capital budgeting template

Example Cash Flows for Projects Y and Z: NPV, PI, IRR, and MIRR

CF/Time t=0 t=1 t=2 t=3 t=4

Project Y (1,200,000) 420,000 480,000 320,000 280,000

Project Z (1,800,000) 450,000 540,000 400,000 710,000

k 12.60%

Net Present Value (NPV)

NPV Solution Detail

Time Cash Flows PV Cash Flows Cash Flows PV Cash Flows

1 420,000 373,001.78 450,000 399,644.76 2 480,000 378,585.92 540,000 425,909.16 3 320,000 224,147.97 400,000 280,184.96 4 280,000 174,182.48 710,000 441,677.00 5 380,000 209,938.28 900,000 497,222.25

PV Inflows 1,359,856.43 2,044,638.13 PV Outflows (1,200,000.00) (1,800,000.00)

NPV 159,856.43 244,638.13

Profitablity Index (PI)

Project Y Project Z

1

/ 1 t N

t

tt

NPV CF k Initial Investment

1

/ 1 / t N

t

tt

PI CF k Initial Investment

Capital Budgeting Methods/Functions: Excel has three traditional capital budgeting functions available as well as two of these functions that are date specific. This worksheet illustrates the use of the NPV, the IRR, and MIRR functions. In addition, using the NPV function to determine a PI (Profitability Index) is all illustrated. Some solution detail is provided below in addition to the Excel function solutions.

The date specific functions are presented in the XNPV and XIRR Example worksheet.

Caution: When using the NPV function, Excel treats the first cash flow as occurring at time period t = 1, not t = 0. In contrast, with all of the other capital budgeting functions; the first cash flow is assumed to occur in period t = 0.

A26

Bob Johnston: Project Cost of Capital.

C35

Bob Johnston: At the project cost of capital. 12.60% in this example.

E35


C36

Bob Johnston: 373,001.78 is the PV of 420,000 to be received in one year at a cost of capital of 12.60%.


Project Y (1,200,000) 420,000 480,000 320,000 280,000

Project Z (1,800,000) 450,000 540,000 400,000 710,000

PI Solution Detail

Profitability

Index (PI)

PV Inflows 1,359,856.43 2,044,638.13 PV Outflows 1,200,000.00 1,800,000.00

PI 1.133 1.136

Internal Rate of Return (IRR)


Project Y (1,200,000) 420,000 480,000 320,000 280,000

Project Z (1,800,000) 450,000 540,000 400,000 710,000

IRR Solution Detail

Project Y Project Z


1 420,000 355,234.10 450,000 383,332.42 2 480,000 343,377.60 540,000 391,849.98 3 320,000 193,618.15 400,000 247,257.29 4 280,000 143,291.18 710,000 373,861.29 5 380,000 164,478.98 900,000 403,699.02


NPV 0.00 (0.00)

Project Y Project Z

IRR : 18.23% IRR: 17.39%

1

/ 1 0t N

t

tt

IRR CF IRR Initial Investment

1

/ 1 / t N

t

tt


C85

Bob Johnston: The actual rate is 18.2318924%.

E85


C86

Bob Johnston: The PV have been determined using the IRR as the interest rate.

E86


Modified Internal Rate of Return (MIRR)


Project Y (1,200,000) 420,000 480,000 320,000 280,000

Project Z (1,800,000) 450,000 540,000 400,000 710,000

Terminal Value and MIRR Solution Detail

Project Y CF # Years FVt = 1 420,000 4 675,154.01t = 2 480,000 3 685,261.62t = 3 320,000 2 405,720.32t = 4 280,000 1 315,280.00t = 5 380,000 0 380,000.00

t = 0 (1,200,000) Sum 2,461,415.95 (t = 5)MIRR 15.45%

Project Z CF # Years FVt = 1 450,000 4 723,379.30t = 2 540,000 3 770,919.32t = 3 400,000 2 507,150.40t = 4 710,000 1 799,460.00t = 5 900,000 0 900,000.00

t = 0 (1,800,000) Sum 3,700,909.02 (t = 5)MIRR 15.51%

1

1 / 1 0t N

t N

tt

MIRR CF k MIRR Initial Investment

Bob Johnston:Terminal Value.

