Question

1a)

Suppose you have $28,000 to invest. You’re considering Miller Enterprises, which is currently selling for $40 per share. You also notice that a call option with a $40 strike price and six months to maturity is available. The premium is $4.00. Miller Enterprise pays no dividends. What is your annualized return from these two investments if, in six months, Miller Enterprise is selling for $48 per share?

b)

suppose a dividend of $0.80 per share is paid. Comment on how the returns would be affected

Answer 1

(A) Dividend is NOT paid

If Shares are purchased:

Number of shares that can be purchased = Investment/Share Price = 28000/40 = 700 shares

Holding Period Return

= [(Selling Price-Investment Price)+Dividend]×Number of shares/[Investment Price×Number of shares]

= [(48-40)+0]×700/[40×700]

= 20%

Holding Period is 6 months

Therefore, Annualized Return(Simple) = 20%×2 = 40%

and Annualized Return(Compounded) = (1+0.2)² - 1 = 44%

If Call Option is purchased:

Number of options that can be purchased = Investment/Option Premium = 28000/4 = 7000

Profit/Loss on Option:

If stock price on expiry > strike price (i.e. 40) then exercise, or lapse.

In this case, EXERCISE.

Profit = [(Stock Price on expiry - Strike Price) - Premium] × Number of Options

= [(48-40)-4]×7000 = 28000

Holding Period return = Profit/Investment = 28000/28000 = 100%

Holding Period is 6 months.

Therefore, Annualized Return(Simple) = 100%×2 = 200%

and, Annualized Return(Compounded) = (1+1)² -1 = 300%

(B) Dividend is Paid

If shares are purchased:

Same as above except

Holding Period Return = [(48-40)+0.8]×700/[700×40] = 22%

Therefore, Annualized Return(Simple) = 22%×2 = 44%

and Annualized Return(Compounded) = (1+0.22)² -1 = 48.84%

If Call Option is purchased:

Dividend is not paid to optionholders.

Therefore, Annualized Yield will be SAME AS ABOVE.

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