Questions: Internal rate of return A project is estimated to cost 402,360 and provide annual net cash flows of 120,000 for 5 years. Present Value of an Annuity of 1 at Compound Interest Year 6 % 10 % 12 % 15 % 20 % 1 0.943 0.909 0.893 0.870 0.833 2 1.833 1.736 1.690 1.626 1.528 3 2.673 2.487 2.402 2.283 2.106 4 3.465 3.170 3.037 2.855 2.589 5 4.212 3.791 3.605 3.353 2.991 6 4.917 4.355 4.111 3.785 3.326 7 5.582 4.868 4.564 4.160 3.605 8 6.210 5.335 4.968 4.487 3.837 9 6.802 5.759 5.328 4.772 4.031 10 7.360 6.145 5.650 5.019 4.192 Determine the internal rate of return for this project, using the Present Value of an Annuity of 1 at Compound Interest table shown above %.

Solution Steps

To determine the internal rate of return (IRR) for the project, we need to find the interest rate at which the present value of the net cash flows equals the initial investment. We will use the Present Value of an Annuity table to find the rate that makes the present value of the annuity ($120,000$ per year for 5 years) equal to the project cost ($402,360$).

1. Calculate the present value of the annuity for each interest rate given in the table.
2. Compare the calculated present value with the project cost.
3. Identify the interest rate that makes the present value closest to the project cost.

Given:

• Project cost: \( \$402,360 \)
• Annual cash flow: \( \$120,000 \)
• Number of years: \( 5 \)

Using the Present Value of an Annuity factors from the table:

• For \( 6\% \): \( 4.212 \)
• For \( 10\% \): \( 3.791 \)
• For \( 12\% \): \( 3.605 \)
• For \( 15\% \): \( 3.353 \)
• For \( 20\% \): \( 2.991 \)

Calculate the present value of the annuity for each interest rate: \[ \text{PV}_{\text{annuity}} = \text{Annual Cash Flow} \times \text{PV Factor} \]

\[ \begin{align_} \text{PV}_{6\%} &= 120,000 \times 4.212 = 505,440 \\ \text{PV}_{10\%} &= 120,000 \times 3.791 = 454,920 \\ \text{PV}_{12\%} &= 120,000 \times 3.605 = 432,600 \\ \text{PV}_{15\%} &= 120,000 \times 3.353 = 402,360 \\ \text{PV}_{20\%} &= 120,000 \times 2.991 = 358,920 \\ \end{align_} \]

Compare the calculated present values with the project cost of \( \$402,360 \):

\[ \begin{align_} \text{PV}_{6\%} &= 505,440 \\ \text{PV}_{10\%} &= 454,920 \\ \text{PV}_{12\%} &= 432,600 \\ \text{PV}_{15\%} &= 402,360 \\ \text{PV}_{20\%} &= 358,920 \\ \end{align_} \]

The interest rate that makes the present value closest to the project cost is \( 15\% \), where the present value exactly matches the project cost:

\[ \text{PV}_{15\%} = 402,360 \]

Final Answer