gordon growth model not checking out

Confused about why this is not checking out.

Stock is valued at 21.875.

industry average required return 11%

industry average trailing dividend yield = 3.7% Bradley suggests that Tanner calculate the implied long-term dividend growth rate for GNSK using the Gordon growth model. Bradley believes that the required return and dividend yield for the industry are the most stable indicators and should be used in the valuation computations. q: Using Bradley’s assumptions regarding GNSK and the data from Exhibit 1, GNSK’s implied long-term dividend growth rate is closest to:

  1. 8.0%.
  2. 7.0%.
  3. 7.3% answer is 2. this was my approach: 21.875= 0.809375 (which i got by doing 3.7% dividend yield multiplied by price) * 1.07= 0.8660312 now 0.8660312/0.04 (11%-7%) = 21.65078. why does my approach not work for this? getting confused

The answer is 3: 7.3%

D1/P0 +G = R

3.7 + G = 11 ==> G = 7.3

If you do the math, .8093 / (.11-0.73) = 21.875

I think they messed up and stated the trailing dividend yield but it should be leading dividend yield.

No it should be 7% - if you back into the growth assuming 3.7% is the trailing yield, you get to 7%. Here are the steps:

  1. 21.875 * 3.7% = 0.8094; this is the implied trailing dividend
  2. 0.8094*(1+g) / (11% - g) = 21.875; now solve for g
  3. g = 7%; when I plug 7% into the equation I get the same $21.65, but that is due to rounding (calculated g was 7.0396…%)

Yes if they meant trailing dividend, then 7% is the closest. If they meant leading dividend, then 7.3% is the closest.

The rounding error throws the trailing dividend off while the if they meant leading dividend, the 7.3% is right on. I never trust the question writers because they get so many things wrong.

Sure, but if the question specifically states trailing dividend yield, then you would solve for it as such. In the context of the question being posed, the answer of 7.3% wouldn’t be correct and is likely there to throw people off.

so its a rounding error. great. thanks Tuchsford