# Presentation: 079136

## Capital-Budgeting

- Techniques

- With a Financial Calculator

- Presentation

## Capital Budgeting Methods

*Number of years needed to recover your initial outlay.*

**Payback Period**

## Capital Budgeting Methods

*Number of years needed to recover your initial outlay.*

**Payback Period**

- P  R  O  J  E  C  T

- Time	A	B
- 0	(10,000.)	 (10,000.)
- 1	3,500	500
- 2	3,500	500
- 3	3,500	4,600
- 4	3,500	10,000

## Capital Budgeting Methods

*Number of years needed to recover your initial outlay.*

**Payback Period**

- 0                  1                    2                   3                   4

- 3,500

- 3,500

- 3,500

- 3,500

- (10,000)

## Capital Budgeting Methods

*Number of years needed to recover your initial outlay.*

**Payback Period**

- 0                  1                    2                   3                   4

- 3,500
- -6,500

- 3,500

- 3,500

- 3,500

- (10,000)

- Cumulative CF

## Capital Budgeting Methods

*Number of years needed to recover your initial outlay.*

**Payback Period**

- 0                  1                    2                   3                   4

- 3,500
- -6,500

- 3,500
- -3,000

- 3,500

- 3,500

- (10,000)

- Cumulative CF

## Capital Budgeting Methods

*Number of years needed to recover your initial outlay.*

**Payback Period**

- 0                  1                    2                   3                   4

- 3,500
- -6,500

- 3,500
- -3,000

- 3,500
- +500

- 3,500

- (10,000)

- Cumulative CF

## Capital Budgeting Methods

*Number of years needed to recover your initial outlay.*

**Payback Period**

- 0                  1                    2                   3                   4

- 3,500
- -6,500

- 3,500
- -3,000

- 3,500
- +500

- 3,500

- (10,000)

- Payback within 3 years

- Cumulative CF

## Capital Budgeting Methods

*Number of years needed to recover your initial outlay.*

**Payback Period**

## Capital Budgeting Methods

*Number of years needed to recover your initial outlay.*

**Payback Period**

- 0                  1                    2                   3                   4

- 500

- 500

- 4,600

- 10,000

- (10,000)

## Capital Budgeting Methods

*Number of years needed to recover your initial outlay.*

**Payback Period**

- 0                  1                    2                   3                   4

- 500
- -9,500

- 500

- 4,600

- 10,000

- (10,000)

- Cumulative CF

## Capital Budgeting Methods

*Number of years needed to recover your initial outlay.*

**Payback Period**

- 0                  1                    2                   3                   4

- 500
- -9,500

- 500
- -9,000

- 4,600

- 10,000

- (10,000)

- Cumulative CF

## Capital Budgeting Methods

*Number of years needed to recover your initial outlay.*

**Payback Period**

- 0                  1                    2                   3                   4

- 500
- -9,500

- 500
- -9,000

- 4,600
- -4,400

- 10,000

- (10,000)

- Cumulative CF

## Capital Budgeting Methods

*Number of years needed to recover your initial outlay.*

**Payback Period**

- 0                  1                    2                   3                   4

- 500
- -9,500

- 500
- -9,000

- 4,600
- -4,400

- 10,000
- +5,600

- (10,000)

- Cumulative CF

## Capital Budgeting Methods

*Number of years needed to recover your initial outlay.*

**Payback Period**

- 0                  1                    2                   3                   4

- 500
- -9,500

- 500
- -9,000

- 4,600
- -4,400

- 10,000
- +5,600

- (10,000)

- Payback within 4 years

- Cumulative CF

## Capital Budgeting Methods

*Number of years needed to recover your initial outlay.*

**Payback Period**

- 0                  1                    2                   3                   4

- 500
- -9,500

- 500
- -9,000

- 4,600
- -4,400

- 10,000
- +5,600

- (10,000)

- Payback within 4 years

- Cumulative CF

- Evaluation:
- Company sets maximum acceptable payback. If Max PB = 3 years, accept project A and reject project C

