Ybusfin Chap 12

7/27/2019 Ybusfin Chap 12

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Basics of Capital Budgeting


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Capital Budgeting

process of decision making with respect toinvestments made in fixed assets - that is, shoulda proposed project be accepted or rejected.

The following criteria are used for deciding whether toaccept or reject projects:

1. Net Present Value (NPV)2. Internal Rate of Return (IRR)3. Modified Internal Rate of Return (MIRR)4. Regular Payback5. Discounted Payback


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Payback Period

the length of time required for an investments net

revenues to cover its cost.

A. Even Returns

Example: A firms has an initial cash outlay of $100,000 and

has an even annual cash return of $25,000. What is itspayback period?

0 1 2 3 4 5 6

-$100,000 $25,000 $25,000 $25,000 $25,000 $25,000

$25,000

PPInvestments

Annual Cash Return=

$100,000

$25,000= 4 years=


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A. Uneven Returns

Example: A firms maximum desired payback period is 3yrs.,

and an investment proposal requires an initial cash outlay of$100,000 and yields the following set of annual cash flows,what is the payback period? should the project be accepted?

Year Free Cash Flow

1 $40,000

2 30,000

3 30,000

4 20,000

+ > 70,000

+ > 100,000

PP 3 Years=

if PP isthe maximum acceptable PP, REJECT the project.


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A. Uneven Returns

Example: A firms maximum desired payback period is 3yrs.,and an investment proposal requires an initial cash outlay of

$100,000 and yields the following set of annual cash flows,what is the payback period? Should the project beaccepted?

Year Free Cash Flow

1 $40,000

2 30,000

3 20,000

4 20,000

+ > 70,000

+ > 90,000

PP 3 + 0.5 = 3.5 Years=

+ > 10,000 / 20,000 = 0.5


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Problem 12 -4 : Payback

PP Investments

Annual Cash Return=

$52,125

$12,000=

4.34 years=


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Problem 12 -7Project A: Payback calculation:0 1 2 3 4 5

| | | | | |-6,000 2,000 2,000 2,000 2,000

2,000

Cumulative CF: -6,000 -4,000 -2,000 0 2,0004,000

Regular PaybackA= 3 years.

Payback calculation:0 1 2 3 4 5

| | | | | |-18,000 5,600 5,600 5,600 5,600

5,600

Cumulative CF: -18,000 -12,400 -6,800 -1,200 4,40010,000

Regular PaybackB = 3 + $1,200/$5,600 = 3.21 years.

+ + +

+ + +


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Discounted Payback Periodthe length of time required for an investmentscash flows, discounted at the investments cost of

capital to cover its cost.

YR

1

2

3

4

5

ACR

6,000

4,000

3,000

2,000

1,000

PViF

0.855

0.731

0.624

0.534

0.456

PF-ACR

5,130

2,924

1,872

1,068

456

Cumulative

5,130

8,054

9,926

X

X

X

X

X

=

=

=

=

=

Ex. Initial outlay = $10,000; interest = 17%

10,0009,926-74

74 / 1,068 = .07

DPP = 3.07 years

+

>

+

>

11,450


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Net Present Value (NPV)

equal to the present value of future net cashflows, discounted at the cost of capital.

NPVTotal PV of ACF 11,450

Investment 10,000

NPV 1,450

NPV >= 0 ;ACCEPT

NPV < 0 ; REJECT-


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Discounted Payback Period - even ACR (annuities)Ex. A company plans to invest in a project with an initialcash outlay of $10,000 with expected annual cashflow/return of $4,000 for 3 yrs. discounted at 15% perannum.

YR

1

2

3

ACR

4,000

4,000

4,000

PViF15%

0.870

0.756

0.658

X

X

X

PV ACR

3,480

3,024

2,632

=

=

=

Cumulative

3,480

6,504

9,136

REJECTinvestmentis not recovered

NPVTotal PV of ACF 9,136

Investment 10,000

NPV ( 864 )

NPV < 0 ; REJECT

-

4,000 X 2.283 = 9,132

Investment 10,000

NPV ( 868 )

-

PVIFA

NPV < 0 ; REJECT


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Net Present Value (NPV)

Ex. Initial outlay = $40,000; interest = 12%

YR

1

2

3

4

5

ACR

15,000

14,000

13,000

12,000

11,000

PViF

0.893

0.797

0.712

0.636

0.567

PF-ACR

13,395

11,158

9,256

7,632

6,237

X

X

X

X

X

=

=

=

=

=

47,678

Initial Outlay - 40,000

NPV 7,678

NPV >0 ; ACCEPT


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Internal Rate of Return

discount rate that forces a projects NPV to equalzero.

if IRR >= cost of capital ;ACCEPTif IRR < cost of capital ;REJECT

if Even Cash Returns

1.Compute for PP. (Investment / Annual Cash Flow)2.Locate the PP in the PViFA table consideringeconomic life of investment as n years.

