Question

Provide all of the steps for the calculations !

1. Assume that IBM is a constant-growth firm with its quarterly dividends paid as an annual dividend at the end of each year. Find total dividends paid in previous year and assume they were paid in one lump sum at the end of the previous year. Assume that the dividend paid during the past year grows at a rate of g and g = 5%. The price estimate of IBM stock would be using the dividend discount model. Let’s assume R is calculated using the Capital Asset Pricing Model (CAPM), where the risk-free rate of return is 3% and the market rate of return is 10%. You can find IBM’s price history and beta at http://finance.yahoo.com/. Compute the value of IBM stock given this information.

2. Now let’s assume the P/E (price-earnings ratio) model gives us a better estimate of IBM stock value. In 2011, IBM’s P/E range was 13.19-13.43 and its 12/31/11 EPS was $13.06. You should assume that EPS will grow by an annual rate of g% (see part 1). Analyst estimates on 12/31/11 are that the P/E will rise by 12-13.5% in the next several years. Find the price range estimated for the stock at the end of the current year using the P/E model. Find the present value of the expected prices using your CAPM R (from part 1) as the discount rate.

3. Compare the two estimates of stock price to IBM’s stock price at the end of the most recent year. Discuss your findings in a 1-page essay. If one of the valuation methods does not work well, be sure to discuss why that may be true.

Answer 1

1) Previous year dividend = 5.9$

Beta = 1.08

Thus R = Rf+b(Rn-Rf)

=3%+1.08(10%-3%)

=3%+7.56%

=10.56%

Price of share = D1/Ke-g

=5.9(1.05)/10.56%-5%

=6.195/5.56%

=111.4209$

2) In 2017 Eps would be

=13.06(1+5%)^6

=13.06(1.05)^6

=13.06(1.34)

=17.50165$

In 2017 PE range would be

=13.19(1.12)^6 - 13.43(1.135)^6

=13.19(1.97) - 13.43(2.13784)

=26.034 - 28.71

Price range = 26.034*17.50 - 28.71*17.50

=455.607 - 502.44

3) Recent price of IBM is 154.49$, thus dividend discount model provide fair view of stock's price. The PE model did not work since it assumes that whole of EPS would be re invested which is not the case with IBM