session 5 capital budgeting

8/3/2019 Session 5 Capital Budgeting

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CAPITAL BUDGETING

Capital Budgeting refers to the methods that managers use to determine which projectsshould be selected and which projects should be rejected.

Imagine a manager has been presented with the following projects. The first is for a newdrink called Sugar Soda and the second is for a drink called Lime Soda. Let’s call these projects Project S and Project L.

Both drinks will cost $1000 to create and market, Sugar Soda is expected to have highinitial sales followed by a decline as parents find out what the drink does to their children(they will bounce off the walls). Lime Soda on the other hand is an acquired taste andsales are expected to increase as consumers begin to acquire a taste for the product. After year 5 the formula for the drinks will be obsolete and the drinks will no longer bemarketed or sold.

The cash flows for these two projects are shown below:Project S Cash Flows

-1500

-1000

-500

0

500

1000

1 2 3 4 5

Time

$

Project L Cash Flows

-1200-1000-800-600-400-200

0200400600800

1 2 3 4 5

Time

$

When considering two projects a manager must know whether the projects are mutually

exclusive projects or independent projects.

• Mutually exclusive projects – when accepting one implies rejected the other.For example if the company only has the capacity to manufacture one new soda.

• Independent projects – when the company can accept either or both projects based only on the project’s expected cash flows. For example if the firm has thecapacity to invest in both beverages.

The following six methods are used to evaluate projects:

1. Net present value (NPV)2. Internal Rate of Return (IRR)3. Modified Internal Rate of Return (MIRR)4. Profitability Index (PI)5. Payback Period6. Discounted Payback

Capital Budgeting 1



1. Net Present Value is also known as the discounted cash flow technique. NPV is theamount the shareholder’s wealth would increase if the firm selected the project – if thisnumber is positive then the firm should select the project.1 Using the following formulawe can find the NPV of the two projects. (Assume a cost of capital (r) of 5%).

( )0 1

N t

t t

CF NPV r =

=+

∑

( ) ( ) ( ) ( )1 2 3 4

500 400 300 1001000 $180.42

1 5% 1 5% 1 5% 1 5%S

NPV = − + + + + =+ + + +

( ) ( ) ( ) ( )1 2 3 4

100 300 400 6001000 $206.50

1 5% 1 5% 1 5% 1 5% L

NPV = − + + + + =+ + + +

Conclusion: Based on NPV, and if the projects are mutually exclusive (i.e. only one project can be selected) then the firm should go with Project L (the Lime Soda).

2. Internal Rate of Return (IRR) the IRR is the discount rate that makes the net presentvalue of the project equal to zero.2 A project’s IRR should be compared to thecompany’s cost of capital or “hurdle rate.” The hurdle rate is the rate that the projectmust exceed to create positive shareholder wealth effects. (Assume the hurdle rate (r) is5%).

( )0

01

N t

t t

CF NPV

IRR=

= =+

∑

( ) ( ) ( ) ( )1 2 3 4

500 400 300 1001000 $0

1 1 1 1

14.5%

S

S

NPV IRR IRR IRR IRR

IRR

= − + + + + =+ + + +

=

( ) ( ) ( ) ( )1 2 3 4

100 300 400 6001000 $0

1 1 1 1

11.8%

L

L

NPV IRR IRR IRR IRR

IRR

= − + + + + =+ + + +

=

Conclusion: Based on IRR, and if the projects are mutually exclusive (i.e. only one project can be selected) then the firm should go with Project S (the Sugar Soda).

Question: Why do the NPV and IRR methods offer different decisions in this example?

• Answer: Because NPV rankings depend on the cost of capital and the timing of the cash flows impacts their present values. Project S has higher short-term cash

1 Key Assumption: All cash flows are reinvested at the company’s cost of capital.2 Key Assumption: All cash flows are reinvested at the project’s IRR.

Capital Budgeting 2



flows while Project L has higher long-term cash flows. Note: Long-term cashflows are much more sensitive to interest rates.

The tables below shows NPVs for the two projects at various interest rates. Notice that at5% Project L offers a higher NPV while at 10% Project S offers a higher NPV.

NPV Sensitivity Analysis

(200)

(100)

0

100

200

300

400

500

0% 5% 10% 15%

Cost of Capital (r)

N e t P r e s e n t V a l u e

Project S Project L

NPV Sensitivity Analysis

(200)

(100)

0

100

200

300

400

500

0% 5% 10% 15%

Cost of Capital (r)

N e t P r e s e n t V a l u e

Project S Project L

Question: At what rate would we be indifferent between these two projects?

• Answer: At the crossover rate. The crossover rate is the rate below which, thetwo methods offer different accept / reject solutions. To calculate the crossover rate for two projects subtract the cash flows at each time and then solve for therate at which the NPV equals zero.

( )( )

( )

( )

( )

( )

( )

( )

( )

( ) ( ) ( ) ( )

1 2 3 4

1 2 3 4

500 100 400 300 300 400 100 6001000 1000 $0

1 1 1 1

400 100 100 5000

1 1 1 1

7.17%

c c c c

c c c c

c

NPV r r r r

r r r r

r

− − − −= − − − + + + + =

+ + + +

− −= + + + +

+ + + +

=

This is calculated easily by using the cash flow register in your financial calculator.

