Question

1. Assume that the risk-free rate of return (Krf) is 3% and the required rate of return on the market (Km) is 8%. A given stock, say, Caterpillar (CAT) has a beta coefficient of 1.03. If the dividend per share during the coming year, meaning D₁, is $4.12 and g = 3.50%, what is the current intrinsic value of the stock?

1. Exactly how much was D₀?

1. How long will it take for the dividend to double, given the growth rate, approximately?

1. Which of the most fundamental assumptions about the Gordon Model/ Constant Growth Dividend Model broke down in the crash of 2008; give an example of a firm that was affected?

Answer 1

Risk free rate = Krf = 3%

g = 3.50%

Market return = Km = 8%

D1 = D0 ( 1 + g )

D0 = D1 / ( 1 + g )

D0 = 4.12 / ( 1 + 3.50 %) = 4.12 / 1.035 = $ 3.980

Intrinsic value of stock using dividend growth model is:

P0 = D1 / ( Km - g )

P0 = 4.12 / ( 8% - 3.50% ) = 4.12 / ( 4.50% ) = 91.5

Intrinsic value of stock is $ 91.5

To double the dividend given the current growth rate :

D0 ( 1 + g ) ^ n = 2 * D0

I.e.

( 1 + 0.035 ) ^ n = 2

1.035 ^ n = 2

n = 21 approx

It would take approximately 21 years to double the dividend given the current growth rate.

Two of the most fundamental assumptions about the Gordon Model that broke down during the crash of 2008 were:

1) The rate of return (r) and cost of capital (K) are constant.

During the crisis, the rate of return of all the companies fell down due to the market crash and the cost of raising capital went up due to shortage of liquidity in the market.

2 ) Growth rate is constant

During the crisis, most companies suffered huge losses and hence could not pay any dividends, let alone growing the dividend at a constant rate.

One example of such organisation would be American International Group ( AIG ). It was deemed too big to fail and was expected to maintain the rate of return on capital and growth rate on dividends. Due to the high exposure, AIG suffered huge losses and was at the door of getting liquidated when the Federal Reseve had to bail it out. As a result, it could neither maintain the rate of return, nor provide any dividends. Also, the cost of raising capital rose sharply, thus countering the funadmental assumption about Gordon Dividend Model.