Gob Fund, a financial sponsor, helped take Bluth Inc. private in a leveraged buyout. Gob Fund made an equity investment of $$30$ on the transaction date $12/7/23.$ Bluth Inc. had $$8$ in debt prior to the transaction, but the LBO increased debt to $$75.$ Gob Fund is interested in computing the expected IRR with the three assumptions below. What is the IRR to the equity holder $($Gob Fund$)?$ Carefully show your work for partial credit.

Assumptions:

$1)$ $$29$ of debt is paid down by the time of exit

$2)$ an exit date of $01/31/27$

$3)$ no changes in the value of the assets $($e$.$g$.,$ cash flows were not increased due to operating improvements and the firm was valued at the same cash flow multuple$)$