In: Finance
Golda is considering a project which requires an amount of ?$3000.00 and another amount of ?$1000.00 ????? 1 ????. After two years’ time, when the project ends, she expects an inflow of ?$4500.00. what is the internal rate of return (???) of this project? Is the above Investment profitable? Assume that Golda can lend and borrow at the same fixed rate of 7.13% per annum.
Computation of IRR using trial and error method:
Computation of IRR using discount rate of 6 %.
Year | Cash Flow © | Computation of PV Factor | PV Factor @ 6 % (F) | PV (C x F) |
0 | -3000 | 1/(1+0.06)^0 | 1 | -3000 |
1 | -1000 | 1/(1+0.06)^1 | 0.94339622642 | -943.3962264 |
2 | 4500 | 1/(1+0.06)^2 | 0.88999644001 | 4004.9839801 |
NPV1 | 61.5877536 |
As NPV is positive, let’s compute NPV at discount rate of 7 %.
Year |
Cash Flow (C) |
Computation of PV Factor |
PV Factor @ 7 % (F) |
PV (C x F) |
|
0 |
-N$3,000 |
1/ (1+0.07) ^0 |
1 |
-N$3,000 |
|
1 |
-1,000 |
1/ (1+0.07) ^1 |
0.93457943925 |
-934.5794393 |
|
2 |
4,500 |
1/ (1+0.07) ^2 |
0.87343872827 |
3,930.4742772 |
|
NPV2 |
-4.1051621 |
IRR = R1 + [NPV1 x (R2 – R1)/ (NPV1 – NPV2)]
= 6 % + [N$61.5877537 x (7 % – 6 %)/ (N$61.5877537 –(-N$4.1051621))]
= 6 % + [N$61.5877537 x 1 %/ (N$61.5877537 + N$4.1051621)]
= 6 % + [N$61.5877537 x 0.01/ (N$65.6929157)]
= 6 % + (N$0.615877537 / N$65.6929157)
= 6 % + 0.009375098
= 6 % + 0.94 % = 6.94 %
Internal rate of the project is 6.94 %
As the IRR of the project, 6.94 % is less than lending and borrowing rate of Golda, the project is not profitable.