Question

Last year, Zachary purchased 40 shares of Stock A at $80 per share, 80 shares of Stock B at $160 per share, and a $750 bond with a 5.25% coupon for $775. Zachary sold both stocks today. Stock A is worth $83 per share and Stock B has a value of $166 per share. Assuming neither stock paid a dividend, which investment has the lowest rate of return?

1)
Stock A and Stock B


2)
Stock A


3)
Stock B


4)
Bond

Can someone please tell me how to solve this?

Answer 1

Stock A:

Zachary bought 40 shares of stock A at $80 a share. So he paid 40*80 = 3200 dollars for the shares of stock A.

He then sells stock A at $83 a share, so 83*40 = 3320 is the amount he gets back. The net result is 3320-3200 = 120. Divide this over the initial cost to get 120/3200 = 0.0375

So the rate of return (ROR) for stock A is 3.75%

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Stock B:

total cost = (number of shares of stock B)*(cost per share of stock B)
total cost = 80*160
total cost = 12800

Then he sells stock B at $166 a share

80*166 = 13280

He nets 13280 - 12800 = 480 dollars from stock B

The ROR for stock B is 480/12800 = 0.0375 = 3.75%

So far, we see that the ROR for both stocks (A and B) are the same at 3.75%

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Bond:

par value = $1000
coupon = (0.0525)*(1000) = $52.50

ROR = (coupon)/(price) = 52.50/775 = 0.0677 = 6.77%

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In summary, we have

ROR for stock A = 3.75%
ROR for stock B = 3.75%
ROR for bond = 6.77%

Stock A and B have a tie for the lowest ROR

so that's why the answer is choice 1) Stock A and Stock B