Question

Your bank account pays an interest rate of 8 percent. You are considering buying a share of stock in XYZ Corporation for $110. After 1, 2, and 3 years, it will pay a dividend of $5. You expect to sell the stock after 3 years for $120. Is XYZ a good investment? Support your answer with calculations.

Answer 1

Answer:

• XYZ is not a good investment because the price today is less than the present value of the revenuest it will produce.

Explanation:

To decide if buying a share of stock in XYZ  Corporation for $110 is a good investment you must calculate the present value of the cash flow stream tha it generates, at the rate of 8% (compunded monthly), and compare with the purchase price of $110.

1. Present value of the three dividends:

Discount each dividend according to the year when it will be paid.

• Montlhly interest rate = 0.08/12

       $PV=\dfrac{\ 5}{(1+0.08/12)^{12}}+\dfrac{\ 5}{(1+0.08/12)^{24}}+\dfrac{\ 5}{(1+0.08/12)^{36}}$

      $PV=\ 12.82$

2. Present value of the $120 (selling price)

The stock will be sold in 3 years (36 months)

        $PV=\dfrac{\ 120}{(1+0.08/12)^{36}}=\ 94.47$

3. Total present value of the stock

Add the two present values found above:

    $Total\text{ }present\text{ }value=\ 12.82+\ 94.47=\ 107.29$

4. Compare with the current $110 price of the stock in XYZ Corporation

Since the investement today $110 is greater than the present value of the cash flows that it will produce this is not a good investment.