(Valuing Stocks)
1 [Constant-Growth DDM Model]
GenGym just paid its annual dividend of $3 per share, and it is widely expected that the dividend will increase by 5% per year infinitely. (a) What price should the stock sell at? The discount rate is 15%. (b) How would your answer change if the discount rate were only 12%? (c) Any conclusions based on the calculation results in question (a) and (b)?
2 [Transform the DDM model] A&C Inc will pay a $5 per share in one year. It sells at $50 a share, and firms in the same industry provide an expected rate of return of 14%. What must be the expected growth rate of the company’s dividend?
3 [Sustainable growth rate: the g in the constant-growth DDM equation] EAA stock currently just paid $1.64 dividend per share and sells for $27 a share. (a) If investors believe the growth rate of dividends is 3% per year, what rate of return do they expect to earn on the stock? (b) If investors’ required rate of return is 10%, what must be the growth rate they expect of the firm? (c) If the sustainable growth rate is 5% and the plowback ratio is 0.4, what must be the rate of return earned by the firm on its new investments?
4 [PVGO]
Cincorp will pay a year-end dividend of $2.40 per share, which is expected to grow at a 4% rate for the indefinite for futures. The discount rate is 12%. (a) What is the stock selling for? (b) If earnings are $3.10 a share, what is the present value of growth opportunities of this firm? [Hint: PVGO is the difference between firm value with growth (reinvesting some earning into the company, i.e., plowback ratio 0) and no-growth value (plowback ratio = 0).]
5 Springboro Tech is a young start-up company. No dividends will be paid on the stock over the next 15 years, because the firm needs to plow back its earnings to fuel growth. The company will pay a $15 per share dividend in 16 years and will increase the dividend by 4 percent per year thereafter. What is the current share price if the required return on this stock is 8 percent?
6 [PVGO and how it is related to NPV that we just learned.]
Meta Company’s stock will generate earnings of $6 per share this year. The discount rate for the stock is 15%, and the rate of return on reinvested earnings also 15%.
(a) Find both the growth rate of dividends and the price of the stock if the company reinvest the following fraction of its earnings in the firm (i) 0%; (ii) 40%; (iii) 60%.
(b) Redo part (a) now assuming that the rate of return on reinvested earnings is 20%, What is the present value of growth opportunity (PVGO) for each reinvested rate?
(c) Considering your answers to parts (a) and (b), can you briefly state the difference between companies experiencing non-growth versus companies with growth opportunities?
Hint: the rate of return on reinvested earnings also 15% (i.e., ROE is 15%. Because retained earning is equity à the rate of return on reinvested/retained earning is 15% à It suggests that ROE (Return on equity) is 15%. )
7 [A challenging question]
TTAL corp has been growing at a rate of 20% per year, and you expect this growth rate in earnings and dividends to continue for another 3 years. (a) If the last dividend just paid was $2, what will be the next dividend? (b) If the discount rate is 15% and the dividends’ constant growth rate after 3 years (e.g., starting from the 4th year) is 4%, what would be the stock price at end of the 3rd year? What should the stock price be today?