Richmond Funds has decide to investment in a new firm that it expects to be worth $50 million in four years when Richmond plans leave the venture. Richmond has established a 45% required return for this project and is planning to make an initial investment of $8 million. What ownership fraction will Richmond Funds require in order to make the investment?

Question

Quizplus · Accepted Answer

Richmond Funds requires a 45% annual return on its investment. To find the ownership fraction, we calculate the future value of the initial investment at the required return rate, and then divide by the expected future value of the firm. The future value of the $8 million investment at a 45% annual return over four years is calculated using the formula FV = PV * (1 + r)^n, where FV is the future value, PV is the present value ($8 million), r is the annual return rate (45%, or 0.45), and n is the number of years (4). FV = $8 million * (1 + 0.45)^4 ≈ $35.8 million. To find the ownership fraction, divide this future value by the expected future value of the firm: $35.8 million / $50 million ≈ 71.6%. Therefore, Richmond Funds would require approximately a 71% ownership stake to meet its required return.

Richmond Funds Has Decide to Investment in a New Firm