In: Finance
Quantitative Problem 1: Hubbard Industries just
paid a common dividend, D0, of $1.80. It expects to grow
at a constant rate of 2% per year. If investors require a 10%
return on equity, what is the current price of Hubbard's common
stock? Round your answer to the nearest cent. Do not round
intermediate calculations.
$_____ per share
Zero Growth Stocks:
The constant growth model is sufficiently general to handle the case of a zero growth stock, where the dividend is expected to remain constant over time. In this situation, the equation is:
Note that this is the same equation developed in Chapter 5 to value a perpetuity, and it is the same equation used to value a perpetual preferred stock that entitles its owners to regular, fixed dividend payments in perpetuity. The valuation equation is simply the current dividend divided by the required rate of return.
Quantitative Problem 2: Carlysle Corporation
has perpetual preferred stock outstanding that pays a constant
annual dividend of $1.90 at the end of each year. If investors
require an 8% return on the preferred stock, what is the price of
the firm's perpetual preferred stock? Round your answer to the
nearest cent. Do not round intermediate calculations.
$_____ per share
Nonconstant Growth Stocks:
For many companies, it is not appropriate to assume that dividends will grow at a constant rate. Most firms go through life cycles where they experience different growth rates during different parts of the cycle. For valuing these firms, the generalized valuation and the constant growth equations are combined to arrive at the nonconstant growth valuation equation:
Basically, this equation calculates the present value of dividends received during the nonconstant growth period and the present value of the stock's horizon value, which is the value at the horizon date of all dividends expected thereafter.
Quantitative Problem 3: Assume today is
December 31, 2017. Imagine Works Inc. just paid a dividend of $1.20
per share at the end of 2017. The dividend is expected to grow at
15% per year for 3 years, after which time it is expected to grow
at a constant rate of 6% annually. The company's cost of equity
(rs) is 9%. Using the dividend growth model (allowing
for nonconstant growth), what should be the price of the company's
stock today (December 31, 2017)? Round your answer to the nearest
cent. Do not round intermediate calculations.
$_____ per share
1]
price of stock = D0 * (1 + g) / (r - g)
price of stock = $1.80 * (1 + 2%) / (10% - 2%)
price of stock = $22.95
2]
price of stock = perpetual dividend / required return
price of stock = $1.90 / 8%
price of stock = $23.75
3]
Value of stock = present value of next 3 years dividend + present value of terminal value at end of 3 years
Terminal value at end of 3 years = Year 3 dividend * (1 + growth rate after 3 years) / (required return - growth rate after 3 years)
Present value = future value / (1 + required return)number of years
The value of stock today = $53.81