A company is considering an iron ore extraction project that requires an initial investment of $1,400,000 and will yield annual cash inflows of $613,228 for three years.The company's discount rate is 9%.Calculate IRR. Present value of ordinary annuity of $1:
$$\begin{array} { | r | r | r | r | r | r | r | r | }
\hline & 10 \% & 12 \% & 14 \% & 15 \% & 16 \% & 18 \% & 20 \% \
\hline 1 & 0.909 & 0.893 & 0.877 & 0.870 & 0.862 & 0.847 & 0.833 \
\hline 2 & 1.736 & 1.690 & 1.647 & 1.626 & 1.605 & 1.566 & 1.528 \
\hline 3 & 2.487 & 2.402 & 2.322 & 2.283 & 2.246 & 2.174 & 2.106 \
\hline 4 & 3.170 & 3.037 & 2.914 & 2.855 & 2.798 & 2.690 & 2.589 \
\hline
\end{array}$$

Question

A company is considering an iron ore extraction project that requires an initial investment of $1,400,000 and will yield annual cash inflows of $613,228 for three years.The company's discount rate is 9%.Calculate IRR. Present value of ordinary annuity of $1:
$$\begin{array} { | r | r | r | r | r | r | r | r | } 
\hline & 10 \% & 12 \% & 14 \% & 15 \% & 16 \% & 18 \% & 20 \% \
\hline 1 & 0.909 & 0.893 & 0.877 & 0.870 & 0.862 & 0.847 & 0.833 \
\hline 2 & 1.736 & 1.690 & 1.647 & 1.626 & 1.605 & 1.566 & 1.528 \
\hline 3 & 2.487 & 2.402 & 2.322 & 2.283 & 2.246 & 2.174 & 2.106 \
\hline 4 & 3.170 & 3.037 & 2.914 & 2.855 & 2.798 & 2.690 & 2.589 \
\hline
\end{array}$$

Quizplus · Accepted Answer

The IRR is the discount rate that makes the net present value (NPV) of the project equal to zero. Given the annual cash inflows of $613,228 for three years and an initial investment of $1,400,000, we need to find the discount rate that satisfies this condition. Using the given table, we look for the present value of an ordinary annuity factor that, when multiplied by the annual cash inflow, equals the initial investment. The closest match is at 15%, where the present value of an ordinary annuity of $1 for three years is approximately 2.283. Multiplying 2.283 by the annual cash inflow of $613,228 gives a value close to the initial investment of $1,400,000, indicating that the IRR is approximately 15%.

A Company Is Considering an Iron Ore Extraction Project That