The net present values of a capital project are as follows: Discount rate % 10 16 NPV $ 6000 (3000). What is…

Question

The net present values of a capital project are as follows: Discount rate % 10 16 NPV $ 6000 (3000). What is the internal rate of return for this project?

ScanSolve AI Tutor · Accepted Answer

To find the Internal Rate of Return (IRR) using the given Net Present Values (NPVs) at different discount rates, we can use linear interpolation.

Identify the given values.
- Lower discount rate ( $L$ ) = $10\%$
- NPV at lower rate ( $NPV_L$ ) = \6,000$
- Higher discount rate ( $H$ ) = $16\%$
- NPV at higher rate ( $NPV_H$ ) = -\3,000$ (The value in parentheses indicates a negative NPV).
Apply the linear interpolation formula for IRR.
The formula is:
$\text{IRR} = L + \frac{NPV_L}{NPV_L - NPV_H} (H - L)$
Substitute the values: $\text{IRR} = 0.10 + \frac{\$6,000}{\$6,000 - (-\$3,000)} (0.16 - 0.10)$ $\text{IRR} = 0.10 + \frac{\$6,000}{\$6,000 + \$3,000} (0.06)$ $\text{IRR} = 0.10 + \frac{\$6,000}{\$9,000} (0.06)$
$\text{IRR} = 0.10 + \frac{2}{3} (0.06)$ $\text{IRR} = 0.10 + 0.04$ $\text{IRR} = 0.14$
Convert the IRR to a percentage.
$\text{IRR} = 0.14 \times 100\% = 14\%$
The calculated Internal Rate of Return is $14\%$ , which corresponds to option C.

The final answer is $\text{C } 14\%$ .

The net present values of a capital project are as follows: Discount rate % 10 16 NPV $ 6000 (3000). What is the internal rate of return for this project?

Answer

Step-by-step solution

Identify the given values.

Apply the linear interpolation formula for IRR.

Convert the IRR to a percentage.

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