Bob Johnston:This is the interest rate that will make the PV of terminal value equal to the PV of the outflow. The "Rate" function in Excel has been used to determine this interest rate.


Bob Johnston:This is the interest rate that will make the PV of the terminal value equal to the PV of the outflow.

E119

Bob Johnston: Terminal Value.

B120

Bob Johnston: This is the interest rate that will make the PV of terminal value equal to the PV of the outflow. The "Rate" function in Excel has been used to determine this interest rate.

E132


B133

Bob Johnston: This is the interest rate that will make the PV of the terminal value equal to the PV of the outflow.

Additional Example Applications for NPV, PI, IRR and MIRR

t=5 CF/Time t=0

380,000 Project M (2,600,000)

900,000 Project N (3,400,000)

k 14.80%

Excel NPV Function Solutions Excel NPV Function Solutions

k 12.60% k Project Y Project Z

NPV NPV




Recommendations:

Accept both Project Y and Project Z as their NPV's are positive.

M26


G34


N34


G36

Bob Johnston: The NPV function in Excel treats the first cash flow as occuring at the end of the first period (t = 1), not in time period t = 0.

N36

Bob Johnston: The NPV function in Excel treats the first cash flow as occuring at the end of the first period, not in time period t = 0.

CF/Time t=0

Project M (2,600,000)

t=5

Project N (3,400,000) 380,000

k 14.80% 900,000

Excel PI Function Solutions Excel PI Function Solutions


PI PI

CF/Time t=0

t=5 Project M (2,600,000)

380,000 Project N (3,400,000)

900,000 k 14.80%

Excel IRR Function Solutions Excel IRR Function Solutions


IRR IRR

Recommendations:

Accept both Project Y and Project Z as their PI's are greater than one.

Recommendations:

Accept both Project Y and Project Z as their IRR's the exceed cost of capital for the projects.

M55


I58

Bob Johnston: There is not a PI function in Excel, however, the NPV function may be used to derive a PI solution.

G60


N60


N62


M81


G85


N85


G87

Bob Johnston: With this function the cash flows need to be in time series order within the worksheet.

CF/Time t=0

Project M (2,600,000)

t=5 Project N (3,400,000)

380,000 k 14.80%

900,000

Excel MIRR Function Solution Excel MIRR Function Solution

Project Y k k 12.60%MIRR MIRR

Excel MIRR Function Solution

Project Z k 12.60%MIRR

1

1 / 1 0t N

t N

tt


Recommendations:

Accept both Project Y and Project Z as their MIRR's exceed the cost of capital for the projects.



M107


H115


H127



t=1 t=2 t=3 t=4 t=5 t = 6

585,000 744,000 645,000 880,000 755,000 1,065,000

995,000 745,000 1,220,000 1,830,000

Excel NPV Function Solutions

14.80%Project M Project N

t=1 t=2 t=3 t=4 t=5 t = 6

585,000 744,000 645,000 880,000 755,000 1,065,000

995,000 745,000 1,220,000 1,830,000

Excel PI Function Solutions


t=1 t=2 t=3 t=4 t=5 t = 6

585,000 744,000 645,000 880,000 755,000 1,065,000

995,000 745,000 1,220,000 1,830,000

Excel IRR Function Solutions


t=1 t=2 t=3 t=4 t=5 t = 6

585,000 744,000 645,000 880,000 755,000 1,065,000

995,000 745,000 1,220,000 1,830,000



Example Cash Flows for Projects Y and Z: NPV, PI, IRR, and MIRR


Project Y (1,200,000) 420,000 480,000 320,000 280,000

Project Z (1,800,000) 450,000 540,000 400,000 710,000

k 12.60%

Net Present Value (NPV)

NPV Solution Detail


1 420,000 373,001.78 450,000 399,644.76 2 480,000 378,585.92 540,000 425,909.16 3 320,000 224,147.97 400,000 280,184.96 4 280,000 174,182.48 710,000 441,677.00 5 380,000 209,938.28 900,000 497,222.25


NPV 159,856.43 244,638.13

Project Y Project Z

1

/ 1 t N

t

tt

NPV CF k Initial Investment




A26


C35


E35


C36

Bob Johnston: 373,001.78 is the PV of 420,000 to be received in one year at a cost of capital of 12.60%.

