a. The total amount of investment is $1,000,000 + $2,500,000 + $3,000,000 = $6,500,000. Therefore, the initial value of the company’s equity is $6,500,000 - $3,500,000 = $3,000,000.

b. To calculate the amount of equity ownership the management should surrender, we need to subtract the amount of investment they are making from the total investment. Therefore, $6,500,000 - $1,000,000 = $5,500,000 is the amount of investment that needs to be covered by equity ownership. Since the initial value of the company’s equity is $3,000,000, the management needs to surrender $5,500,000 - $3,000,000 = $2,500,000 in equity ownership.

c. At the end of year five, the venture investor will receive a return of 15% per year on their investment of $2,500,000 for five years, which is $2,500,000 x 0.15 x 5 = $1,875,000. The bank loan requires an interest of 10% per year on the $3,000,000 borrowed, which is $3,000,000 x 0.10 x 5 = $1,500,000. Therefore, the total amount of return is $1,875,000 + $1,500,000 = $3,375,000. The rate of return on investment is calculated by dividing the total return by the initial investment, which is $3,375,000 / $6,500,000 = 0.519 or 51.9%.