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. Therefore, the total return they will receive is $2,500,000 x 1.15^5 = $4,563,281. The rate of return on their investment is (4,563,281 - 2,500,000) / 2,500,000 x 100% = 82.53%. The company’s executives did not receive a return on their investment since they used their funds to acquire equity ownership in the company.