10-1

CHAPTER 10The Basics of Capital Budgeting

Problem solving

Lidija Dedi

10-2Problem 1:

Projects X i Y have following cash flows

Year Project X Project Y

0 (40.000) (40.000)

1 6.000 10.000

2 6.000 10.000

3 8.000 10.000

4 10.000 10.000

5 10.000 10.000

6 20.000 10.000

10-3

Calculate for projects X and Y:

Payback periodDiscounted payback period Net present valueInternal rate of return

The firm’s cost of capital is 10 %

10-4

a) Payback period for project X

Godina Projekt X

0 (40.000)

1 6.000

2 6.000

3 8.000

4 10.000

5 10.000

6 20.000

10-5

Year Project X Cumulative cash flows

1 6.000 6.000

2 6.000 12.000

3 8.000 20.000

4 10.000 30.000

5 10.000 40.000

6 20.000

Payback period = 5 years

a) Payback period for project X

10-6

Payback period for project Y

years.

.

CF

I

t

400010

00040

periodpayback

CF equalfor periodpayback

10-7

b) Discounted payback period

p pP

t

P

t

tkttt IICF

k)(CFI

1 10 1

1

costs Investment 0I

10-8

Discounted payback period for X

Year Project X

0 (40.000)

1 6.000

2 6.000

3 8.000

4 10.000

5 10.000

6 20.000

10-9

Year Project X PVIF(10%)

0 (40.000) 1,0000

1 6.000 0,9091

2 6.000 0,8264

3 8.000 0,7513

4 10.000 0,6830

5 10.000 0,6209

6 20.000 0,5645

Discounted payback period for X

10-10

Year Project X

PVIF (10%) Discounted cash flows

0 (40.000) 1,0000 (40.000)

1 6.000 0,9091 5.454,60

2 6.000 0,8264 4.958,40

3 8.000 0,7513 6.010,40

4 10.000 0,6830 6.830,00

5 10.000 0,6209 6.209,00

6 20.000 0,5645 11.290,00

Discounted payback period for X

10-11

Year Discounted Cash Flows

Cumulative discounted CF

0 (40.000)

1 5.454,60 5.454,60

2 4.958,40 10.413,00

3 6.010,40 16.423,40

4 6.830,00 23.253,40

5 6.209,00 29.462,40

6 11.290,00 40.000-29.462,40 =10.537,60

10.537,60/11.290 =0,93

Discounted payback period = 5,93 years

Discounted payback period for X

10-12Discounted payback period for project Y

Year Project Y

0 (40.000)

1 10.000

2 10.000

3 10.000

4 10.000

5 10.000

6 10.000

10-13

Year Project Y PVIF (10%)

0 (40.000) 1,0000

1 10.000 0,9091

2 10.000 0,8264

3 10.000 0,7513

4 10.000 0,6830

5 10.000 0,6209

6 10.000 0,5645

Discounted payback period for project Y

10-14Discounted payback period for project Y

Year Project Y

PVIF (10%) Discounted CF

0 (40.000) 1,0000 (40.000)

1 10.000 0,9091 9.090,10

2 10.000 0,8264 8.264,00

3 10.000 0,7513 7.513,00

4 10.000 0,6830 6.830,00

5 10.000 0,6209 6.209,00

6 10.000 0,5645 5.645,00

10-15

Year Discounted CF

Cumulative discounted CF

0 (40.000)1 9.090,10 9.090,10

2 8.264,00 17.354,10

3 7.513,00 24.867,10

4 6.830,00 31.697,10

5 6.209,00 37.906,10

6 5.645,00 2.093,90/5.645,00 = 0,37

Discounted payback period = 5,37 years

Discounted payback period for project Y

10-16c) Net Present Value for project X

Year Project X

PVIF (10%) Discounted CF

0 (40.000) 1,0000 (40.000)1 6.000 0,9091 5.454,602 6.000 0,8264 4.958,403 8.000 0,7513 6.010,404 10.000 0,6830 6.830,005 10.000 0,6209 6.209,006 20.000 0,5645 11.290,00 CF 40.752,40

IC (40.000)

NET PRESENT VALUE = 752,40

10-17

Net Present Value for project Y

Project Y – equal Cash Flows

0I IVCFNPV Tkt

5533

000403553400010

.NPV

., x .NPV

10-18c) Iternal Rate of Return X

Year Project X

PVIF (10%) Discounted CF

0 (40.000) 1,0000 (40.000,00)1 6.000 0,9091 5.454,602 6.000 0,8264 4.958,403 8.000 0,7513 6.010,404 10.000 0,6830 6.830,005 10.000 0,6209 6.209,006 20.000 0,5645 11.290,00 CF 40.752,40

