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.
- 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%).
- 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
- 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
Book Value per Share =
=
= $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
=
= $40.91
.