Question

	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021	2022	2023	2024	2025	2026
BVPS, start of year	7	7.61	8.51	9.51	10.73	11.77	13.17	14.4	15.91	17.58	19.43	21.47	23.72	25.38	27.16	29.06
EPS	0.81	1.1	1.3	1.52	1.64	2	2.03	2.16	2.39	2.64	2.91	3.22	2.37	2.54	2.72	2.91
ROE	0.116	0.145	0.153	0.16	0.153	0.17	0.154	0.15	0.15	0.15	0.15	0.15	0.1	0.1	0.1	0.1
Payout Ratio	0.247	0.182	0.231	0.197	0.366	0.3	0.394	0.3	0.3	0.3	0.3	0.3	0.3	0.3	0.3	0.3
Dividends per Share (Div)	0.2	0.2	0.3	0.3	0.6	0.6	0.8	0.65	0.72	0.79	0.87	0.97	0.71	0.76	0.81	0.87
Retained Earnings	0.61	0.9	1	1.22	1.04	1.4	1.23	1.51	1.67	1.85	2.04	2.25	1.66	1.78	1.9	2.03
BVPS, end of year	7.61	8.51	9.51	10.73	11.77	13.17	14.4	15.91	17.58	19.43	21.47	23.72	25.38	27.16	29.06	31.1
Dividend Growth Rate									0.105	0.105	0.105	0.105	-0.263	0.07	0.07	0.07
Cost of capital, r	0.10		PIV Div 2017 - 2022		$    3.34			PV at 2022	23.72
ROE 2018 - 2022	0.15		NPV including PV in 2022		$   16.82			PV at 2024	27.16
ROE 2023 -2024	0.10
Payout ratio 2018 -2022	0.30		PV DIV 2017 - 2024		$    4.15
Payout ratio 2023 -	0.30		NPV including PV at 2024		$   16.82
Note: Valuation date is start of 2017. Dividends assumed paid at end of year.

What is Reeby Sports worth per share? We will value the company using George
Reeby's forecasts.
The spreadsheet accompanying this solution sets out a forecast in the same
general format as Table 4.5. Historical results from 2011 to 2016 are also shown.Earnings
per share (EPS)equals return on equity (ROE) times starting book value per share
(BVPS). EPS is divided between dividends and retained earnings, depending on the
dividend payout ratio.BVPS grows as retained earnings are reinvested.
The keys to Reeby Sports’ future value and growth are profitability (ROE) and
the reinvestment of retained earnings. Retained earnings are determined by dividend
payout. The spreadsheet sets ROE at 15% for the six years from 2018 to 2022. If Reeby
Sports will lose its competitive edge by 2022, then it cannot continue earning more than
its10% cost of capital. Therefore ROE is reduced to 10%startingin 2023.1
The payout ratio is set at .30 from 2018 onwards. Notice that the long-term
growth rate, which settles inafter 2023, is ROE × ( 1 – dividend payout ratio) = .10 × (1 -
.30) = .07.
The spreadsheet allows you to vary ROE and the dividend payout ratio separately
for 2018-2022 and for 2023-2024.2But let’s start with the initial input values. To
calculate share value, we have to estimate a horizon value at H = 2022 and add its PV to
the PV of dividends from 2017 to 2022. Using the constant-growth DCF formula,
PV = 0.71 = 23.72 H .10- .07
The PV of dividends from 2017 to 2022 is $3.43 at the start of 2017, so share value is:3
6
PV = 3.43+ 23.72 = $16.82
(1.1)
The spreadsheet also calculates the PV of dividends through 2024 and the horizon
value at 2024. Notice that the PV at the start of 2017 remains at $16.82. This makes sense, since the value of a firm should not depend on the investment horizon chosen to calculate
PV. (If you calculate a value that does depend on the horizon, you have made a mistake.)
We have reduced ROE to the 10% cost of capital after 2022, assuming that Reeby
Sports will have exhausted valuable growth opportunities by that date. With PVGO = 0,
PV = EPS/r.4So we could discard the constant-growth DCF formula and just divide EPS
in 2023 by the cost of capital:
PVH = 2.37 = $23.72 .10
This PVis identical to the PV from the constant-growth DCF formula. It doesn’t matter
how fast a company grows after the horizon date H if it only earns its cost of capital.
How much of Reeby Sports’ value is due to PVGO?You can check by setting
ROE = .10 for 2018 and all later years.You should get PV = $13.82. Thus PVGO = 16.82
– 13.82 = $3.00 per share for investments made in 2017onward.
George Reeby has also identified a "comparable," Molly Sports. We could use its
P/E ratio of 13.1 to calculate horizon value in 2022 and PV at the start of 2017. Using
the original inputs for ROE, EPS in 2023 is 2.37.5
H
6
PV 13.1 2.37 $31.05
PV 3.43 31.05 $20.96
(1.10)
= ´ =
= + =
We couldalso use Molly’s P/E ratio to calculate Reeby Sports’ PV at the start of 2017
directly from 2017 EPS:
PV = 13.1 ´ 2.03 = $26.59

The Question is ?
Both values based on Molly’s P/E are higher than our DCF calculations. Is Molly
significantly more profitable than Reeby Sports, or does our spreadsheet understate
Reeby Sports’ prospects?
What if Reeby Sports could continue to earn ROE = .15 for two extra years, until
2024?You can check by changing ROE for 2023-2024 from .10 to .15. (The ROE for
2025 and 2026 is hard-wired at .10.)You should get NPV of $18.04, somewhat higher
than our original DCF calculations, but not enough for Reeby Sports to match Molly’s P/E.You may wish to experiment to find inputs that generate P/E = 13 for Reeby Sports
at the start of 2017. Do you think these inputs are reasonable?

Answer 1

Though both values based on Molly’s P/E ratio are higher than DCF calculations still it would not be correct to say that Molly is significantly more profitable than Reeby sport as the spreadsheet has certainly understated the prospects of Reeby Sports.

The prospects of Reeby Sports as presented in the spreadsheet has been made on the basis of past experience of the management and the future prospects of the entity. Thus, to change Return on Equity from 0.10 to 0.15 or even higher would not be a reasonable approach to calculate Net Present Value (NPV). Thus, the changes in the inputs without any significant reasons will not be a reasonable and correct approach to calculate NPV. Also the concept of prudence suggests that the prospects of a business organization should be conservative rather than extravagant as the concept of prudence suggests that it is always better to account for all possible losses but not all possible profits.