High-level Waterfall / IRR Hurdle Question

It's been years since I made a waterfall and now I'm stuck on a specific formula. I want to know if a formula exists to determine the proceeds required in an exit year to achieve a specific IRR.

Using a 5 year hold for example and a 10.00% IRR hurdle, I basically just took (1+10.00%)^5 to determine what multiple is required (1.61x). I then applied that multiple to the Year 0 equity contribution, then subtracted whatever distributions where made in Years 1-4. However, the resulting Year 5 required proceeds yields a 10.53% IRR, not a 10.00% IRR, presumable because the cash flow distributions in Years1-4 are not consistent, they vary.

Is it possible to run a formula like this without using goalseek?

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