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?

  1. 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

  1. 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

  1. 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?

FVn = PVo(1 + g)n

PVo = $.70 FV5 = $1.30 n = 5

1.30 = .70(1 + g)5

(1 + g)5 = 1.857

The term (1 + g)5 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% +1.857 - 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.

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

FVn = PVo(1+ g)n

PVo = $2.00; FV6 = $4.00; n = 6

4.00 = 2.00(1 + g)6

(1 + g)6 = 2.000

The term (1 + g)6 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%).

  1. 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

  1. 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.