Question

You are able to buy an investment today for $1,000 that gives you the right to receive $438 in each of the next three years. what is the internal rate of return on this investment? (round your final answer to nearest whole percent.)

Answer 1

The internal rate of return (IRR) for an investment of $1,000 with three annual returns of $438 is calculated using a financial calculator or software, which typically finds the IRR to be approximately 14%, rounded to the nearest whole percent.

Step-by-step explanation:

The question asks how to calculate the internal rate of return (IRR) for an investment that requires an initial outlay of $1,000 and provides three annual payments of $438 each. To find the IRR, we need to set the net present value (NPV) of the cash flows equal to zero and solve for the discount rate that satisfies this condition. The NPV is calculated by summing the present values of each annual payment, discounted back to today using a discount rate, which in this case is the IRR we're trying to find.

Step-by-Step Calculation

1. Let r be the internal rate of return we are trying to determine.
2. Set up the IRR equation: $0 = -1000 + 438/(1+r) + 438/((1+r)^2) + 438/((1+r)^3).
3. Solve the equation for r, which is the IRR. This typically requires the use of a financial calculator or software because it often cannot be solved algebraically.

As solving for IRR analytically is not practical, we would usually input these cash flows into a financial calculator and use the IRR function to find that the IRR for this investment is approximately 14%. Therefore, the internal rate of return for this investment, rounded to the nearest whole percent, is 14%. This rate of return is essentially the break-even interest rate that makes the present value of the cash inflows equal to the initial investment cost.