3.Interpolate if necessary.


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Internal Rate of Return

if Uneven Cash Returns

1.Compute for tentative PP.(Investment / Total Annual Cash Flow/# of yrs.)

2 & 3. as even ACR.


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Ex. Compute for the IRR of an investment of $100,000with annual cash net income of 20,000. The projectseconomic life is 10 yrs. and cost of capital is 12%.

PPInvestments

Annual Cash Return=

$100,000

$20,000= 5 years=

STEP 1:

STEP 2:

Locate the PP= 5 in the PViFA table considering economic life of investment as10yrs.

Between 15% & 16%

15%

STEP 3:

16%

5.019

4.833

1% .186

5.0000.019 15% + (

0.019.186 X 0.01) = 0.15+

.0010215 =0.1510215

15.10%

0.167 16% - (0.019.186 X 0.01) = 0.16 -

.0089784

=0.151021515.10%

15.10% IRR > 12% cost of capital ;

ACCEPT


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Ex. Determine the IRR of a $7,000 project with free cashflow of 1,000 for 10 yrs. given a cost of capital is 5%.

PPInvestments

Annual Cash Return=

$7,000

$1,000= 7 years=

STEP 1:

Between 7% & 8%

7%

STEP 3:

8%

7.024

6.710

1% .314

7.0000.024 7% + (

0.024.314 X 0.01) = 0.07+

.0007643

= 7.08%

STEP 2:

0.290 8% -

(

0.290

.314X 0.01

)= 0.08 -

.009235

6= 7.08%

7.08% IRR > 5% cost of capital ; ACCEPT


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IRR: if Uneven Cash ReturnsEx. An investment of $60,000 is expected to earn thefollowing cash flows: yr1 - $20,000; yr2 - $25,000; yr3 -$30,000. The prevailing interest rate on capital is 10%.Find the IRR of the project.

tentativePP

Investments

Annual Cash Return=

$60,000

$75,000/ 3= 2.4=

STEP 1:

STEP 2:

Locate the PP= 2.4 in the PViFA table considering economic life of investment as3yrs.

Between 12% & 13 %

12%STEP 3:

13%

2.402

2.361

1% .041

2.400.002 12% + (

0.002. 041 X 0.01) = 0.12+

.0004878

= 12.05%

.039 13% - (.039. 041 X 0.01) = 0.13 -

.0095121

= 12.05%



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IRR: seatwork

An investment of $40,000 is expected to earn thefollowing cash flows: yr1 - $15,000; yr2 - $14,000; yr3 -

$13,000; yr4 - $12,000; yr5 - $11,000. The prevailinginterest rate on capital is 12%. Find the IRR of the project.

tentativePP

Investments

Annual Cash Return

=$40,000

$65,000/ 5= 3.077=solution:

Locate the PP= 3.077 in the PViFA table considering economic life of investmentas 5yrs.

Between 18% & 19 %

18%

19%

3.127

3.058

1% .069

3.0770.05 18% + (

0.05. 069 X 0.01) = 0.12+

.00724637 = 18.72%

.019 19% - (.019. 069 X 0.01) = 0.13 -.00275362= 18.72%



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Modified Internal Rate of Return (MIRR)

discount rate at which the present value of aprojects cost is equal t the present value of its

terminal value.Terminal Value (TV)

sum of the future values of the ACR/cash inflows,compounded at the firms cost of capital.

Steps:

1. Determine the present value of the projects free cashoutflows. ( Usually the investment is already in PV).

2.Determine the TV of the project - total FV of cashinflows/returns.

3.TV / Initial Outlay = answer, locate at the FVIF table;between ?where n= economic life.

4.Interpolate if necessary.


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Ex. UNEVEN ACRA project with an initial outlay of $6,000 with a 3 year life and a cost ofcapital of 10% has the following cash flows associated with it:

YR

1

2

3

ACR

2,000

3,000

4,000

FViF10%

1.210

1.100

same

X

X

FV

2,420

3,300

4,000

=

=

=

0 1 2 3

-$6,000 $2,000 $3,000 $4,000

TV 9,720

TV / IO9,720

6,000= 1.620= locate FViF, n = 3 yrs, between 17% and 18%.


