FINA 4125
Prof Longobardi
Techniques for Valuation – First Review – Solutions
Instructions: Do not round off any intermediate calculations. Final dollar answers should be rounded to two
decimal places. Final interest rate answers should be rounded to 8 decimal places if expressed as a decimal or 6
decimal places if expressed as a percent. Assume the required rate of return is i =12%. Show all your work.
1.
Consider the following two investment projects:
Cash flows of project A:
0
1
2
3
-150 100
50
5
Cash flows of project B:
0
1
2
3
4
5
-150
40
40
a)
90
40
40
Using a cutoff period of 2 years, find the best investment using the payback criterion
and the discounted payback period rule.
PBA = 2 years; PBB = 2 + (150 – 130)/40 = 2.5 years. Project A looks better since
payback is within the cutoff period.
A:
Year
1
2
3
CF
$100
$50
$5
PV(CF)
$100/1.12 = $89.29
$50/1.122 = $39.86
$5/1.123 = $3.56
Cumulative
$89.29
$89.29 + $39.86 = $129.15
$129.15 + $3.56 = $132.71
Project A never pays back by the discounted payback period rule.
B:
Year
1
2
3
4
CF
$90
$40
$40
$40
PV(CF)
$90/1.12 = $80.36
$40/1.122 = $31.89
$40/1.123 = $28.47
$40/1.124 = $25.42
Cumulative
$80.36
$31.89 + $80.36 = $112.25
$112.25 + $28.47 = $140.72
$140.72 + $25.42 = $166.14
DPBPRB = 3 + (150 – 140.72)/25.42 = 3 + 9.28/25.42 = 3.37 years.
b)
Find the best investment using the NPV criterion.
NPVA=-$17.30; NPVB=$38.33. Project B is better since NPV > 0; it should accepted.
c)
Why is NPV better?
NPV considers all cash flows; payback does not.
NPV considers the time value of money; payback does not.
NPV has no arbitrary cut-off point; payback does not.
1
FINA 4125
Prof Longobardi
Techniques for Valuation – First Review – Solutions
2.
Consider the following two mutually exclusive investment projects:
Cash flows of project A:
0
1
2
3
-300
150
150
150
Cash flows of project B:
0
1
2
3
-1650
a)
750
750
750
4
5
150
150
4
5
750
750
Analyze each project individually using the profitability index. Which one of the
mutually exclusive investments appears best?
540.7164
= 1.802388; appears bettter.
300
2,703.58215
PI B =
= 1.638536
1,650
PI A =
b)
Now, look at the incremental flows using profitability index. Is it worth taking
project B instead of project A?
Cash flows of project B-A:
0
1
2
3
-1350
c)
600
4
5
600
600
600
600
PI B - A =
2,162.8657
= 1.6021. Yes, since PI B - A > 1
1,350
Repeat all of the analysis in (a) and (b) except now use NPV.
NPVA = $240.74; NPVB = $1,053.58; NPVB- A = $812.86
Project B is the better project because it has the higher NPV.
d)
Which is the better investment? Explain.
B is the better investment. NPVB is the higher of the two and PI B-A says that the
additional value in B is worthwhile since PI B-A > 1; i.e., Project B adds the most
worth to the firm.
2
FINA 4125
Prof Longobardi
Techniques for Valuation – First Review – Solutions
3.
Consider the following two investment projects:
Cash flows of project A:
0
1
-15
30
Cash flows of project B:
0
1
2
-150
150
150
a)
Analyze the projects individually using IRR. Which one looks better using only
IRR?
IRRA=100%; IRRB=61.80%. Project A looks better.
b)
Use IRR to analyze the incremental investment of taking project B instead of project
A. What is your conclusion?
IRRB-A=58.84%. The extra investment in B is worthwhile since IRRB-A> the hurdle rate of
12%. Therefore, B is better than A.
c)
Repeat all of the analysis in (a) and (b) except now use NPV.
NPVA = $11.79; NPVB = $103.51; NPVB-A = $91.72; NPVB is the better project.
d)
Which is the better investment? Explain.
B is better; NPVB > NPVA > 0. The incremental IRR B-A concludes that the investment in B (over
A) is worthwhile; i.e., B adds more worth to the firm.
3
FINA 4125
Prof Longobardi
Techniques for Valuation – First Review – Solutions
4.
Consider the following two projects:
Cash flows of project A:
0
1
2
3
150
150
150
150
4
5
150 -975
Cash flows of project B:
0
1
2
3
151
150
150
150
a)
4
5
150 -1100
Find the IRR’s of the two projects. Based on IRR, which initially looks like the
better project? Which is actually better? Explain.