For the TI BAII PlusEnter: CF (CF0) = 0; ↓ (C01) = 400; ENTER ↓ (F01) = 1; ENTER ↓ (C02) = 100;ENTER ↓ (F02) = 1; ENTER ↓ (C03) = -100; ENTER ↓ (F03) = 1; ENTER ↓ (C04) =-500; ENTER ; IRR ; CPT

Answer: 7.1673%

Capital Budgeting 3



3. Modified Internal Rate of Return (MIRR) – the modified IRR assumes that cashflows are reinvested at the company’s cost of capital.3 The cash flows are first broughtforward to their future values at the company’s cost of capital. Next the “terminal value”is calculated by summing all of the future value cash flows. Finally the terminal value is brought to the present vale of the initial investment at the MIRR rate. (Assume a cost of

capital of 5%).

( )

( )

( )

( )

1

0

0

1

1 1

1

N N

N t t

t N t

N

Cash Inflow r Cash Outflow

r MIRR

Terminal value PV of costs =

MIRR

PV of terminal value

−

=

=

+

=+ +

+

=

∑∑

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )( )

( )

( )

( )

4 1 3 1 2 1 1 1

4

4

4

1/4

500 1 5% 400 1 5% 300 1 5% 100 1 5%$10001

$1, 434.81$1000

1

$1, 434.811 1.4348

$1000

1 1.4348 1.0945

9.45%

S

S

s

s

S

=MIRR

=MIRR

MIRR

MIRR

MIRR

− − − −

+ + + + + + ++

+

+ = =

+ = =

=

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

( )

( )

( )

( )

4 1 3 1 2 1 1 1

4

4

4

1/4

100 1 5% 300 1 5% 400 1 5% 600 1 5%$1000

1

$1, 466.51$1000

1

$1, 466.511 1.4665

$1000

1 1.4665 1.1005

10.05%

L

L

L

L

L

=MIRR

=MIRR

MIRR

MIRRMIRR

− − − −+ + + + + + +

+

+

+ = =

+ = =

=

Conclusion: Based on MIRR, and if the projects are mutually exclusive (i.e. only one project can be selected) then the firm should go with Project L (the Lime Soda). Note: Ata 10% cost of capital Project S would be superior based on the MIRR calculation.

3 IRR assumes that cash flows are invested at the IRR rate.

Capital Budgeting 4



4. Profitability Index (PI) – The profitability index is the present value of the project’scash flows divided by the cost. (Assume a 5% cost of capital) PI tells us how much profit we can earn for each dollar invested.

( )0

0

1

N t

t t

CF

r PV of future cash flows PI

Initial cost CF

= += =∑

( ) ( ) ( ) ( )1 2 3 4

500 400 300 100

1 5% 1 5% 1 5% 1 5%

1000

$1180.421.18

$1000

S PI

+ + ++ + + +

=

= =

( ) ( ) ( ) ( )1 2 3 4

100 300 400 600

1 5% 1 5% 1 5% 1 5%

1000

$1206.501.21

1000

L PI

+ + ++ + + +

=

= =

Conclusion: Based on PI, and if the projects are mutually exclusive (i.e. only one projectcan be selected) then the firm should go with Project L (the Lime Soda). According tothe Profitability Index calculation at a 5% cost of capital Project L will yield $1.21 for every dollar invested in the project. Note: At a 10% cost of capital Project S would besuperior based on the PI calculation.

5. Payback Period – The payback period is the expected number of years required torecover the original investment.

The payback period method has three main flaws: 1) dollars received in different yearsare all given the same weight 2) cash flows beyond the payback year are not considered3) payback period analysis does not provide an indication of how much shareholder wealth should increase (like NPV) and 4) payback period analysis does not indicate howmuch the project will yield over the cost of capital (like IRR).

Payback Number of years prior to full recovery

Unrecovered cost at start of year

Cash flow during full recovery year

=

+

$1002 2.33

$300S Payback years= + =

Capital Budgeting 5



$2003 3.33

$600 L Payback years= + =

Project S Cash Flows

Year 0 = -$1000

Year 1 = 500Year 2 = 400Year 3 = 300Year 4 = 100

Cumulative CFs

-$1000

-500-100200300


Year 0 = -$1000

Year 1 = 100Year 2 = 300Year 3 = 400Year 4 = 600

Cumulative CFs

-$1000

-900-600-200400

Conclusion: Based on the payback method, and if the projects are mutually exclusivethen the firm should go with Project S (the Sugar Soda).

6. Discounted Payback – This method is similar to the payback period method exceptthe cash flows are discounted by the project’s cost of capital. The discounted payback period is the number of years required to recover the investment from the discounted net

cash flows. (Assume a cost of capital of 5%)

*

*

Discounted Payback Number of years prior to ful l recovery*

Unrecovered cost at start of year*

Cash flow during full recovery year

considers discounted cash flows

=

+

Project S Cash Flows

Year 0 = -$1000Year 1 = 500Year 2 = 400Year 3 = 300Year 4 = 100

Discounted CFs

-1000/(1.05)0 = -$1000.00500/(1.05)1 = 476.19400/(1.05)2 = 362.81300/(1.05)3 = 259.15100/(1.05)4 = 82.27

Cumulative CFs

-$1000.00-523.81-161.00

98.15180.42

$161.002 2.62

$259.15S Payback years= + =


Year 0 = -$1000Year 1 = 100Year 2 = 300

Year 3 = 400Year 4 = 600

Discounted CFs

-1000/(1.05)0 = -$1000.00100/(1.05)1 = 95.83300/(1.05)2 = 272.11

400/(1.05)3

= 345.54600/(1.05)4 = 493.62

Cumulative CFs

-$1000.00-904.76-632.65

-287.12206.50

$2873 3.58

$493 L Payback years= + =

Conclusion: Based on the discounted payback method, and if the projects are mutuallyexclusive then the firm should go with Project S (the Sugar Soda).

Capital Budgeting 6

session 5 capital budgeting

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