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17%

Interpolate:

18%

1.602

1.643

1% .041

1.6200.018 17% + (

0.018.041 X 0.01) = 0.17 +

.00439024

= 17.44%

0.23 18% - (0.290.041 X 0.01) = 0.18 - .05609756 = 17.44%


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Ex. EVEN ACRInvestment : $12,000Required Rate of Return: 12%

ACR: P4,000/year

Economic life: 4years

YR

1

2

3

4

ACR

4,000

4,000

4,000

4,000

FViF12%1.405

1.254

1.120

X

X

X

X

FV

5,620

5,016

4,480

=

=

=

=

TV 19,116same 4,000

0 1 2 3 4

-$12,000 $4,000 $4,000 $4,000 $4,000

Solution:

PV/IO = $12,000

TV = $4,000 ( FViFA 4yrs, 12% )= $4,000 ( 4.779 )

TV = 19.116

TV / IO19,116

12,000= 1.593= locate FViF, n = 4 yrs, between 12% and 13%.


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12%

Interpolate:

13%

1.574

1.630

1% .056

1.5930.019 12% + (

0.019. 056 X 0.01) = 0.12 +

.00339285

= 12.34%

0.37 13% - (0.37. 056 X 0.01) = 0.13 - .00660714 = 12.34%

MIRR t k


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MIRR: seatworkAn investment of $50,000 has an annual cash return of1st year: $17,000; 2nd year: $22,000; 3rd year: $28,000.The company has a 15% cost of capital. What is theMIRR?

YR

1

2

3

ACR

17,000

22,000

28,000

FViF15%

1.322

1.150

same

X

X

FV

22,474

25,300

28,000

=

=

=

TV 75,774

TV / IO75,774

50,000= 1.515=

locate FViF, n = 3 yrs, between 14% and15%.

14%

Interpolate:

15%

1.482

1.521

1% .039

1.5150.033 14% + (0.033. 039 X 0.01) = 0.14 + .0084615 = 14.85%0.006 15% - (

0.006. 039 X 0.01) = 0.15 - .0015384 = 14.85%

REJECT


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Assignment: Chapter VII ( Credit Risk )

Describe the following:

1. Credit Risk

2. Character3. Capacity4. Capital5. Collateral

6. Condition7. Credit Information8. General Mercantile Agency9. Credit Bureaus

10. Bank Credit Department


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18%

Interpolate:

19%

3.127

3.058

1% .069

3.0770.05 18% +

(

0.05

. 069X 0.01

)= 0.18 +

.0072463

7

= 18.72%

0.19 19% - (0.19. 069 X 0.01) = 0.19 - .00275362 = 18.72%


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YR

1

2

3

4

ACR

100

300

400

700

FViF

1.405

1.254

1.120

same

FV

140.50

376.20

448

700

X

X

X

X

=

=

=

=

1,664.70

Project X - Initial Outlay: $1,000 ; @ 12%

YR

1

2

3

4

ACR

1,000

100

50

50

FViF

1.405

1.254

1.120

same

FV

1,405

125.4

56

50

X

X

X

X

=

=

=

=

1,636.40

Project Y - Initial Outlay: $1,000 ; @ 12%

TV / IO1,664.70

1,000= 1.6647=

13%

Project X Interpolate:

14%

1.630

1.689

1% .059

1.66470.0347 13% + (

0.0347. 059 X 0.01) = 0.13 +

.00322034

= 12.34%

0.0243 14% - (0.0243.059 X 0.01) = 0.14 - .00660714 = 12.34%

MIRR: seatwork


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MIRR: seatwork

What is the MIRR of an investment of $180,000 with anannual cash return of $38,000 for the next 10 years with acost of capital of 14%?

IO = 180,000

TV = 38,000 ( 19.337 )= 734,806

TV / IO734,806

180,000= 4.082=

locate FViF, n = 10 yrs, between 15% and 16%.

15%

Interpolate:

16%

4.046

4.411

1% .365

4.0820.036 15% + (

0.036. 365 X 0.01) = 0.15 + .0009863 = 15.10%

0.329 16% - ( 0.37. 365 X 0.01) = 0.16 - .0090136 = 15.10%

ACCEPT


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TV / IO1,636.40

1,000= 1.6364=

13%

Project Y Interpolate:

14%

1.630

1.689

1% .059

1.63640.0064 13% + (

0.0064. 059 X 0.01) = 0.13 +

.00108475

= 13.11%

0.0526 14% - (0.0526.059 X 0.01) = 0.14 - .00411864 = 13.11%

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Ybusfin Chap 12