You have been offered a unique investment opportunity. If you invest $ 9,100 today, you will receive $ 455 one year from now, $ 1365 two years from now, and 9100 in ten years. a. What is the NPV of the opportunity if the cost of capital is 6.1 % per year? Should you take the opportunity? b. What is the NPV of the opportunity if the cost of capital is 2.1 % per year? Should you take it now?
a) NPV = -$2424.90
Reject the project since NPV is negative.
Year | Project Cash Flows (i) | DF@ 6.1% | DF@ 6.1% (ii) | PV of Project ( (i) * (ii) ) |
0 | -9100 | 1 | 1 | (9,100.00) |
1 | 455 | 1/((1+6.1%)^1) | 0.943 | 428.84 |
2 | 1365 | 1/((1+6.1%)^2) | 0.888 | 1,212.56 |
3 | 0 | 1/((1+6.1%)^3) | 0.837 | - |
4 | 0 | 1/((1+6.1%)^4) | 0.789 | - |
5 | 0 | 1/((1+6.1%)^5) | 0.744 | - |
6 | 0 | 1/((1+6.1%)^6) | 0.701 | - |
7 | 0 | 1/((1+6.1%)^7) | 0.661 | - |
8 | 0 | 1/((1+6.1%)^8) | 0.623 | - |
9 | 0 | 1/((1+6.1%)^9) | 0.587 | - |
10 | 9100 | 1/((1+6.1%)^10) | 0.553 | 5,033.70 |
NPV | (2,424.90) |
b) NPV = $ 47.44
Accept the project since NPV is positive
Year | Project Cash Flows (i) | DF@ 2.1% | DF@ 2.1% (ii) | PV of Project ( (i) * (ii) ) |
0 | -9100 | 1 | 1 | (9,100.00) |
1 | 455 | 1/((1+2.1%)^1) | 0.979 | 445.64 |
2 | 1365 | 1/((1+2.1%)^2) | 0.959 | 1,309.43 |
3 | 0 | 1/((1+2.1%)^3) | 0.940 | - |
4 | 0 | 1/((1+2.1%)^4) | 0.920 | - |
5 | 0 | 1/((1+2.1%)^5) | 0.901 | - |
6 | 0 | 1/((1+2.1%)^6) | 0.883 | - |
7 | 0 | 1/((1+2.1%)^7) | 0.865 | - |
8 | 0 | 1/((1+2.1%)^8) | 0.847 | - |
9 | 0 | 1/((1+2.1%)^9) | 0.829 | - |
10 | 9100 | 1/((1+2.1%)^10) | 0.812 | 7,392.37 |
NPV | 47.44 |
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