Question

3. Nonconstant growth stock

As companies evolve, certain factors can drive sudden growth. This may lead to a period of nonconstant, or variable, growth. This would cause the expected growth rate to increase or decrease, thereby affecting the valuation model. For companies in such situations, you would refer to the variable, or nonconstant, growth model for the valuation of the company’s stock.

Consider the case of Portman Industries:

Portman Industries just paid a dividend of $2.88 per share. The company expects the coming year to be very profitable, and its dividend is expected to grow by 20.00% over the next year. After the next year, though, Portman’s dividend is expected to grow at a constant rate of 4.00% per year.

Assuming that the market is in equilibrium, use the information just given to complete the table.

Term	Value
Dividends one year from now (D₁)
Horizon value (Pˆ1P̂1)
Intrinsic value of Portman’s stock

The risk-free rate (rRFrRF) is 5.00%, the market risk premium (RPMRPM) is 6.00%, and Portman’s beta is 1.80.

What is the expected dividend yield for Portman’s stock today?

A. 13.38%

B.11.53%

C. 9.60%

D. 12.00%

Answer 1

Dividend One Year from now (D1)

Dividend One Year from now (D1) = D0 x (1 + g)

= $2.88 x (1 + 0.20)

= $2.88 x 1.20

= $3.4560

“Dividend One Year from now (D1) = $3.4560”

Horizon Value (P1)

As per Capital Assets Pricing Model (CAPM), Cost of Equity (Ke) is calculated by using the following formula

Cost of Equity (Ke) = Rf + [Beta x Market Risk Premium]

= 5.00% + [1.80 x 6.00%]

= 5.00% + 10.80%

= 15.80%

Horizon Value (P1) = D1(1 + g) / (Ke – g)

= $3.4560(1 + 0.04) / (0.1580 – 0.04)

= $3.5942 / 0.1180

= $30.46

“Horizon Value (P1) = $30.46”

Intrinsic Value of Portman’s Stock

Intrinsic Value of Portman’s Stock = D1/(1 + r)1 + Horizon Value/(1 + r)1

= $3.4560/(1 + 0.1580)¹ + $30.46/(1 + 0.1580)¹

= [$3.4560/1.1580] + [$30.46/1.1580]

= $2.99 + $6.30

= $29.29 per share

“Intrinsic Value of Portman’s Stock = $29.29”

Expected Dividend Yield for Portman’s Stock

Expected Dividend Yield for Portman’s Stock = [D1 / P0] x 100

= [$3.4560 / $29.29] x 100

= 11.80%