A mature defensive utility company is expected to pay a dividend (D1) of Rs. 12.00 per share at the end of the next year. The company's cost of equity is estimated at 10.0% per annum, and dividends are projected to grow perpetually at a constant rate of 4.0% per annum. What is the theoretical intrinsic value of the share under the Gordon Growth Model?

[ A ]Rs. 120.00 per share

[ B ]Rs. 300.00 per share

[ C ]Rs. 85.71 per share

[ D ]Rs. 200.00 per share[ CORRECT ]

Takeaway

Option D is correct: Rs. 200.00 per share

Derivation

The Gordon Growth Model values a perpetual stream of growing dividends: P0 = D1 / (k - g), where D1 is the expected dividend at the end of Year 1, k is the cost of equity, and g is the constant perpetual dividend growth rate (with the condition that k > g). Given: D1 = Rs. 12.00, k = 10.0% (0.10), g = 4.0% (0.04). P0 = 12.00 / (0.10 - 0.04) = 12.00 / 0.06 = Rs. 200.00 per share. This tests the mathematical application of the Dividend Discount Model for mature companies. The primary candidate trap is dividing D1 by k without subtracting growth (12 / 0.10 = Rs. 120.00) or adding growth (12 / 0.14 = Rs. 85.71).

Why the others fail

A — Rs. 120.00 per share

Rs. 120.00 erroneously divides dividend by cost of equity (12 / 0.10) without subtracting the 4% perpetual growth rate.

B — Rs. 300.00 per share

Rs. 300.00 is an arithmetic error resulting from mistakenly assuming a growth rate of 6% (12 / 0.04 = 300).

C — Rs. 85.71 per share

Rs. 85.71 erroneously adds the growth rate to the cost of equity in the denominator (12 / 0.14) instead of subtracting it.