Profitablity Index (PI)


Project Y (1,200,000) 420,000 480,000 320,000 280,000

Project Z (1,800,000) 450,000 540,000 400,000 710,000

PI Solution Detail

Profitability

Index (PI)

PV Inflows 1,359,856.43 2,044,638.13 PV Outflows 1,200,000.00 1,800,000.00

PI 1.133 1.136

Internal Rate of Return (IRR)


Project Y (1,200,000) 420,000 480,000 320,000 280,000

Project Z (1,800,000) 450,000 540,000 400,000 710,000

IRR Solution Detail

Project Y Project Z


1 420,000 355,234.10 450,000 383,332.42

Project Y Project Z

IRR : 18.23% IRR: 17.39%

1

/ 1 0t N

t

tt

IRR CF IRR Initial Investment

1

/ 1 / t N

t

tt


C85


E85


C86


E86


2 480,000 343,377.60 540,000 391,849.98 3 320,000 193,618.15 400,000 247,257.29 4 280,000 143,291.18 710,000 373,861.29 5 380,000 164,478.98 900,000 403,699.02


NPV 0.00 (0.00)

Modified Internal Rate of Return (MIRR)


Project Y (1,200,000) 420,000 480,000 320,000 280,000

Project Z (1,800,000) 450,000 540,000 400,000 710,000

Terminal Value and MIRR Solution Detail

Project Y CF # Years FVt = 1 420,000 4 675,154.01t = 2 480,000 3 685,261.62t = 3 320,000 2 405,720.32t = 4 280,000 1 315,280.00t = 5 380,000 0 380,000.00

t = 0 (1,200,000) Sum 2,461,415.95 (t = 5)MIRR 15.45%

Project Z CF # Years FVt = 1 450,000 4 723,379.30t = 2 540,000 3 770,919.32t = 3 400,000 2 507,150.40t = 4 710,000 1 799,460.00

1

1 / 1 0t N

t N

tt



Bob Johnston:This is the interest rate that will make the PV of terminal value equal to the PV of the outflow. The "Rate" function in Excel has been used to determine this interest rate.



E119


B120

Bob Johnston: This is the interest rate that will make the PV of terminal value equal to the PV of the outflow. The "Rate" function in Excel has been used to determine this interest rate.

t = 5 900,000 0 900,000.00t = 0 (1,800,000) Sum 3,700,909.02 (t = 5)

MIRR 15.51%



E132


B133

Bob Johnston: This is the interest rate that will make the PV of the terminal value equal to the PV of the outflow.


t=5 CF/Time t=0

380,000 Project M (2,600,000)

900,000 Project N (3,400,000)

k 14.80%

Excel NPV Function Solutions Excel NPV Function Solutions


NPV 159,856.43 244,638.13 NPV




Recommendations:

Accept both Project Y and Project Z as their NPV's are positive.

M26


G34


N34


G36

Bob Johnston: The NPV function in Excel treats the first cash flow as occuring at the end of the first period (t = 1), not in time period t = 0.

N36


CF/Time t=0

Project M (2,600,000)

t=5

Project N (3,400,000) 380,000

k 14.80% 900,000

Excel PI Function Solutions Excel PI Function Solutions


PI 1.133 1.136 PI

CF/Time t=0

t=5 Project M (2,600,000)

380,000 Project N (3,400,000)

900,000 k 14.80%

Excel IRR Function Solutions Excel IRR Function Solutions


IRR 18.23% 17.39% IRR

Recommendations:

Accept both Project Y and Project Z as their PI's are greater than one.

M55


I58

Bob Johnston: There is not a PI function in Excel, however, the NPV function may be used to derive a PI solution.

