
Inflation has been built into financial statements already.
Operating costs are about 90% of revenues.
The equipment can be sold at the end of the project for an
estimated $20,000.
Speedo has estimated the appropriate discount rate to be 10%.
Example: Speedo LZR-2
15. 12
See the text for the details of the case.
Relevant or not?
250k developing fabric?
100k test marketing swimsuits?
Example: Speedo LZR-2
13
Starting point: Year 0 outflows
16. Equipment -200
NWC -20
Total -220
Example: Speedo LZR-2
14
Depreciation
Why do we care about depreciation?
Taxes
Tax shield = depreciation * tax rate
Now, do you want tax shields sooner or later?
Tax law allows accelerated depreciation (Modified Accelerated
Cost Recovery System or MACRS)
Example: Speedo LZR-2
17. 15
Tax Shield coming sooner implies that the Present Value of the
tax shield will be larger
Example: Speedo LZR-2
16
18. Example: Speedo LZR-2
MACRS increases the present value of an investment’s tax
benefits.
Speedo (rounded):Year
Investment%Depr1200.3366.002200.4590.003200.1530.004200.
0714.00
17
Example: Speedo LZR-2Year 1Year 2Year
3Revenues4,000.003,000.002,000.00Oper costs-3,600.00-
2,700.00-1,800.00Depreciation-66.00-90.00-30.00Inc before
tax334.00210.00170.00Tax (40%)-133.60-84.00-68.00Net
Inc200.40126.00102.00+ Depreciation+66.00+90.00+30.00Oper
CF266.40216.00132.00
19. 18
Equipment can be sold at end of year 3 for 20,000.
So, additional CF:
Book value: 14
Capital gain: 20 – 14 = 6
Taxes: 6 * .4 = 2.4
CF: 20 – 2.4 = 17.6
Put it all together!
Capital investment
Change in NWC
Operating CFs (need depreciation)
CF from Salvage
Evaluate!
Example: LZR-2
21. 133.332014.291053.75
244.453224.49189.57.22
314.8119.217.4914.48.556.68
47.4111.5212.4911.527.76.18
511.528.939.226.935.71
65.768.927.376.235.28
7 8.936.555.94.89
8 4.456.555.94.52
9 6.565.94.46
10 6.555.94.46
11 3.295.94.46
12 5.94.46
13 5.914.46
14 5.94.46
15 5.914.46
16 2.994.46
17-20 4.46
21 2.23
Tax Depreciation Schedules by Recovery-Period Class
Table 6.1Period012345671Capital
Investment10,000(1,949)2Accumulated
depreciation1,5833,1674,7506,3337,9179,500- 03Year-end book
value10,0008,4176,8335,2503,6672,083500- 04Working
capital5501,2893,2614,8903,5832,002- 05Total book value
(3+4)10,0008,9678,1228,5118,5575,6662,502-
06Sales52312,88732,61048,90135,83419,7177Cost of goods
sold8377,72919,55229,34521,49211,8308Other
Costs4,0002,2001,2101,3311,4641,6111,7729Depreciation1,583
1,5831,5831,5831,5831,58310Pretax profit (6-7-8-
9)(4,000)(4,097)2,36510,14416,50911,1484,5321,44911Tax at
35%(1,400)(1,434)8283,5505,7783,9021,58650712Profit after
tax (10-11)2,600(2,663)1,5376,59510,7317,2462,946942
Table
6.2Period012345671Sales52312,88732,61048,90135,83419,7172
Cost of goods sold8377,72919,55229,34521,49211,8303Other
costs4,0002,2001,2101,3311,4641,6111,7724Tax on
22. operations(1,400)(1,434)8283,5505,7783,9021,5865Cash flow
from operations (1-2-3-
4)(2,600)(1,080)3,1208,17712,3148,8294,5296Change in
working
capital(550)(739)(1,972)(1,629)1,3071,5812,0027Capital
investment and disposal(10,000)1,4428Net cash flow
(5+6+7)(12,600)(1,630)2,3816,20510,68510,1366,1103,4449Pre
sent value at
20%(12,600)(1,358)1,6543,5915,1534,0742,046961Net Present
value= +3520 (sum of 9)
Table 6.4Tax Depreciation Schedules by Recovery-Period
ClassYear(s)3-Year5-Year7-Year10-Year15-Year20-
Year133.332014.291053.75244.453224.49189.57.22314.8119.21
7.4914.48.556.6847.4111.5212.4911.527.76.18511.528.939.226.
