1) General Cereal Common Stock Dividends Have Been Growing at an Annual Rate of 7 Percent

1) General Cereal common stock dividends have been growing at an annual rate of 7 percent per year over the past 10 years. Current dividends are $1.70 per share. What is the current value of a share of this stock to an investor who requires a 12 percent rate of return if the following conditions exist?

a. Dividends are expected to continue growing at the historic rate for the foreseeable future.

Po = D1/(ke - g) g = 0.07 Do = $1.70 ke = .12 Dl = Do(1 + g) = 1.70(1 + 0.07) = $1.819 Po = 1.819/(0.12 - 0.07) = $36.38

b. The dividends growth rate is expected to increase to a 9 percent per year.

g = 0.09 Do = $1.70 ke = 0.12 D1 = 1.70(1 + 0.09) = $1.853 Po = 1.853/(0.12 - 0.09) = $61.77

c. The dividends growth rate is expected to decrease to 6.5 percent per year.

g = 0.065 Do = $1.70 ke = 0.12 D1 = $1.70(1 + 0.065) = $1.8105

Po = $1.8105/(0.12 - 0.065) = $32.92

2) The Foreman Company's earnings and common stock dividends have been growing at an annual rate of 6 percent over the past 10 years and are expected to continue growing at this rate for the foreseeable future. The firm currently pays an annual dividend of $5 per share. Determine the current value of a share of Foreman common stock to investors with each of the following required rates of return:

a. 12 percent Po = D1/(ke - g) g = .06 Do = $5 ke = .12 Dl = Do(1 + g) = 5(1 + .06) = $5.30

Po = 5.30/(.12 - .06) = $88.33 b. 14 percent g = .06 D1 = $5.30 ke = .14 Po = 5.30/(.14 - .06) = $66.25 c. 16 percent g = .06 Dl = $5.30 ke = .16 Po = 5.30/(.16 - .06) = $53

d. 6 percent g = .06 D1 = $5.30 ke = .06 Po = 5.30/(.06 - .06) = Undefined ke = g, which violates assumption of constant-growth model.

e. 4 percent g = .06 Dl = $5.30 ke = .04 Po = 5.30/(.04 - .06) = $-265. ke < g, which violates assumption of constant-growth model.

4) Over the past 5 years, the dividends of the Gamma Corporation have grown from $0.70 per share to the current level of $1.30 per share. This growth rate is expected to continue for the foreseeable future. What is the value of a share of Gamma Corporation common stock to an investor who requires a 20 percent on an investment?

n FVn = PVo(1 + g) PVo = $.70 FV5 = $1.30 n = 5 1.30 = .70(1 + g)5 (1 + g)5 = 1.857 5 The term (1 + g) represents the future value interest factor (FVIFg,5) found in Table I at the back of the book. Reading across the Period = 5 row, one finds (1 + g)5 between the i = 13% and i = 14% columns. Interpolating between these values yields i = 13% + 1.85 7 - 1 .842 x (14% - 13%) = 13.2% 1.925 - 1.842 Therefore g = .132 ( or 13.2%)

Po = D1/(ke - g) Do = $1.30 ke = .20 D1 = Do(1 + g) = 1.30(1 + .132) = $1.4716

Po = 1.4716/(.20 - .132) = $21.64

6) The chairman of Heller industries told a meeting of financial analysts that he expects the firm's earnings and dividends to double over the next 6 years. The firm's current (that is, as of year 0) earnings and dividends per share are $4 and $2.

a. Estimate the compound annual dividend growth rate over the 6-year period.

n FVn = PVo(1+ g) PVo = $2.00; FV6 = $4.00; n = 6 4.00 = 2.00(1 + g)6 (1 + g)6 = 2.000 6 The term (1 + g) represents the future value interest factor (FVIFg,6) in Table I at the back of the book. Reading across the Period = 6 row, one finds (1 + g)6 in the i  12% column. Therefore g  0.12 (or 12%).

b. Assuming the forecasted growth rate will go on forever, how much is this stock worth today if investors require an 18% rate of return?

Po = D1/(ke - g) ke = 0.18; g = 0.12; D1 = $2.240 Po = 2.240/(0.18 - 0.12) = $37.33

c. Why might the stock price calculated in not represent an accurate valuation to an investor with an 18% required rate of return?

The firm's earnings and dividends probably cannot continue to grow indefinitely at 12% (above-normal rate). Eventually the growth rate will decline - which violates an assumption of the constant-growth model.

9) Calculate the book value per share based on the reported stockholder's equity account for Bridgford Foods in fiscal year ending November 2, 2005:

Shareholder's equity - (' 000) Preferred stock, without par value Authorized -- 1,000 shares Issued and outstanding --none Common stock, $1.00 pr value -- $10,505 Capital in excess of par value -- 17,475 Retained Earnings -- 29,355 Total Shareholder's equity -- $57,335

Stock Equity Book Value per Share = Number of Common Shares Outstanding

$57,335 = 10,505

= $5.46

11) The Kummins Engine Company common stock has a beta of 0.9. The current risk- free rate of return is 5 percent and the market risk premium is 6 percent. The CEO of the company is quoted in a press release as saying that the firm will pay a dividend of $1.80/share in the coming year and expects the dividends to grow at a constant rate of 6 percent for the foreseeable future. Using the constant growth model, what value would you assign to this stock?

RE = Rf + (Rm)

= 5% + 0.9(6%)

= 10.4%

Ke = 0.104, D1 = $1.8, g = 0.06

D1 P0 = (ke - g )

$1.80 = (0.104- 0.06)

= $40.91