Overview: It is now very early January $2024$ and leveraged buyout specialist Kevin Black of KBO Inc, feels very good about his investments in Doug Fire Development Ltd as the firm is about to be sold.

Purchase of Doug Fire: On January $1,2017,$ KBO paid $$500\mathrm{.}0$ million to purchase all $7\mathrm{.}7$million outstanding shares of Doug Fire. KBO has operated Doug Fire as a stand$-$alone subsidiary of KBO.

Financing Acquisition: Kevin financed this buyout by borrowing $90\%$ of the purchase price from First MacKinnon Bank and negotiated the following terms.

$$ Interest rate is $8\%$ per annum paid in arrears.

$$ Interest does not have to be paid yearly. Interest is capitalized and added to the amount of the loan outstanding; provided Doug Fire meets certain operating cash flow tests and does not pay a dividend. Doug Fire has been compliant with all these terms and consequently has capitalized interest each of the past $5$ years.

$$ The loan and all capitalized interest must be repaid if KBO sells more than $70\%$ of its share ownership of Doug Fire.

Very Successful $5$ Years: Under KBO excellent management, Doug Fire dramatically increased revenues by very creative product innovation and dynamic marketing strategies. Additionally, over this $5$ years Doug Fire experienced a sharp increase in gross margins and overall profitability as noted in the following table:

As of $31$st December $2018$

Revenue $=$ $$305,070,000$

Gross Margin $21\%$

Operating Expenses: $$41,000,000$

Taxes: $26\%$

Shares Outstanding: $7,700,000$

As of $31$st December $2023$

Revenue $=$ $$558,160,000$

Gross Margin: $30\%$

Operating Expenses: $$67,000,000$

Taxes: $26\%$

Shares Outstanding: $7,700,000$

Private Equity Offer: A large private equity firm has made an offer to buy $85\%$ of Doug Fire at a PE Ratio of $12$ times $2023$ earnings, in an all$-$cash transaction.

Honeywell International Inc Offer: made a $$1\mathrm{.}0$ billion cash offer to buy $100\%$ of Doug Fire.

QUESTIONS:

A$)$ Calculate the profit KBO would make accepting the Private Equity Offer $($show all calculations$)?$

B$)$ Calculate the arithmetic and geometric return KBO would earn by accepting the Private Equity Offer.

C$)$ Calculate the profit KBO will make accepting the Honeywell offer show all calculations?

D$)$ Calculate the arithmetic and geometric return KBO would earn by accepting the Honeywell offer.

E$)$ Which offer should KBO $($elaborate on the rationale for your recommendation$)?$