G60


N60


N62


M81


G85


N85


G87

Bob Johnston: With this function the cash flows need to be in time series order within the worksheet.

CF/Time t=0

Project M (2,600,000)

t=5 Project N (3,400,000)

380,000 k 14.80%

900,000

Excel MIRR Function Solution Excel MIRR Function Solution

Project Y k k 12.60%MIRR 15.45% MIRR


Project Z k 12.60%MIRR 15.51%

Recommendations:

Accept both Project Y and Project Z as their IRR's the exceed cost of capital for the projects.

1

1 / 1 0t N

t N

tt




M107


H115


H127


Recommendations:

Accept both Project Y and Project Z as their MIRR's exceed the cost of capital for the projects.



t=1 t=2 t=3 t=4 t=5 t = 6

585,000 744,000 645,000 880,000 755,000 1,065,000

995,000 745,000 1,220,000 1,830,000

Excel NPV Function Solutions


251,003.63 (107,995.21)

t=1 t=2 t=3 t=4 t=5 t = 6

585,000 744,000 645,000 880,000 755,000 1,065,000

995,000 745,000 1,220,000 1,830,000

Excel PI Function Solutions


1.097 0.97

t=1 t=2 t=3 t=4 t=5 t = 6

585,000 744,000 645,000 880,000 755,000 1,065,000

995,000 745,000 1,220,000 1,830,000

Excel IRR Function Solutions


18.01% 13.40%

t=1 t=2 t=3 t=4 t=5 t = 6

585,000 744,000 645,000 880,000 755,000 1,065,000

995,000 745,000 1,220,000 1,830,000



16.58% 13.88%

EXCEL Spreadsheet Illustration of Capital Investment Examples

General NPV and IRR Functions in Excel CF/Time t=0 t=1 t=2 t=3 t=4 t=5

Project Y (1,200,000) 420,000 480,000 320,000 280,000 380,000

Project Z (1,800,000) 450,000 540,000 400,000 710,000 900,000

k 12.60%

NPV IRR

Project Y 159,856 18.23%

Project Z 244,638 17.39%

Date Specific NPV and IRR Functions in Excel CF Dates 1-Jan-02 1-Jan-03 1-Jan-04 1-Jan-05 1-Jan-06 1-Jan-07

Project Y (1,200,000) 420,000 480,000 320,000 280,000 380,000

Project Z (1,800,000) 450,000 540,000 400,000 710,000 900,000

k 12.60%

Capital Budgeting Methods/Functions: XNPV and XIRR The basic NPV and IRR functions in Excel treat the cash flows as if they all occur in one period (one year) intervals. In fact, with most projects cash flows occur at intervals different from once a year.

The XNPV and XIRR functions determine NPV and IRR respectively by the exact dates when cash flows are expected to occur. When using this functions it is necessary to specific for each cash flow a date when the cash flow occurred.

Bob Johnston:The NPV function in Excel treats the first cash flow in a row or column as occurring in time period t =1, not t = 0.

Bob Johnston:The IRR function in Excel treats the first cash flow in a column or row as occurring in time period t = 0.

Bob Johnston:The XNPV function in Excel treats the first cash flow in a row or column as occurring on the date defined for the specific cash flow cell.

A20

Robert Johnston: Project Cost of Capital.

B25

Bob Johnston: The NPV function in Excel treats the first cash flow in a row or column as occurring in time period t =1, not t = 0.

C25

Bob Johnston: The IRR function in Excel treats the first cash flow in a column or row as occurring in time period t = 0.

A38



XNPV XIRR Project Y

Project Z


B43

Bob Johnston: The XNPV function in Excel treats the first cash flow in a row or column as occurring on the date defined for the specific cash flow cell.


