Suppose the Pale Hose Corp. is expected to pay a dividend next year of $1.75 per share. Both sales and proﬁts for Pale Hose are expected to grow at a rate of 15% for the following two years and then
At 2% per year thereafter indeﬁnitely. Dividend growth is expected to match sales growth. If the
Required return is 14%, what is the value of a share of Pale Hose?

Question

Quizplus · Accepted Answer

To calculate the value of Pale Hose Corp's share, we can use the dividend discount model (DDM) as follows:

D1 = $1.75 (given)
g1 = 15% (sales and profit growth rate)
g2 = 15% (sales and profit growth rate)
g3 onwards = 2% (growth rate after 2 years)
r = 14% (required return)

First, we need to calculate the dividends for the next two years:

D2 = D1 x (1 + g1) = $1.75 x (1 + 15%) = $2.01
D3 = D2 x (1 + g2) = $2.01 x (1 + 15%) = $2.31

Then, we can use the dividend discount model formula to calculate the present value of the expected future dividends:

PV = D1/(1+r) + D2/(1+r)^2 + D3/(1+r)^3 + ... + Dn/(r-gn)

where n is the year when the growth rate becomes constant (in this case, n = 2).

PV = $1.75/(1+14%) + $2.01/(1+14%)^2 + $2.31/(1+14%)^3 + ... + $2.31/(14%-2%)

PV = $1.53 + $1.55 + $1.58 + ... + $82.14

PV = $17.92

Therefore, the value of a share of Pale Hose Corp. under these assumptions is $17.92. The closest answer choice is C.