Homework Sourse14 Toolkit Decision Rules PBAK IRR NPV Calculating NPV IR
14. (Toolkit – Decision Rules – PBAK, IRR, NPV) Calculating NPV & IRR: Your next project provides an annual cash flow of $15,400 for nine years and costs $67,000 today. Is this a good project at 8% required return? How about 20%?
Question 14 options:
Yes, Yes
Yes, No
No, Yes
No, No
| Yes, Yes | |
| Yes, No | |
| No, Yes | |
| No, No |
Solution
Correct option is > Yes, No
Reason: NPV is positive for 8% required rate of return and NPV is negative for 20% required rate of return.
NPV with 8% required return
Year
Cash flows = CF
Df = 1/(1+8%)^Year
Present Value = CF x Df
0
-67,000.00
1.000000
-67,000.00
1
15,400.00
0.925926
14,259.26
2
15,400.00
0.857339
13,203.02
3
15,400.00
0.793832
12,225.02
4
15,400.00
0.735030
11,319.46
5
15,400.00
0.680583
10,480.98
6
15,400.00
0.630170
9,704.61
7
15,400.00
0.583490
8,985.75
8
15,400.00
0.540269
8,320.14
9
15,400.00
0.500249
7,703.83
Total PV = NPV =
29,202.07
NPV is sum of present values cash flows
NPV =
29,202.07
IRR is rate at which NPV = 0 and do trial error to get it
IRR =
17.67%
NPV with 20% required return
Year
Cash flows = CF
Df = 1/(1+20)^Year
Present Value = CF x Df
0
-67,000.00
1.000000
-67,000.00
1
15,400.00
0.833333
12,833.33
2
15,400.00
0.694444
10,694.44
3
15,400.00
0.578704
8,912.04
4
15,400.00
0.482253
7,426.70
5
15,400.00
0.401878
6,188.91
6
15,400.00
0.334898
5,157.43
7
15,400.00
0.279082
4,297.86
8
15,400.00
0.232568
3,581.55
9
15,400.00
0.193807
2,984.62
Total PV = NPV =
-4,923.12
NPV is sum of present values cash flows
NPV =
-4,923.12
IRR is rate at which NPV = 0 and do trial error to get it
IRR =
17.67%
| Year | Cash flows = CF | Df = 1/(1+8%)^Year | Present Value = CF x Df |
| 0 | -67,000.00 | 1.000000 | -67,000.00 |
| 1 | 15,400.00 | 0.925926 | 14,259.26 |
| 2 | 15,400.00 | 0.857339 | 13,203.02 |
| 3 | 15,400.00 | 0.793832 | 12,225.02 |
| 4 | 15,400.00 | 0.735030 | 11,319.46 |
| 5 | 15,400.00 | 0.680583 | 10,480.98 |
| 6 | 15,400.00 | 0.630170 | 9,704.61 |
| 7 | 15,400.00 | 0.583490 | 8,985.75 |
| 8 | 15,400.00 | 0.540269 | 8,320.14 |
| 9 | 15,400.00 | 0.500249 | 7,703.83 |
| Total PV = NPV = | 29,202.07 |
