# DDM & Required Rate of Return Problem

From a Schweser practice exam An analyst develops the following information to value a common stock: - last year’s earnings per share (E0) = \$4.00 - expected constant growth rate of dividends = 4% - Real risk-fee rate = 4% - Inflation Premium = 5% - ROE, expected to remain constant over the future = 20% - Dividend Payout, expected to remain stable = 30% - Stock’s Beta = 1.4 - Expected market return = 14% Using the infinte period dividend discount model, which of the following is the most accurate estimate of required rate of return (ke) and next year’s dividend (D1)? __ Ke_____ D1 A. 15.92% 1.20 B. 15.92% 1.37 C. 18.00% 1.20 D. 18.00% 1.37 The answer is B. I can get the Dividend but am stuck on how they get 15.92% for the required rate of return.

Nominal Rate = (1.04)(1.05) - 1 = 9.2 CAPM = .092 + 1.4(.14 - .092) = 15.92

On a side note, how did you get the dividend with this information? I’m on the phone and can’t concentrate at this moment…

and the other half is this find current dividend, then find G dividend = \$1.20 (\$4 * .3) G = ROE * rr rr = 1 - DPO rr = 1 - .3 = .7 ROE = .2 (given to us – thank god!) g = .2 * .7 = 14% so next yrs div = \$1.20(1.14) —> 1.37 BOOM gimme more. answer is B

g= ROE*RR= 0.20x0.70 = 0.14 D1 = \$4(0.30)*1.14= \$1.368 … need current stock price though to back into Ke

to be clear = div = DPO * EPS b/c we know that DPO = DPS/EPS. so we can solve for DPS if we have the other two variables comment: this is a tricky one, but this is what Level 1 is – they want us to know like 4-5 different formulas AT ONCE and be able to plug and chug in < 90 seconds

somehow g predicted by RR times ROE is 14%. The q says Div grows at 4%.

soxboys21 Wrote: ------------------------------------------------------- > Nominal Rate = (1.04)(1.05) - 1 = 9.2 > > CAPM = .092 + 1.4(.14 - .092) = 15.92 this uses CAPM to solve for Ke, but the question instructed to use the DDM…

Char-Lee Wrote: ------------------------------------------------------- > soxboys21 Wrote: > -------------------------------------------------- > ----- > > Nominal Rate = (1.04)(1.05) - 1 = 9.2 > > > > CAPM = .092 + 1.4(.14 - .092) = 15.92 > > > this uses CAPM to solve for Ke, but the question > instructed to use the DDM… Do you have an easier way to come up with 15.92% in the answer???

soxboys21 Wrote: ------------------------------------------------------- > Char-Lee Wrote: > -------------------------------------------------- > ----- > > soxboys21 Wrote: > > > -------------------------------------------------- > > > ----- > > > Nominal Rate = (1.04)(1.05) - 1 = 9.2 > > > > > > CAPM = .092 + 1.4(.14 - .092) = 15.92 > > > > > > this uses CAPM to solve for Ke, but the > question > > instructed to use the DDM… > > Do you have an easier way to come up with 15.92% > in the answer??? that’s the point… i would do exactly what you did BUT since the question directed otherwise I was expecting to see a stock price (which is required to solve for Ke)

> > Do you have an easier way to come up with 15.92% > in the answer?!?!? only 3 ways to ket kost of Eq = CAPM, DDM, or equity above cost of debt premia so we have no stock price, so I go with CAPM

saurya_s Wrote: ------------------------------------------------------- > somehow g predicted by RR times ROE is 14%. The q > says Div grows at 4%. thats a typo likely

We all think the book meant to write 14% and messed up and wrote 4%