## Capital Budgeting Methods

*Present Value of all costs and benefits of a project.*

**Net Present Value**

## Capital Budgeting Methods

*Present Value of all costs and benefits of a project.*
*Concept is similar to Intrinsic (Fundamental) Value of an asset but subtracts cost of acquiring the project and any other negative cash flows.*

**Net Present Value**

-  NPV = PV of Inflows - PV of Outflows

## Capital Budgeting Methods

*Present Value of all costs and benefits of a project.*
*Concept is similar to Intrinsic Value of a security but subtracts of cost of project.*

**Net Present Value**

-  NPV = PV of Inflows - Initial Outlay

- NPV  =            +            +          +···+        – IO

- _  __CF_1_  _
- (1+ k )

- _  __CF_2_  _
- (1+ k )2

- _  __CF_3_  _
- (1+ k )3

- _  __CF_n_  _
- (1+ k )n

## Capital Budgeting Methods

**Net Present Value**

- 0                  1                    2                   3                   4

- 500

- 500

- 4,600

- 10,000

- (10,000)

- k=10%

## Capital Budgeting Methods

**Net Present Value**

- 0                  1                    2                   3                   4

- 500

- 500

- 4,600

- 10,000

- (10,000)

- 455

- k=10%

- _ __$500 _
-  (1.10)

## Capital Budgeting Methods

**Net Present Value**

- 0                  1                    2                   3                   4

- 500

- 500

- 4,600

- 10,000

- (10,000)

- 455

- 413

- k=10%

- _ __$500 _
-  (1.10) 2

## Capital Budgeting Methods

**Net Present Value**

- 0                  1                    2                   3                   4

- 500

- 500

- 4,600

- 10,000

- (10,000)

- 455

- 413

- 3,456

- k=10%

- _ __$4,600 _
-  (1.10) 3

## Capital Budgeting Methods

**Net Present Value**

- 0                  1                    2                   3                   4

- 500

- 500

- 4,600

- 10,000

- (10,000)

- 455

- _6,830_

- 413

- 3,456

- k=10%

- _ __$10,000 _
-  (1.10) 4

## Capital Budgeting Methods

**Net Present Value**

- 0                  1                    2                   3                   4

- 500

- 500

- 4,600

- 10,000

- (10,000)

- 455

- $11,154

- _6,830_

- 413

- 3,456

- k=10%

## Capital Budgeting Methods

**Net Present Value**

- 0                  1                    2                   3                   4

- 500

- 500

- 4,600

- 10,000

- (10,000)

- 455

- _6,830_

- 413

- 3,456

- k=10%

- PV Benefits > PV Costs

- $11,154 > $ 10,000

- $11,154

## Capital Budgeting Methods

**Net Present Value**

- 0                  1                    2                   3                   4

- 500

- 500

- 4,600

- 10,000

- (10,000)

- 455

- _6,830_

- 413

- 3,456

- k=10%

- PV Benefits > PV Costs

- $11,154 > $ 10,000

- NPV > $0

- $1,154 > $0

- $11,154

- $1,154 = NPV

## Financial Calculator

*Additional Keys used to enter Cash Flows and compute the Net Present Value (NPV)*

**HP10B Calculator**

**Capital Budgeting Solutions**

## Financial Calculator

*Additional Keys used to enter Cash Flows and compute the Net Present Value (NPV)*

**HP10B Calculator**

**Capital Budgeting Solutions**

- Used to add CF0, CF1,
- CF2, . . . CFN into memory

## Financial Calculator

*Additional Keys used to enter Cash Flows and compute the Net Present Value (NPV)*

**HP10B Calculator**

**Capital Budgeting Solutions**

## Financial Calculator

*Additional Keys used to enter Cash Flows and compute the Net Present Value (NPV)*

**HP10B Calculator**

**Capital Budgeting Solutions**

- Computes the NPV

## Capital Budgeting Methods

**Net Present Value**

- 0                  1                    2                   3                   4

