Final answer:
The institutional investor can invest approximately 91.61% of the $100 million portfolio in stocks after securing the rest to pay off a maturing bond issue with zero-coupon bonds yielding 6%.
Step-by-step explanation:
The question focuses on determining how much of the portfolio can be invested in stocks while ensuring that the institutional investor can pay off the maturing bond issue. The institutional investor has a total obligation of $10 million (10,000 bonds × $1,000 each) in 3 years. The money manager can invest in a 6% zero-coupon bond to fund this future liability. To find out how much is needed to invest today at 6% to have $10 million in 3 years, the present value of this future sum must be calculated using the formula PV = FV / (1 + r)^n, where PV is the present value, FV is the future value (the $10 million needed), r is the rate (6% or 0.06), and n is the number of years (3).
The calculation is as follows:
This means that the institutional investor needs to invest approximately $8.4 million in the zero-coupon bonds now to fulfill the future $10 million obligation. The remainder of the portfolio, which would be $100,000,000 - $8,393,178.31 = $91,606,821.69, can be invested in stocks. To find the percentage of the total portfolio that this represents:
Therefore, the money manager can invest 91.61% of the total portfolio in stocks to ensure that the bond payments can be met when they mature in 3 years.