IRRA=8.8769%; IRRB=12.9921%. B initially looks better since IRRB > the hurdle rate of
12%. A is actually better because these are “financing” types of projects, not investment
projects. Hence, the IRR criterion must be reversed; i.e., IRRA < the hurdle rate of 12%;
therefore, it’s better.
b)
Find the NPV’s of the two projects. Which one is better?
NPVA=$52.36; NPVB=-$17.57. Accept A (better project) and reject B (NPVB < 0).
c)
Do the incremental IRR analysis of taking project B instead of project A. Does
this match your NPV result? Explain.
Cash flows of project B-A:
0
1
1
2
3
4
5
0
0
0
0
-125
IRRB-A=162.6527804%; NPVB-A=-$69.93. IRRB-A says extra investment in B is NOT
worthwhile since the IRR > the hurdle rate of 12% (remember this is a financing project).
Therefore, prefer A as the NPV indicates.
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FINA 4125
Prof Longobardi
Techniques for Valuation – First Review – Solutions
5.
Consider the following investment project:
Project cash flows:
0
1
2
-100
250
-300
a)
Use your calculator’s NPV function to find the NPV of this project for 0 £ r £ 300%.
Use 10% increments for r and calculate 31 NPV’s. Then use a graph with NPV on
the vertical axis and r on the horizontal axis and plot the 31 points you determined.
NPV
100%
200%
300%
r
- $50
- $100
- $150
b)
What did you find about the project’s IRR and NPV? Explain.
There is no IRR and NPV is always negative.
5
FINA 4125
Prof Longobardi
Techniques for Valuation – First Review – Solutions
6.
Consider the following investment project:
Project cash flows:
0
1
2
-252.86
605
-360
a)
What are the IRR’s of this project? Hint try NPV @ 11% and NPV @ 28.2622%.
IRR = 11% and 28.3% (approximately).
b)
Compare the IRR’s to the hurdle (discount) rate. Does the IRR rule imply this is a
good investment?
Yes, since 12% is between 11% and 28.3% as seen in (c) below.
c)
Use a graph (like that in part (a) of question 7) to graph NPV, @ 5, 10, 15, 20, 25,
and 30%. Given your discount rate, should this project be accepted? Explain.
The project should be should be accepted as long as the hurdle rate is between 11% and 28.3%,
which it is.
NPV
10%
20%
30%
r
- $8
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FINA 4125
Prof Longobardi
Techniques for Valuation – First Review – Solutions
7.
Hardchoice Corp. is a firm considering prospective capital budgeting projects. Selected
data on the projects follow:
Project
A
B-A
C
D
Year 0
-400
+
-200
-400
Year 1
100
100
140
Year 2
110
100
130
Year 3
120
100
120
Year 4
130
100
110
Year 5
140
100
100
a) Consider only projects A and B by examining the incremental project cash flows B-A.
They are mutually exclusive opportunities. If the IRRB-A = 12% and the discount rate is
15% then what is your decision?
B over A is analyzed as a financing project. So, where IRRB-A=12% and RRR=15%
IRRB-A<RRR means invest in B.
12%<15%
then we should invest in B.
Accept project B; reject project A since IRRB-A<15% and B over A is evaluated as a
financing project.
b) Ignoring the information in question (a), assume instead that projects A and C are
independent, Hardchoice is subject to capital rationing (i.e., it may not be able to afford
both projects), and the relevant discount rate is 10%.
i)
What is the IRR of Project A? Project C?
IRRA: 14.2975%
0 = −$400 +
$100
$110
$120
$130
$140
+
+
+
+
2
3
4
1+ IRRA (1+ RRA ) (1+ IRRA ) (1+ IRRA ) (1+ IRRA )5
IRRC: 41.0415%
0 = −$200 +
ii)
$100
$100
+
1+ IRRC 1+ IRR
C
(
2
+
$100
3
+
$100
4
+
$100
) (1+ IRR ) (1+ IRR ) (1+ IRR )
C
C
5
C
How would you rank Project A compared to Project C? (1 mark)
Both investment projects – so I would rank the one with the higher IRR (i.e.,
project C) as better – no issues of timing or scale.
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FINA 4125
Prof Longobardi
Techniques for Valuation – First Review – Solutions
c) Consider the following statements and circle the Roman numeral corresponding to the
one that is true.
I
The NPV of project D will be much more sensitive to changes in the discount rate
than will the NPV of project A.
II
If projects C and D are mutually exclusive, incremental analysis indicates that one
should reject project C and accept project D.
III
It is possible for projects A and D to have the same NPV.
IV
All of the above are true.
V
None of the above is true.
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