- 500

- 500

- (10,000)

- k=10%

**CF****j**

**Nj**

**IRR/YR**

**NPV**

- 4,600

- 10,000

## Capital Budgeting Methods

**Net Present Value**

- 0                  1                    2                   3                   4

- 500

- 500

- (10,000)

- k=10%

**CF****j**

**Nj**

**IRR/YR**

**NPV**

- 4,600

- 10,000

## Capital Budgeting Methods

**Net Present Value**

- 0                  1                    2                   3                   4

- 500

- 500

- (10,000)

- k=10%

**CF****j**

**Nj**

**IRR/YR**

**NPV**

- 4,600

- 10,000

## Capital Budgeting Methods

**Net Present Value**

- 0                  1                    2                   3                   4

- 500

- 500

- (10,000)

- k=10%

**CF****j**

**Nj**

**IRR/YR**

**NPV**

- 4,600

- 10,000

## Capital Budgeting Methods

**Net Present Value**

- 0                  1                    2                   3                   4

- 500

- 500

- (10,000)

- k=10%

**CF****j**

**Nj**

**IRR/YR**

**NPV**

- 4,600

- 10,000

## Capital Budgeting Methods

**Net Present Value**

- 0                  1                    2                   3                   4

- 500

- 500

- (10,000)

- k=10%

**CF****j**

**Nj**

**IRR/YR**

**NPV**

- 4,600

- 10,000

## Capital Budgeting Methods

**Net Present Value**

- 0                  1                    2                   3                   4

- 500

- 500

- (10,000)

- k=10%

**1,153.95**

**N**

**I/YR**

**PV**

**PMT**

**FV**

**P/YR**

**CF****j**

**Nj**

**IRR/YR**

**NPV**

- 4,600

- 10,000

- Compute NPV

## Capital Budgeting Methods

**Net Present Value**

- 0                  1                    2                   3                   4

- 3,500

- (10,000)

- k=10%

- 3,500

- 3,500

- 3,500

## Capital Budgeting Methods

**Net Present Value**

- 0                  1                    2                   3                   4

- 3,500

- (10,000)

- k=10%

- 3,500

- 3,500

- 3,500

- NPV  =            +            +          +           – 10,000

- _ __3,500 _
- (1+ .1 )

- _ __3,500 _
- (1+ .1)2

- _ __3,500 _
- (1+ .1 )3

- _ __3,500 _
- (1+ .1 )4

## Capital Budgeting Methods

**Net Present Value**

- 0                  1                    2                   3                   4

- 3,500

- (10,000)

- k=10%

- 3,500

- 3,500

- 3,500

- NPV  =            +            +          +           – 10,000

- _ __3,500 _
- (1+ .1 )

- _ __3,500 _
- (1+ .1)2

- _ __3,500 _
- (1+ .1 )3

- _ __3,500 _
- (1+ .1 )4

- PV of 3,500 Annuity for 4 years at 10%

## Capital Budgeting Methods

**Net Present Value**

- 0                  1                    2                   3                   4

- 3,500

- (10,000)

- k=10%

- 3,500

- 3,500

- 3,500

- NPV  =            +            +          +           – 10,000

- _ __3,500 _
- (1+ .1 )

- _ __3,500 _
- (1+ .1)2

- _ __3,500 _
- (1+ .1 )3

- _ __3,500 _
- (1+ .1 )4

- = 3,500(                      ) - 10,000

- _        __1        _
- .10(1+.10)4

- _ __1 _
- .10

- =  11,095 – 10,000 = $1,095

## Financial Calculator

*Additional Keys used to enter Cash Flows and compute the Net Present Value (NPV)*

**HP10B Calculator**

**Capital Budgeting Solutions**

- Enters multiple equal
- Cash Flows

## Capital Budgeting Methods

**Net Present Value**

- 0                  1                    2                   3                   4

- (10,000)

- k=10%

**CF****j**

**Nj**

**IRR/YR**

**NPV**

- 3,500

- 3,500

- 3,500

- 3,500

- Enter Initial Outlay

## Capital Budgeting Methods

**Net Present Value**

- 0                  1                    2                   3                   4