935.7165.768.927.376.235.2878.936.555.94.8984.456.555.94.52
96.565.94.46106.555.94.46113.295.94.46125.94.46135.914.461
45.94.46155.914.46162.994.4617-204.46212.23
Table
6.5Period012345671Sales52312887326104890135834197172Co
st of goods sold8377729195522934521492118303Other
Costs40002200121013311464161117724Tax
depreciation20003200192011525765Pretax profit (1-2-3-4)-
4000-451474898071694011579553919496Taxes at 35%-1400-
15802623432592940531939682
Table
6.6Period012345671Sales52312887326104890135834197172Co
st of goods sold8377729195522934521492118303Other
costs40002200121013311464161117724Tax-1400-
158026234325929405319396825Cash flow from operations (1-
2-3-4)-2600-934368682951216386784176-6826Change in
working capital-550-739-1972-16291307158120027Capital
investment and disposal-1000019498Net cash flow (5+6+7)-
12600-148429476323105349985575732699Present Value=
+3802 (sum of 9)-12600-123720473659508040131928912Net
present value= +3802 (sum of 9)
7.1Plotting data Fig
29. Time is an important element of the decision
Cash flows of investment can be measured
But, there may be some uncertainties
Classification of decisions
Accept or reject
Choose best of a set (mutually exclusive)
Ranking (projects are independent and cash is limited)
Capital budgeting
Independent vs. mutually exclusive projects
Independent projects:
if the cash flows of one are unaffected by the acceptance of the
other.
Multiple projects can be chosen.
Mutually exclusive projects:
if the cash flows of one can be adversely impacted by the
acceptance of the other.
Only ONE of several potential projects can be chosen
30. 3
Financial managers should accept a project when its perceived
benefits exceed perceived costs. In general, value is created
when benefits exceed costs.
NPV = Total PV of future CFs - Initial Investment
When firms accept all positive Net Present Value investments,
they maximize the value of their shareholders.
Net Present Value (NPV)
31. Net Present Value (NPV)
Sum of the PVs of all cash inflows and outflows of a project:
Estimating NPV:
1. Estimate future cash flows: how much? and when?
2. Estimate discount rate
3. Estimate initial costs
Reinvestment assumption
Assumes all cash flows are reinvested at discount rate
Rule
Accept if NPV > 0
Reject if NPV < 0.
Ranking Criteria
Choose the highest NPV
32. What is Project S’ NPV?
WACC = 10%
Year
CFt
PV of CFt
0
-
100
-
$100.00
1
70
63.64
2
50
41.32
3
20
15.02
NPVS
=
$ 19.98
Excel: =NPV(rate,CF1:CFn) + CF0
Here, CF0 is negative, rate is discount rate or WACC.
33. 6
Rationale for the NPV Method
NPV = PV of inflows – Cost
= Net gain in wealth
If projects are independent, accept if NPV > 0.
If projects are mutually exclusive, accept projects with the
highest positive NPV, those that add the most value.
34. 7
IRR is the discount rate that forces PV of inflows equal to cost,
and the NPV = 0:
Reinvestment assumption: All future cash flows assumed
reinvested at the IRR
Solving for IRR with a financial calculator:
Enter CFs in Cash Flow register.
Press IRR.
Solving for IRR with Excel:
=IRR(CF0:CFn)
Internal Rate of Return (IRR)
35. 8
How is a project’s IRR similar to a bond’s YTM?
They are the same thing.
Think of a bond as a project. The YTM on the bond would be
the IRR of the “bond” project.