IC (40.000)

NET PRESENT VALUE = 752,40

10-19

Year Project XCF

PVIF (10%) Factor Amount

PVIF (11%) Factor

Amount

1 6.000 0,9091 5.454,60 0,9009 5.405,40

2 6.000 0,8264 4.958,40 0,8116 4.869,60

3 8.000 0,7513 6.010,40 0,7312 5.849,60

4 10.000 0,6830 6.830,00 0,6587 6.587,00

5 10.000 0,6209 6.209,00 0,5935 5.935,00

6 20.000 0,5645 11.290,00 0,5346 10.692,00

NT 40.752,40

39.338,60

IT (40.000) (40.000)

ČISTA SADAŠNJA VRIJEDNOST 752,40

- 661,40

c) Iternal Rate of Return X

10-20Interpolation

11

10

2

1

y

IRRy

y

40,661

0

40,752

2

1

- x

x

x

%,,IRR

) ( y

) ( - -

- + y=

531053010

40,75280,413.1

110

40,752040,75240,661

101110

)x(xxx

yyyy 1

12

121

10-21Internal Rate of Return for project Y

Equal Cash Flows

9975313

4

1114412

400010

00040

22

11

, xy

x = IRR y

, xy

.

.VI I VtIV T

RT

R

INTERPOLATION

%,IRR =

, , + y =

),(, - ,

- + y =

9812

%9812978012

1114441114499753

121312

10-22

Problem 2: ABC company is considering a project

with the following expected cash flows:

Year

Project Cash Flow

0 - 700

1 200

2 370

3 225

4 700

10-23- The project’s WACC is 10 percent- What is the project’s payback period and discounted payback

10-24

Problem 3: You are considering the purchase of an

investment that would pay you $5.000 per year for Years 1-5, $3.000 per year for Years 6-8, and $2.000 per year for Years 9 and 10

If you require a 14 percent rate of return, and the cash flows occur at the end of each year, then how much should you be willing to pay for this investment?

10-25

Problem 4: ABC Inc. requires a new machine. Two

companies have submitted bids, and you have been assigned the task of choosing one of the machines. Cash flow analysis indicates the following:

Year Machine A (CF)

Machine B (CF)

0 - 2.000 - 2.000

1 0 832

2 0 832

3 0 832

4 3.877 832

10-26

What is the internal rate of return for each machine?

10-27

Problem 5: The firm’s project has a cost of $275.000

and is expected to provide after-tax annual cash flows of $73.306 for eight years.

The firm’s management is uncomfortable with the IRR reinvestment assumption and prefers the modified IRR approach.

You have calculated a cost of capital for the firm of 12 percent.

What is the project’s MIRR?

10-28

Problem 6:

A company is analyzing two mutually exclusive projects, S and L, whose cash flows are shown below:

1.000 - 1.100

0 2 1

350

3

50 S L 0 - 1.100 300 1.500

Years

10-29

The company cost of capital is 12 percent

What is the regular IRR of the better project, that is, the project which the company should choose if it wants to maximize its stock price?

10-30

Problem 7: ABC corporation is considering a project

with the following cash flows:

Year Project Cash Flow

(000)

0 ?

1 1.000

2 1.500

3 2.000

4 2.500

10-31

The project has a simple payback period of exactly two years.

The project’s cost of capital is 12% What is the project’s modified

internal rate of return (MIRR)?

10-32

Problem 8:

Alpha Hotels is considering two mutually exclusive projects, Project A and project B.

The cash flows from the projects are summarized below:

year 0 1 2 3 4

Project A

- 200.000

50.000 50.000 80.000 100.000

Project B

- 100.000

25.000 25.000 50.000 50.000

10-33

The two projects have the same risk. At what cost of capital would the two

projects have the same net present value?

10-34

Problem 9:

ABC corporation estimates that its cost of capital is 11 percent

The company is considering two mutually exclusive projects whose after-tax cash flows are as follows:

10-35

Year Project SCash flow

Project LCash Flow

0 - 3.000 - 9.000

1 2.500 - 1.000

2 1.500 5.000

3 1.500 5.000

4 - 500 5.000

What is the modified internal rate of return of the project with highest NPV?