- (10,000)

- k=10%

**CF****j**

**Nj**

**IRR/YR**

**NPV**

- 3,500

- 3,500

- 3,500

- 3,500

- Enter Cash Flow

## Capital Budgeting Methods

**Net Present Value**

- 0                  1                    2                   3                   4

- (10,000)

- k=10%

**4.00**

**N**

**I/YR**

**PV**

**PMT**

**FV**

**P/YR**

**CF****j**

**Nj**

**IRR/YR**

**NPV**

- 3,500

- 3,500

- 3,500

- 3,500

- Nj = 4

- Enter Multiple Cash Flows

## Capital Budgeting Methods

**Net Present Value**

- 0                  1                    2                   3                   4

- (10,000)

- k=10%

**4.00**

**N**

**I/YR**

**PV**

**PMT**

**FV**

**P/YR**

**CF****j**

**Nj**

**IRR/YR**

**NPV**

- 3,500

- 3,500

- 3,500

- 3,500

- Nj = 4

- 4

- Enter Multiple Cash Flows

## Capital Budgeting Methods

**Net Present Value**

- 0                  1                    2                   3                   4

- (10,000)

- k=10%

**CF****j**

**Nj**

**IRR/YR**

**NPV**

- 3,500

- 3,500

- 3,500

- 3,500

- Enter Required Rate

## Capital Budgeting Methods

**Net Present Value**

- 0                  1                    2                   3                   4

- (10,000)

- k=10%

- 3,500

- 3,500

- 3,500

- 3,500

- Compute NPV

## Net Present Value Profile

*Graphs the Net Present Value of the project with different required rates*

- Connect the Points

## Net Present Value Profile

- 10%

- 5%

- 0

- Cost of Capital

- N
- P
- V

- 6,000

- 3,000

- 20%

- 15%

*Graphs the Net Present Value of the project with different required rates*

-    NPV(0%)  =            +            +            +             – 10,000

- _   __500 _
- (1+ 0 )

- _  __500   _
- (1+ 0)2

- _ __4,600 _
- (1+ 0 )3

- _ __10,000 _
- (1+ 0)4

- = $5,600

## Net Present Value Profile

*Graphs the Net Present Value of the project with different required rates*

- Connect the Points

## Net Present Value Profile

*Graphs the Net Present Value of the project with different required rates*

## Net Present Value Profile

*Compare NPV of the two projects for different required rates*

- 10%

- 5%

- 0

- Cost of Capital

- N
- P
- V

- 6,000

- 3,000

- 20%

- 15%

- Project B

- Crossover point

- Project A

## Net Present Value Profile

*Compare NPV of the two projects for different required rates*

- 10%

- 5%

- 0

- Cost of Capital

- N
- P
- V

- 6,000

- 3,000

- 20%

- 15%

- Project B

- Crossover point

- Project A

- For any discount rate < crossover point  choose B

## Net Present Value Profile

*Compare NPV of the two projects for different required rates*

- 10%

- 5%

- 0

- Cost of Capital

- N
- P
- V

- 6,000

- 3,000

- 20%

- 15%

- Project B

- Crossover point

- For any discount rate > crossover point  choose A

- Project A

- For any discount rate < crossover point  choose B

## Capital Budgeting Methods

**Internal Rate of Return**

*Measures the rate of return on a project*

- Definition:
- The IRR is the discount rate in which NPV = 0

## Capital Budgeting Methods

**Internal Rate of Return**

*Measures the rate of return on a project*

- Definition:
- The IRR is the discount rate in which NPV = 0

- NPV = $0

## Capital Budgeting Methods

**Internal Rate of Return**

*Measures the rate of return on a project*

- Definition:
- The IRR is the discount rate in which NPV = 0

- 10%

- 5%

- 0

- Cost of Capital

- N
- P
- V

- 6,000

- 3,000

- 20%

- 15%

- Project B

- NPV = $0

- IRRA 15%

- IRRB 14%

## Capital Budgeting Methods

- 0                  1                    2                   3                   4

