Homework SourseCordia Corporation is planning a 15 year project with an ini
Cordia Corporation is planning a 15 year project with an initial investment of $2,500,000.
The project will have $400,000 cash inflows per year in years 1-5 ;
$200,000 cash inflows in years 6-10, and
$40,000 cash inflows in years 11-15.
a) Determine this project\'s intemal rate of return.
b) If Cordia\'s opportunity cost of capital is 8%, should they accept or reject this project?
c) Explain your reason for your decision in part (b).
Solution
a) Computation of IRR:
IRR is an interest rate where the net present value of inflows are outflows equals zero.
With the help of trial and error method we can find the IRR:
First let us find from 5% rate and then we can increase or decrease as per the requirement (here, our target is to get NPV= 0).
rate = 5%
rate = 6%
Year
Cash flows
discounting factor
PV
discounting factor
PV
0
(2,500,000)
1
(2,500,000)
1
(2,500,000)
1
400,000
0.952381
380,952
0.943396
377,358
2
400,000
0.907029
362,812
0.889996
355,999
3
400,000
0.863838
345,535
0.839619
335,848
4
400,000
0.822702
329,081
0.792094
316,837
5
400,000
0.783526
313,410
0.747258
298,903
6
200,000
0.746215
149,243
0.704961
140,992
7
200,000
0.710681
142,136
0.665057
133,011
8
200,000
0.676839
135,368
0.627412
125,482
9
200,000
0.644609
128,922
0.591898
118,380
10
200,000
0.613913
122,783
0.558395
111,679
11
40,000
0.584679
23,387
0.526788
21,072
12
40,000
0.556837
22,273
0.496969
19,879
13
40,000
0.530321
21,213
0.468839
18,754
14
40,000
0.505068
20,203
0.442301
17,692
15
40,000
0.481017
19,241
0.417265
16,691
NPV
16,559
(91,423)
IRR = 5% + [(16,559-0)/ (16,559-(-91,423))] = 5% + 0.15 = 5.15%
b) If Cordia\'s opportunity cost of capital is 8%, then NPV will be:
rate = 8%
Year
Cash flows
discounting factor
PV
0
(2,500,000)
1
(2,500,000)
1
400,000
0.925926
370,370.37
2
400,000
0.857339
342,935.53
3
400,000
0.793832
317,532.90
4
400,000
0.73503
294,011.94
5
400,000
0.680583
272,233.28
6
200,000
0.63017
126,033.93
7
200,000
0.58349
116,698.08
8
200,000
0.540269
108,053.78
9
200,000
0.500249
100,049.79
10
200,000
0.463193
92,638.70
11
40,000
0.428883
17,155.31
12
40,000
0.397114
15,884.55
13
40,000
0.367698
14,707.92
14
40,000
0.340461
13,618.44
15
40,000
0.315242
12,609.67
NPV
(285,465.82)
They should reject this project.
c) The NPV in part b is negative, thus, we should reject this project in part (b).
| rate = 5% | rate = 6% | ||||
| Year | Cash flows | discounting factor | PV | discounting factor | PV |
| 0 | (2,500,000) | 1 | (2,500,000) | 1 | (2,500,000) |
| 1 | 400,000 | 0.952381 | 380,952 | 0.943396 | 377,358 |
| 2 | 400,000 | 0.907029 | 362,812 | 0.889996 | 355,999 |
| 3 | 400,000 | 0.863838 | 345,535 | 0.839619 | 335,848 |
| 4 | 400,000 | 0.822702 | 329,081 | 0.792094 | 316,837 |
| 5 | 400,000 | 0.783526 | 313,410 | 0.747258 | 298,903 |
| 6 | 200,000 | 0.746215 | 149,243 | 0.704961 | 140,992 |
| 7 | 200,000 | 0.710681 | 142,136 | 0.665057 | 133,011 |
| 8 | 200,000 | 0.676839 | 135,368 | 0.627412 | 125,482 |
| 9 | 200,000 | 0.644609 | 128,922 | 0.591898 | 118,380 |
| 10 | 200,000 | 0.613913 | 122,783 | 0.558395 | 111,679 |
| 11 | 40,000 | 0.584679 | 23,387 | 0.526788 | 21,072 |
| 12 | 40,000 | 0.556837 | 22,273 | 0.496969 | 19,879 |
| 13 | 40,000 | 0.530321 | 21,213 | 0.468839 | 18,754 |
| 14 | 40,000 | 0.505068 | 20,203 | 0.442301 | 17,692 |
| 15 | 40,000 | 0.481017 | 19,241 | 0.417265 | 16,691 |
| NPV | 16,559 | (91,423) |
