Question

An investor buys 100 shares of stock selling at $50 per share using a margin of 50%. The stock pays its annual dividends of $1.00 per share in 3 months. A margin loan can be obtained at an annual interest cost of 7.75%. Determine what return on invested capital the investor will realize if the stock price increases to $60 within six months

Answer 1

The investor's realized return on invested capital, after accounting for dividends received and margin interest paid, is 40.13% when the stock's price increases to $60 over six months.

Step-by-step explanation:

The student's question involves calculating the return on invested capital for an investor who uses margin to buy stocks. When purchasing 100 shares at a price of $50 each with a 50% margin, the investor initially invests $2,500 and borrows the same amount. The annual interest on the margin loan is 7.75%, so for six months, the interest cost is $96.88 (7.75% of $2,500 for half a year). In three months, the investor receives dividends of $100 ($1.00 per share). If the stock price increases to $60 in six months, the capital gain is $10 per share, or $1,000 in total. To find the return on invested capital, calculate the net profit, which is the capital gain plus dividends received minus the margin interest paid. This yields a net profit of $1,003.13 ($1,000 + $100 - $96.88).

To calculate the return on the invested capital, divide the net profit by the initial investment: $1,003.13 / $2,500 = 40.13%. Thus, the realized return on invested capital for the investor is 40.13%.

Answer 2

The return on invested capital the investor will realize is 40.125%

Step-by-step explanation:

First calculate the equity and borrowed fund investment

Equity investment = 100 shares x $50 x 50% = $2,500

Borrowed investment = 100 shares x $50 x 50% = $2,500

Now calculate the dividend and interest value

Dividend = 100 shares x $1 per share = $100

Interest paid = $2,500 x 7.75% x 6/12 = 96.875

Now calculate the price appreciation

Price apreciation = 100 Shares x ( $60 per share - $50 per share = $1,000

Now use the following formula to calculate the return on investment

Return on investment = ( Dividend - Interest payment + Price apprecaition ) / Equity Investment

Return on investment = ( $100 - $96.875 + $1,000 ) / $2,500

Return on investment = $1,003.125 / $2,500

Return on investment = 0.40125

Return on investment = 40.125%