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Question

A project has the following cash flows:

012345- $ 500$ 202- $ X$ 196$ 350$ 451\begin{matrix} \text{0} & \text{1} & \text{2} & \text{3} & \text{4} & \text{5}\\ \text{- \$ 500} & \text{\$ 202} & \text{- \$ X} & \text{\$ 196} & \text{\$ 350} & \text{\$ 451}\\ \end{matrix}

This project requires two outflows at Years 0 and 2, but the remaining cash flows are positive. Its WACC is 10%, and its MIRR is 14.14%. What is the Year 2 cash outflow?

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Since the MIRR is the rate at which the present value of all cash outflowsoutflows would equal the present value of the terminal value (future value of all cash inflowsinflows grown a reinvestment rate of WACC - 10% in this case) discounted using the MIRR, we can solve for the year 2 cash flow by finding the terminal value of all cash inflows and then discounting it to year 0 by the MIRR. The resulting present value of the terminal value should be equal to the present value of all cash outflows. From there we can compute the value of cash flow on year 2.

In other words:

PV of all cash outflows discounted using WACC\textbf{using WACC} = PV of terminal value of cash inflows discounted using MIRR\textbf{using MIRR}

Where:

Terminal value = future value of all cash inflowsinflows grown using WACC\textbf{using WACC}

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