In: Finance
IBM will pay its first dividend of 1.00, two years from today. The dividends will grow at a rate of 5% per annum until the 7th year. After that, the dividends will grow at a rate of 3% until the end of the 15th year.After that the dividends will grow at a rate of 2% forever. Of return of IBM stock is 10% per annual what should be the Pv of the stock?
| Dividend and its present value | |||||
| Year | Dividend | PVF at 10% | Present value | ||
| 1 | 0 | 0.909091 | 0 | ||
| 2 | 1 | 0.826446 | 0.826446 | ||
| 3 | 1.05 | 0.751315 | 0.788881 | ||
| 4 | 1.1025 | 0.683013 | 0.753022 | ||
| 5 | 1.157625 | 0.620921 | 0.718794 | ||
| 6 | 1.215506 | 0.564474 | 0.686122 | ||
| 7 | 1.276282 | 0.513158 | 0.654934 | ||
| 8 | 1.31457 | 0.466507 | 0.613257 | ||
| 9 | 1.354007 | 0.424098 | 0.574231 | ||
| 10 | 1.394627 | 0.385543 | 0.537689 | ||
| 11 | 1.436466 | 0.350494 | 0.503473 | ||
| 12 | 1.47956 | 0.318631 | 0.471433 | ||
| 13 | 1.523947 | 0.289664 | 0.441433 | ||
| 14 | 1.569665 | 0.263331 | 0.413342 | ||
| 15 | 1.616755 | 0.239392 | 0.387038 | ||
| Present value of dividend | 8.37 | ||||
| Expected dividend of Year-16 = 1.62 + 2% = 1.65 | |||||
| Horizon Value = Expected dividend /(Required rate-growth rate) | |||||
| 1.65 / (10-2)% = 20.63 per share | |||||
| Present value of horizon value = 20.63 *0.239392 = 4.94 | |||||
| Price of Stock = 8.37 +4.94 = 13.31 | |||||
| Answer is $ 13.31 | |||||