Armishaw next presents Exhibit 2, which contains the basis for his estimates for the share price (as of 15 January 2014) if he assumes a terminal value in 2023 arising from treating 2023’s residual income as a perpetuity.
EXHIBIT 2
VITALITY FOODGROUP BASIS FOR TERMINAL VALUE AND REVISED PRICE ESTIMATE, 15 JANUARY 2014
| Forecasted residual income (RI) per share at end of 2023 | $5.32 |
| Estimated return on equity (ROE) in 2023 | 20% |
| Nature of stream beyond 2023 | Perpetuity |
| Growth rate beyond 2023 | 0% |
| Cost of equity | 15% |
| Dividend payout | 40% |
Stack questions Armishaw’s assumption in his 2014 valuation (Exhibit 2) that a perpetuity would best describe the terminal value of the stream and suggests that residual income should fade over time. Stack further suggests that a persistence factor of 0.50 might be appropriate.
Q. Using the information in Exhibit 2, comparing Armishaw’s approach to terminal value to Stack’s approach, Stack’s assumption leads to a 2024 value that is approximately:
- $6.50 lower than Armishaw’s approach.
- $6.74 lower than Armishaw’s approach.
- $26.30 higher than Armishaw’s approach.
Solution
A is correct.
| Armishaw’s assumption | VT = 5.32/0.15 = $35.47 | Perpetuity of $5.32 per year starting in 2024 |
| Stack’s assumption | ||
| Estimated 2024 growth rate | 0.20 × 0.60 = 0.12 | ROE2023 × Retention ratio |
| Residual income in 2024 | 5.32 × 1.12 = 5.96 | RI2024 = RI2023 × (1 + 0.12) |
| Terminal value 2024 | 5.96/(1 + 0.15 – 0.50) = $9.17 | VT = RI2024/(1 + r – w) |
| Difference in VT | 9.17 – 35.47 = –26.30 | Stack’s vs. Armishaw’s assumptions |
| Difference in PV(VT) | –26.30/(1.1510) = –$6.50 | Stack’s estimate will be $6.50 lower |
Where r = required return on equity; w = persistence factor for residual income; VT = terminal value at forecast horizon.
我的疑问是答案里直接用可持续增长率作为2024年RI的增长率，这样做的依据是什么？公式应该是RI*persisitence factor/1+r-w 啊？