CF/Time t=0 t=1 t=2

Project M (2,600,000) 585,000 744,000

Project N (3,400,000) 995,000 745,000

k 14.80%

NPV IRR

Project Y 251,004 18.01%

Project Z (107,995) 13.40% Additional Example Applications for XNPV and XIRR

CF/Time 15-Feb-2003 15-Feb-2004 15-Feb-2005

Project M (2,600,000) 585,000 744,000

Project N (3,400,000) 995,000 745,000

k 14.80%





K20


L25


M25


K38



XNPV XIRR Project M

Project N


t=3 t=4 t=5 t=6

645,000 880,000 755,000 1,065,000

1,220,000 1,830,000

15-Feb-2006 15-Feb-2007 15-Feb-2008 15-Feb-2009

645,000 880,000 755,000 1,065,000

1,220,000 1,830,000


General NPV and IRR Functions in Excel CF/Time t=0 t=1 t=2 t=3 t=4 t=5

Project Y (1,200,000) 420,000 480,000 320,000 280,000 380,000

Project Z (1,800,000) 450,000 540,000 400,000 710,000 900,000

k 12.60%

NPV IRR

Project Y 159,856 18.23%

Project Z 244,638 17.39%

Date Specific NPV and IRR Functions in Excel CF Dates 1-Jan-02 1-Jan-03 1-Jan-04 1-Jan-05 1-Jan-06 1-Jan-07

Project Y (1,200,000) 420,000 480,000 320,000 280,000 380,000

Project Z (1,800,000) 450,000 540,000 400,000 710,000 900,000






A20


B25


C25


XNPV XIRR Project Y 159,659 18.22%

Project Z 244,242 17.38%


B41

Bob Johnston: The XNPV function in Excel treats the first cash flow in a row or column as occurring on the date defined for the specific cash flow cell.

CF/Time t=0 t=1 t=2

Project M (2,600,000) 585,000 744,000

Project N (3,400,000) 995,000 745,000

k 14.80%

NPV IRR

Project Y 251,004 18.01%

Project Z (107,995) 13.40% Additional Example Applications for XNPV and XIRR

CF/Time 15-Feb-2003 15-Feb-2004 15-Feb-2005

Project M (2,600,000) 585,000 744,000

Project N (3,400,000) 995,000 745,000

k 14.80%





K20


L25


M25


K38


XNPV XIRR Project M 249,943 18.00%

Project N (108,912) 13.39%

t=3 t=4 t=5 t=6

645,000 880,000 755,000 1,065,000

1,220,000 1,830,000

15-Feb-2006 15-Feb-2007 15-Feb-2008 15-Feb-2009

645,000 880,000 755,000 1,065,000

1,220,000 1,830,000



Cost ofYear Cash Flow Capital NPV

0 (145.00) 0% ($10.00)1 100.00 3% ($1.88)2 100.00 3.91% $0.00 3 100.00 6% $3.49 4 100.00 9% $6.74 5 (265.00) 12% $8.37

15% $8.75 18% $8.17

IRR # 1 3.91% 21% $6.88 IRR # 2 30.28% 24% $5.03

27% $2.79 30% $0.25

30.28% $0.00 33% ($2.49)36% ($5.38)39% ($8.35)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

-15

-10

-5

0

5

10

Two IRRs

Cost of Capital

Net

Pre

sent

Val

ue

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

-15

-10

-5

0

5

10

Two IRRs

Cost of Capital

Net

Pre

sent

Val

ue

CF/Time t=0 t=1 t=2 t=3 t=4 t=5

Project M (2,600,000) 585,000 744,000 645,000 880,000 755,000

Project N (3,400,000) 995,000 745,000 1,220,000 1,830,000

k 14.80%

NPV PI IRR MIRR

Project Y 251,004 1.097 18.01% 16.58%

Project Z (107,995) 0.968 13.40% 13.88%

CF Dates 15-Jul-01 15-Jul-02 15-Jul-03 15-Jul-04 15-Jul-05 15-Jul-06

Project Y (2,600,000) 585,000 744,000 645,000 880,000 755,000

Project Z (3,400,000) 995,000 745,000 1,220,000 1,830,000

XNPV XIRR Project Y 250,332 18.01%

Project Z (108,698) 13.39%

A7


t = 6

1,065,000

15-Jul-07

1,065,000

capital budgeting template

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