EXAMPLE: Suppose a 10-year bond with a 9% annual coupon
and $1,000 par value sells for $1,134.20.
Solve for IRR = YTM = 7.08%, the annual return for this
project/bond.
9
Rules for the IRR Method
For independent projects:
Take all projects with IRR>r*
r*=the opportunity cost of capital or required rate of return
For mutually exclusive projects:
36. Take the project with the highest IRR, if IRR>r*
10
What is the IRR of the following project?
The IRR does not always exist!
Potential problems with IRRYear012Project A100-200150
37. Lending or Borrowing?
Potential problems with IRR
12
Potential problems with IRR
The following cash flow generates NPV=$ 3.3 million at 10%.
It has IRRs of (-44%) and +11.6%.
38. Cash Flows (millions of Australian dollars)
13
When the sign of the cash flows changes more than once, you
get multiple rates of return
The IRR does not always unique!
Potential problems with IRR
40. If cash flows have the traditional pattern (one or several
negative cash flows followed by only positive cash flows), then
the NPV is positive whenever the IRR is greater than the
opportunity cost of capital – Thus, the IRR rule usually works.
Potential problems with IRR
FlowsNumber of IRRsIRR criterionNPV criterionFirst cash flow
is (-) and all remaining cash flows are (+)1Accept if IRR>R
Reject if IRR<RAccept if NPV>0
Reject if NPV<0
First cash flows is (+) and all remaining cash flows are (-
)1Accept if IRR<R
Reject if IRR>R
Accept if NPV>0
Reject if NPV<0
Some cash flows after first are (+) and some cash flows after
first are (-)Maybe more than 1No valid IRRAccept if NPV>0
Reject if NPV<0
General rules
41. Potential problems with IRR: scale issue
Mutually Exclusive Projects
Mutually exclusive
Only ONE of several potential projects can be chosen
Independent: Accepting/rejecting one project does not affect the
decision of the other projects
Scale issues
IRR sometimes ignores the magnitude of the project.
42. 17
Potential problems with IRR: scale issue
In this case, can IRR be salvaged?
Look at smaller project
Acceptable? Yes.
So, should you invest extra $$$ for larger project.
Look at incremental CFs: INCREMENTAL IRR
Now, which project is better?
18
Timing Issues
43. Preferred project depends on the discount rate, not the IRR
(mutually exclusive projects)
Potential problems with IRR: timing issue
0 1 2 3
$10,000 $1,000 $1,000
-$10,000
Project A
0 1 2 3
$1,000 $1,000 $12,000
-$10,000
Project B
44. 19
Potential problems with IRR: timing issue
20
20
Potential problems with IRR: timing issue
10.55% = IRR
To find crossover rate: Find INCREMENTAL IRR!
45. 21
The number of years required to recover a project’s cost, or
“How long does it take to get our money back?”
Calculated by adding project’s cash inflows to its cost until the
cumulative cash flow for the project turns positive.
Payback period
46. The payback period is the number of years, t*, such that
For independent projects
Accept all projects for which t*<K (where K is the cutoff)
For mutually exclusive projects:
Accept the project with the lowest t* as long as t*<K (where K
is the cutoff)
Mutually exclusive: Only ONE of several potential projects can
be chosen
Payback period
48. 24
Examine the three projects and note the mistake we would make
if we insisted on only taking projects with a payback period of 2
years or less.
Payback period
25
Strengths and Weaknesses of Payback
Strengths
Provides an indication of a project’s risk and liquidity.
Easy to calculate and understand.
49. Weaknesses
Ignores the time value of money.
Ignores CFs occurring after the payback period.
26
The discounted payback period is the number of years, t*, such
that
For non-mutually excusive projects
Accept all projects for which t*<K
For mutually exclusive projects:
Accept the project with the lowest t* as long as t*<K (where K
is the cutoff)
Discounted payback period
50. Discounted Payback Period
Uses discounted cash flows rather than raw CFs.
