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10-1
CHAPTER 10The Basics of Capital Budgeting
Problem solving
Lidija Dedi
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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
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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 %
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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
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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
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10-6
Payback period for project Y
years.
.
CF
I
t
400010
00040
periodpayback
CF equalfor periodpayback
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10-7
b) Discounted payback period
p pP
t
P
t
tkttt IICF
k)(CFI
1 10 1
1
costs Investment 0I
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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
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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
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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
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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
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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
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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
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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
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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
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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
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10-17
Net Present Value for project Y
Project Y – equal Cash Flows
0I IVCFNPV Tkt
5533
000403553400010
.NPV
., x .NPV
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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
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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
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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
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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
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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
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10-23- The project’s WACC is 10 percent- What is the project’s payback period and discounted payback
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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?
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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
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10-26
What is the internal rate of return for each machine?
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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?
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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
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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?
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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
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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)?
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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
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10-33
The two projects have the same risk. At what cost of capital would the two
projects have the same net present value?
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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:
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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?