Question

You paid cash for $1,500 worth of stock a year ago. Today the portfolio is worth $2,380.

a. What rate of return did you earn on the investment?
b. Now suppose that you bought the same stock but bought it on margin. The initial margin requirement was 60%. (Recalculate your rate of return, ignoring any interest due).
c. Recalculate the rates of return for a cash purchase in the event that the stock is worth $875 today. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)
d. Recalculate the rates of return for a margin purchase in the event that the stock is worth $875 today. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)

Answer 1

a. The rate of return earned on the investment is 58.67%. b. If bought on margin, the rate of return is -36.53%. c. If the stock is worth $875 today with a cash purchase, the rate of return is -41.67%. d. If the stock is worth $875 today with a margin purchase, the rate of return is -76.7%.

Step-by-step explanation:

a. To calculate the rate of return earned on the investment, we use the formula: Rate of Return = (Final Value - Initial Value) / Initial Value

Using the given values, the rate of return is: (2380 - 1500) / 1500 = 0.5867 or 58.67%

b. If the investment was made on margin with an initial margin requirement of 60%, the calculation for rate of return would be the same as in part a, but using the total investment amount (initial amount + borrowed amount) as the initial value. Since the borrowed amount is 40% of the initial amount, the initial value is $1500 / (1 - 0.6) = $3750. The rate of return would then be: (2380 - 3750) / 3750 = -0.3653 or -36.53%

c. If the stock is worth $875 today with a cash purchase, the rate of return would be: (875 - 1500) / 1500 = -0.4167 or -41.67%

d. If the stock is worth $875 today with a margin purchase, the rate of return would be: (875 - 3750) / 3750 = -0.767 or -76.7%