Question

High Growth Period:

Growth rate during period = 10%

Payout rate during period = 40%

Stable Growth Period:

Growth rate during period = -1%

Payout rate during period = 80%

Please assume all other inputs remain unchanged. Please show your work.

There are two stocks. Assume a capitalization rate of 10%.

1. Stock A is expected to pay a dividend of $15 next year. Thereafter, dividend growth is expected to be -2% per annum forever (note that dividends are declining).
2. Stock B is expected to pay a dividend of $15 next year. Thereafter, dividend growth is expected to be 2% a year for 5 years (i.e., until year 6) and zero thereafter.

If the market capitalization rate is 10%, which stock is the more valuable? Show your work.

Answer 1

(a) Market Capitalization Rate = R = 10 %, Perpetual Dividend Growth Rate post Next Year = - 2 % and Expected Dividend Next Year = $ 15

Current Stock Price = 15 / [0.1-(-0.02)] = $ 125

(b) Expected Dividend Next Year = D1 = $ 15, Growth Rate = 2 % for 5 years upto the end of Year 6. Growth Rate post Year 6 = 0 %

Market Capitalization Rate = 10 %

D1 = $15, D2 = 15 x 1.02 = $ 15.3, D3 = 15.3 x 1.02 = $ 15.606, D4 = 15.606 x 1.02 = $ 15.91812, D5 = 15.91812 x 1.02 = $ 16.23648, D6 = 16.23648 x 1.02 = $ 16.56121

D7 = D6 = $ 16.56121 (no growth)

Terminal Value of Perpetual Dividend at the end of Year 6 = 16.56121 / 0.1 = 165.6121 $

PV of Terminal Value = 165.6121 / (1.1)^(6) = $ 93.48371

PV of Dividends between Year 1 and Year 6 = 15 / 1.1 + 15.3 / (1.1)^(2) + 15.606 / (1.1)^(3) + 15.91812 / (1/1)^(4) + 16.23648 / (1.1)^(5) + 16.56121 / (1.1)^(6) = $ 68.30825

Therefore, Current Stock Price = 68.30825 + 93.48371 = $ 161.792

As is observable, Stock B is more valuable, as compared to Stock A.