Question

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 $1.44 per share. The company expects the coming year to be very profitable, and its dividend is expected to grow by 16.00% over the next year. After the next year, though, Portman’s dividend is expected to grow at a constant rate of 3.20% per year. (Note: Do not round your intermediate calculations.)

Term	Value
Dividends one year from now (D1D1)	________ (Note: Rounded to four decimal places)
Horizon value (Pˆ1)P̂1	______ ( Note: Rounded to two decimal places)
Intrinsic value of Portman’s stock	_________ (Note: Rounded to two decimal places)

The risk-free rate (rRFrRF) is 4.00%, the market risk premium (RPMRPM) is 4.80%, and Portman’s beta is 1.30.

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

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

5.63%

7.52%

7.04%

6.82%

Now let’s apply the results of your calculations to the following situation:

Portman has 200,000 shares outstanding, and Judy Davis, an investor, holds 3,000 shares at the current price (computed above). Suppose Portman is considering issuing 25,000 new shares at a price of $20.17 per share. If the new shares are sold to outside investors, by how much will Judy’s investment in Portman Industries be diluted on a per-share basis?

$0.84 per share

$0.34 per share

$0.49 per share

$0.40 per share

Thus, Judy’s investment will be diluted, and Judy will experience a total   of   .

Answer 1

Dividend One Year from now (D1)

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

= $1.44 per share x (1 + 0.16)

= $1.44 per share x 1.16

= $1.6704 per share

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]

= 4.00% + [1.30 x 4.80%]

= 4.00% + 6.24%

= 10.24%

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

= $1.6704(1 + 0.0320) / (0.1024 – 0.0320)

= $1.7239 / 0.0704

= $24.49 per share

Intrinsic Value of Portman’s Stock

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

= $1.6704/(1 + 0.1024)¹ + $24.49/(1 + 0.1024)¹

= [$1.65704 / 1.1024] + [$24.49 / 1.1024]

= $1.52 + $22.21

= $23.73 per share

Expected Dividend Yield for Portman’s Stock

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

= [$1.6704 / $23.73] x 100

= 7.04%