Disc PaybackL = 2 + / = 2.7 years;
If our cutoff rule was 2 years, this project would be rejected.
41.32
60.11
CFt
Cumulative
0
1
2
3
73. Calculating the Weighted Average Cost of Capital
WACC = wdrd(1 – T) + wprp + wcrs
The w’s refer to the firm’s capital structure weights:
wd=weight of the debt
wp=weight of the preferred stock
wc=weight of the common equity
The r’s refer to the cost of each component:
rd=before-tax cost of the debt
rp =cost of the preferred stock
rs =cost of the common equity
75. used as a measure of rd.
5
Cost of Preferred Stock
WACC = wdrd(1 – T) + wprp + wcrs
rp is the marginal cost of preferred stock, which is the return
investors require on a firm’s preferred stock.
D is the preferred dividend.
P is the current price of the preferred stock.
Preferred dividends are not tax-deductible, so no tax
adjustments necessary.
76. 6
The Cost of Common Equity
Cost of equity is more challenging to estimate than the cost of
debt or the cost of preferred stock because common
stockholder’s rate of return is not fixed as there is no stated
coupon rate or dividend.
The costs will vary for two sources of equity:
Retained earnings (No flotation costs)
Note retained earnings are not a free source of capital. There is
an opportunity cost.
rs=cost of the retained earning
New issue (incurs flotation costs)
re=cost of new common stock
77. Cost estimation techniques
Three Ways to Determine the Cost of Common Equity, rs
The Dividend Growth Model: rs = (D1/P0) + g
The Capital Asset Pricing Model: rs = rf + β(rM – rf )
Bond-Yield-Plus-Risk-Premium:
rs = Bond yield + risk premium= rd + RP
78. The Dividend Growth Model
Investors’ required rate of return (For Retained Earnings):
D1 = Dividend expected one year hence
P0 = Current price of common stock
g = growth rate
The Dividend Growth Model
Investors’ required rate of return (For new issues)
D1 = Dividends expected one year hence
NP = Net proceeds per share
= Stock price – flotation cost per share
F=the percentage flotation cost required to sell the new stock
g = growth rate
79. The Dividend Growth Model
Example: A company expects dividends this year to be $1.10,
based upon the fact that $1 were paid last year. The firm
expects dividends to grow 10% next year and into the
foreseeable future. Stock is trading at $35 a share.
Cost of retained earnings:
Cost of new stock (with a $3 floatation cost per share):
80. The Capital Asset Pricing Model
CAPM: rs = rf + β(rM – rf )
rf = Risk Free rate
rm =market risk return
rm – rf = Market Risk Premium
Capital Asset Pricing Model
Example: If beta is 1.25, risk-free rate is 1.5% and expected
return on market is 10%
– rf)
= .015 + 1.25(.10 – .015)
= 12.125%
81. Capital Asset Pricing Model Variable estimates
CAPM is easy to apply. Also, the estimates for model variables
are generally available from public sources.
Risk Free Rate: Wide range of US government securities on
which to base risk-free rate
Beta: Estimates of beta are available from a wide range of
services, or can be estimated using regression analysis of
historical data.
Market risk premium: It can be estimated by looking at history
of stock returns and premium earned over risk-free rate.
82. Bond-Yield-Plus-Risk-Premium Approach
rd = 10% and RP = 4%.
This RP(risk premium) is not the same as the CAPM RPM.
This method produces a ballpark estimate of rs, and can serve as
a useful check.
rs = rd + RP
rs = 10.0% + 4.0% = 14.0%
15
What factors influence a company’s composite WACC?
Market conditions.
The firm’s capital structure and dividend policy.
The firm’s investment policy. Firms with riskier projects
generally have a higher WACC.
83. 16
Should the company use the composite WACC as the hurdle rate
for each of its projects?
NO! The composite WACC reflects the risk of an average
project undertaken by the firm. Therefore, the WACC only
represents the “hurdle rate” for a typical project with average
risk.
Different projects have different risks. The project’s WACC
should be adjusted to reflect the project’s risk.