Cash Flows (in thousands of USD) Year 0 1 2 3 4 5 6 7 Project 1 -100 10 20 0 0 1
ID: 2774228 • Letter: C
Question
Cash Flows (in thousands of USD)
Year
0
1
2
3
4
5
6
7
Project 1
-100
10
20
0
0
110
0
0
Project 2
-100
0
0
0
40
50
80
10
Project 3
-250
0
15
20
30
40
150
110
Project 4
-500
150
150
-100
50
100
150
200
Project 5
-400
100
100
-100
200
200
-80
130
In the above table, five projects were proposed from different departments of the firm trying to compete for the total $1,000,000 capital budget for next year. The CFO made it clear at the meeting that any project with zero or negative NPV should not be funded. Given it is a pharmaceutical firm, the CFO and the key managers are used to concepts of investing in the long-term projects and/or relatively risky projects, and/or projects with volatile cash flows over time. In addition, most of the members on the committee are cautiously optimistic about the future outlook of the economy. Around the time of the meetings, there were rumors that the Federal Reserve Bank is considering increasing the prime interest rates
1) What are the IRR for each project? Would you rely on IRR to make your capital budgeting decisions in this case? Why or why not?
Cash Flows (in thousands of USD)
Year
0
1
2
3
4
5
6
7
Project 1
-100
10
20
0
0
110
0
0
Project 2
-100
0
0
0
40
50
80
10
Project 3
-250
0
15
20
30
40
150
110
Project 4
-500
150
150
-100
50
100
150
200
Project 5
-400
100
100
-100
200
200
-80
130
Explanation / Answer
The cash flows of various projects and IRR of each project are as follows
Year
0
1
2
3
4
5
6
7
IRR
Project 1
-100
10
20
0
0
110
0
0
8.3368%
Project 2
-100
0
0
0
40
50
80
10
11.7795%
Project 3
-250
0
15
20
30
40
150
110
6.9777%
Project 4
-500
150
150
-100
50
100
150
200
8.2507%
Project 5
-400
100
100
-100
200
200
-80
130
8.5613%
Comparing IRR values of different projects is not an effective method of selecting a project. The IRR is a measure where NPV of the project is equal to zero. The IRR should be compared with the Weighted Average Cost of Capital of the firm to check whether IRR is higher or lower than the WACC. If WACC is higher than IRR then the project will end up with a negative value and will not be acceptable due to negative npv value. In addition there are rumours that Federal Reserve is expected to increase the prime rates. If this happens the WACC will go further up as the banks will adjust their lending rates based on Federal Reserve prime rates. Hence comparing projected based on NPV values derived using WACC may be a better measure.
Working
Let r be the discount rate which makes the net present value of the project equal to zero. Then IRR can be calculated by using the formula
-Initial invt + Cash Flow Year 1/1+r) + Cash Flow year 2/(1+r)^2 + .. + Cash Flow year n/(1+r)^n = 0
For Project 1, Substituting the above values
Year
0
1
2
3
4
5
6
7
NPV
Project 1
-100
10
20
0
0
110
0
0
Discount rate (%)
8
Discounted Cash Flow
-100
9.2593
17.15
0
0
74.9
0
0
1.27
Discount rate (%)
9
Discounted Cash Flow
-100
9.1743
16.83
0
0
71.5
0
0
-2.5
IRR = 0.08 + NPV(8%) * (0.08 -0.09)/(NPV(9%) – NPV(8%))
= 0.08 + ((1.27 * -0.01)/(-2.5-1.27)
= 0.08 + (-0.0127/-3.77)
= 0.08 + 0.0033687 = 0.0833687 or 8.3368%
For Project 2,Substituting the above values
Year
0
1
2
3
4
5
6
7
NPV
Project 1
-100
0
0
0
40
50
80
10
Discount rate (%)
11
Discounted Cash Flow
-100
0
0
0
26.3
29.7
42.8
4.82
3.61
Discount rate (%)
13
Discounted Cash Flow
-100
0
0
0
24.5
27.1
38.4
4.25
-5.653
IRR = 0.11 + [3.61 * (0.11-0.13)/(-5.653-3.61]
= 0.11 + [-0.0722/-9.263]
= 0.11 + 0.00779445 = 0.11779445 or 11.779445%
For Project 3,Substituting the above values
Year
0
1
2
3
4
5
6
7
NPV
Project 1
-250
0
15
20
30
40
150
110
Discount rate (%)
6
Discounted Cash Flow
-250
0
13.35
16.8
23.8
29.9
106
73.2
12.7
Discount rate (%)
8
Discounted Cash Flow
-250
0
12.86
15.9
22.1
27.2
94.5
64.2
-13.28
IRR = 0.06 + [12.7 * (0.06-0.08)/(-13.28-12.7)] = 0.06 + [-0.254/-25.98]
= 0.06 + 0.00977675 = 0.06977675 or 6.9777%
For Project 4,Substituting the above values
Year
0
1
2
3
4
5
6
7
NPV
Project 1
-500
150
150
-100
50
100
150
200
Discount rate (%)
7
Discounted Cash Flow
-500
140.19
131
-82
38.1
71.3
100
125
23.52
Discount rate (%)
9
Discounted Cash Flow
-500
137.61
126.3
-77
35.4
65
89.4
109
-14.09
IRR = 0.07 + [23.52 * (0.07-0.09)/(-14.09-23.52)] = 0.07 + [-0.4704/-37.61]
= 0.07 + 0.0125073 = 0.0825073 or 8.25073%
For Project 5,Substituting the above values
Year
0
1
2
3
4
5
6
7
NPV
Project 1
-400
100
100
-100
200
200
-80
130
Discount rate (%)
8
Discounted Cash Flow
-400
92.593
85.73
-79
147
136
-50
75.9
7.506
Discount rate (%)
10
Discounted Cash Flow
-400
90.909
82.64
-75
137
124
-45
66.7
-19.24
IRR = 0.08 + [(7.506*(0.08-0.10))/(-19.24-7.506)] =0.08 + [-0.15012/-26.746]
= 0.08 + 0.0056128 = 0.0856128 or 8.56128%
Year
0
1
2
3
4
5
6
7
IRR
Project 1
-100
10
20
0
0
110
0
0
8.3368%
Project 2
-100
0
0
0
40
50
80
10
11.7795%
Project 3
-250
0
15
20
30
40
150
110
6.9777%
Project 4
-500
150
150
-100
50
100
150
200
8.2507%
Project 5
-400
100
100
-100
200
200
-80
130
8.5613%
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