- (10,000)

- 500

- 500

- 4,600

- 10,000

**Internal Rate of Return**
**For Project B**

- Compute IRR

- Enter the Cash Flows into memory

## Capital Budgeting Methods

- 0                  1                    2                   3                   4

- (10,000)

- 3,500

- 3,500

- 3,500

- 3,500

- Enter the Cash Flows into memory

**Internal Rate of Return**
**For Project A**

- Compute IRR

## Capital Budgeting Methods

**Discounted Payback**
**For Project C**

## Capital Budgeting Methods

**Discounted Payback for Project C**

*Determines the point in time when investment is recovered taking into account the Time Value of Money*

- Discounted Payback:
- Determine T* where

## Capital Budgeting Methods

**Discounted Payback for Project C**

*We know that discounted payback occurs after regular payback*
*For Project C regular payback is 4 years*

- Try the following:
- CF0 = -13,000
- C01 =  3,500
- F01 = 4
- Compute NPV at 10%
-  [NPV] [10] [ENTER] [up arrow] [CPT]
- NPV = -1,905.47

## Capital Budgeting Methods

**Discounted Payback for Project C**

*We know that discounted payback occurs after regular payback*

- Try the following:
- CF0 = -13,000
- C01 =  3,500
- F01 = 5
- Compute NPV at 10%
-  [NPV] [10] [ENTER] [up arrow] [CPT]
- NPV = +267.75

## Capital Budgeting Methods

**Discounted Payback for Project C**

*Discounted Payback occurs slightly before year 5.*
*Conclude Discounted Payback is at Year 5.*
*Summary:*
- Similar to NPV calculation except that we increase the project size [time horizon] until NPV is equal to zero.

## Capital Budgeting Methods

**Modified Internal Rate of Return for Project D**

- Corrects for the reinvestment rate assumption built into the internal rate of return calculation
- Gets around the problem of multiple internal rates of return
- Requires a reinvestment rate [usually the cost of capital used in NPV analysis]

## Capital Budgeting Methods

**Modified Internal Rate of Return for Project D**

*All negative cash flows are converted to present Value*
*All positive cash flows are converted to Future Value at end of Project*

- The MIRR is the solution to the following:

## Capital Budgeting Methods

**Modified Internal Rate of Return for Project D**

*Enter the only the negative Cash Flows and compute NPV*

- CF0 = -13,000
- C01 = 0
- F01 = 2
- C02 = -3,000
- F02 = 3
- [NPV] [10] [ENTER] [UP ARROW] [CPT]
- NPV = -19,165.75

## Capital Budgeting Methods

**Modified Internal Rate of Return for Project D**

*Enter the only the positive Cash Flows and compute NFV   *
- NOTE: Cannot do in one step so use a trick:
- compute NPV and then convert this to Future Value

- CF0 = 0
- C01 = 5,000
- F01 = 2
- C02 = 0
- F02 = 3
- C03 = 9,000
- F03 = 4
- [NPV] [10] [ENTER] [UP ARROW] [CPT]
- NPV = 26,391.82

## Capital Budgeting Methods

**Modified Internal Rate of Return for Project D**

*Enter the only the positive Cash Flows and compute NFV   *
- NOTE: Cannot do in one step so use a trick:
- compute NPV and then convert this to Future Value

- NPV = 26,391.82
- Switch to Standard 5 parameter mode:
- PV= 26,391.82
- I=10
- PMT = 0
- N=9
- [CPT] [FV]
- FV = -62,230.53

## Capital Budgeting Methods

**Modified Internal Rate of Return for Project D**

*Now solve for the implied interest rate*

- NPV = -19,165.75
- NFV = -62,230.53
- PV = -19,165.75
- PMT = 0
- N = 9
- FV = +62,230.53
- [CPT] [I]
- I = 13.98
- so MIRR = 13.98%