Stock pricing With Dividend Growth Model Lecture 4 Stock pricing With Dividend Growth Model

5 possible cases No growth (constant dividend) Constant growth Non-constant growth Super-normal growth Changing $ amount of dividends

Case #1: No growth No growth = Constant Dividend D0 = D1 = D2 = D3 = … = D∞ = D Valuation formula: P0 = D/k where P0 = Share price at time 0 D = constant dividend k = discount rate Interesting fact: P0 = P1 = P2 = P3 = … = P∞ = D/k

Numerical Example ABC Company recently paid a dividend of $2 per share. The company has a stable dividend policy. What is ABC’s share price if the required return on its shares is 10%?

Case #2: Constant growth g = constant dividend growth rate (given) D0 = Most recently paid dividends D1 = Dividend in the period coming up Dt = Dividend in t periods Valuation formula: P0 = D1/(k-g) where P0 = Share price at time 0 D1 = dividend expected in the next period k = discount rate g = constant dividend growth rate

Numerical Example DEF Corporation has just paid a dividend of $1.50. Stock market pundits anticipate that the company’s dividends will grow by 2% per year. What is DEF’s share price given that investors require a return of 11% on its stocks?

Case #3: Non-constant growth Dividends will grow, but not at a constant growth rate where D1 = D0(1+g1) D2 = D1(1+g2) = D0(1+g1) (1+g2) D3 = D2(1+g3) = D0(1+g1) (1+g2) (1+g3) DT = DT-1(1+gT) = D0(1+g1) (1+g2) (1+g3) … (1+gT)

Numerical Example GHI Inc., has just paid a $1.20 per share dividend. Due to a new project taken on by GHI, the company’s dividends are expected to grow by 5% next year, 7% in two years, and 9% in three years, and 3% thereafter. What is GHI’s current share price given that the required return on its stocks is 12%?

Non-constant growth example (cont.)

Case #4: Super-normal growth Special case of non-constant growth case Short period of very high growth Then normal constant growth at some point T, till infinity Steps for calculating current share price: Calculate individual dividends for each supernormal growth year as well as normal growth dividend for one year beyond supernormal growth year Calculate share price at time T-1, where T is the first year of normal constant growth using PT-1 = DT/(r – normal growth rate) Calculate P0 = PV(Supernormal dividends) + PV(Share price at time T-1)

Numerical Example The earnings and dividends of JKL Fencelink Inc., are expected to grow by 30% per year for the next two years, then by 20% per year for another two years, before settling down to a normal growth rate of 8% per year forever. If JKL has just recently paid a dividend of $0.50 per share, what is its current share price according to the dividend growth model? Assume a required rate of return of 10%.

Supernormal growth example (cont.)

Supernormal growth example (cont.)

Case #5: Changing $ dividends Usually given: $ dividends for a few eriods into the future $ price at the end period, T Steps for calculating current share price with changing dollar dividends: Calculate present value using PV(lump sum) for each of the given dividends Calculate present value of share price at time T Calculate P0 = PV(dividends) + PV(ending share price)

Numerical Example MN Omnipresence Ltd. has just paid a dividend of $2.50 per share. The company has undertaken a new project which will require certain levels of cash investments over the next 5 years, and therefore the company has announced that it will reduce dividends to $1.00 , $1.20, $1.40. $1.60, and $1.80 per share for each of the next 5 years, respectively. At the end of the 5 years, MNO estimates that its share price will rise to $75 per share. What is the current share price of MNO given a required return of 10%?

Nonconstant dividends example (cont.)

General process of calculating stock price Step 1: Write down all the available information Step 2: Figure out if it is a case of zero-growth, constant growth, non-constant growth, super-normal growth, or different $ dividends. Step 3: Do calculations according to the case type: P0 = PV(all future dividends or cash flows)

Practice makes easy peasy Try this one, it’s a bit more difficult, but you can do it: PQ Recon Corporation has just paid a dividend of $1 per share. To undertake a project, the company plans to reduce dividends to $0 for the next 3 years, after which dividends will grow (from its current level) for 3 years at 30% per year, before settling down to normal growth of 10% per year. If the company does not take on this project, dividends will grow at the normal rate of 10%. Is it worthwhile for this company to take on this project, given a required rate of return of 15%? Answer: Yes, it is worthwhile to take on this project. Without project, share price = $22; with project, share price = $23.43. Share price will be maximized with the project.