# Growth Duration Q

Josh Bentley, CFA, is considering recommending the purchase of Mega Advertising Corp. (MAC). Bentley has gathered the following information on MAC and the market index. MAC Index Price-to-earnings (P/E) ratios 25 16 Dividend yield 0.01 0.03 Return on book equity 0.20 0.12 Retention ratio 0.80 0.50 Bentley believes that MAC will achieve supernormal growth for five more years before its comparative advantage diminishes. Bentley should recommend: A) shorting MAC stock because it is overpriced as demonstrated by the high P/E ratio. B) shorting MAC stock because the firm cannot meet the supernormal growth expectations priced into the stock. C) purchasing MAC stock because the market price only accounts for three years of supernormal growth. D) purchasing MAC stock because high expected growth rates always result in high price-to-earnings (P/E) ratios.

A

B I get 6.3 years.

um… C

any explanations?

C PEG is much higher for index…

Its B. got 6.3 years for high growth period

and we know D is incorrect, so C is best i think

Your answer: A was incorrect. The correct answer was B) shorting MAC stock because the firm cannot meet the supernormal growth expectations priced into the stock. Bentley should recommend shorting MAC stock because the firm cannot meet the supernormal growth expectations priced into the stock. Although the stock is overvalued, the statement “…as demonstrated by the high P/E…” implies that all high P/E stocks are overvalued, and this is not necessarily true. The growth duration relationship is given as follows: To determine the growth duration of MAC we must first solve for the growth rate of MAC and the index using the sustainable growth formula: growth = return on equity (ROE) × retention ratio. The growth rate for MAC = 0.20 × 0.80 = 0.16 or 16%. The growth rate for the index = 0.12 × 0.50 = 0.06 or 6%. Next we can calculate the growth duration of MAC: 0.4463 = T × 0.0708 6.3037 = T Nib - How do apply the 6.3037 to his estimate of 5 years? Is the 6.3037 the market estimate?

wow. i was hitting e^x on my calculator instead of ln. i should be shot and killed.

what’s this growth duration formula? it’s not on in my head yet… talk to me goose.

Yea, the market is currently pricing in 6.3 years of high growth, but you estimated that there will only be 5. You think the market is pricing in a higher period of growth than what you think is actually going to happen, so you short.

so the left side is the natural log of the High PE divided by the Low PE and we set that = to T times (1 + growth +div yield) for the hig PE divided by (1 + growth + div yield) for the low PE. is that right?

Yes

oy…totally forgot this formula. good thing i remember it now.

awesome. good refresher. thanks everyone.

–>0.4463 = T × 0.0708 -->6.3037 = T Where do you get 0.4463 and 0.0708?

ln(25/16) and ln(1.17/1.09)

ln (hi g PE/norm g pe) = T * LN ((1+hg g + hg div yield)/)(1+ng g + ng div yield))