Answers
Let's revisit the following concepts before we get into solving this question:
- Growth rate in any period is a function of Return on equity (ROE) and retention ratio (RR) in the prior period.
- Growth, g_{n+1} = ROE x RR_{n} where g_{n+1} = growth rate in Earnings per share (EPS) in the period n+1 and RR_{n} = Retention ratio in the period n
- EPS_{n+1} = EPS_{n} x (1 + g_{n+1})
- Free cash flow to the equity holder, FCFE = EPS x (1 - RR)
- Terminal value of FCFE at the end of period N = FCFE_{TV, N} = FCFE_{N+1} / (Ke - g_{N+1}) where Ke = Cost of equity capital and g_{N+1} = terminal growth rate or growth rate from period N+1 onwards
- Share price today = PV of all the future FCFE = PV of future FCFE over the period t = 1 to t = N + PV of terminal value of FCFE at the end of period N.
Once these concepts are understood, we can synthesize these into the table below. Please see the column "Linkage" to understand how each row has been calculated.
Year, (n) | Linkage | 1 | 2 | 3 | 4 | N = 5 | N+1 = 6 |
EPS | EPS_{n} | 3.0700 | 3.7104 | 4.4844 | 4.9615 | 5.4893 | 5.7183 |
Retention Ratio | RR_{n} | 100.00% | 100.00% | 51.00% | 51.00% | 20.00% | 20.00% |
ROE | ROE | 20.86% | 20.86% | 20.86% | 20.86% | 20.86% | 20.86% |
Growth rate | g_{n+1} = ROE x RR_{n} | 20.86% | 20.86% | 10.64% | 10.64% | 4.17% | |
FCFE | EPS_{n} x (1 - RR_{n}) | - | - | 2.1974 | 2.4311 | 4.3914 | 4.5747 |
Terminal growth rate | g_{N+1} = g_{6} | 4.17% | |||||
Cost of equity | K_{e} | 8.80% | |||||
Terminal Value of FCFE at the end of year 5 | FCFE_{TV,5} = FCFE_{6} / (K_{e} - g_{6}) | 98.8472 | |||||
PV factor | (1+K_{e})^{-n} | 0.9191 | 0.8448 | 0.7764 | 0.7136 | 0.6559 | |
PV of FCFE | FCFE x PV factor | - | - | 1.7061 | 1.7350 | 2.8805 | |
PV of Terminal Value | TV x PV factor for year 5 | 64.8366 | |||||
Share Price | Sum of PV of FCFE and PV of TV | 71.1581 |
Hence, estimated price for Halliford stock = $ 71.16 per share
.