Valuing shares, earnings and dividends

1. Valuing shares, earnings and dividends Corporate Finance 33

2. Valuing shares: assets, dividends and earnings • The principal determinants of share prices • Estimate share value using a variety of approaches • The most important input factors • Net asset valuation • Dividend valuation models • Price earning ratio models

3. Share valuation: the challenge • Two skills are needed to be able to value shares: • 1 Analytical ability, to be able to understand and use mathematical valuation models • 2 Good judgement is needed • Assets such as cars and houses are difficult enough to value with any degree of accuracy • Corporate bonds generally have a regular cash flow (coupon) and an anticipated capital repayment • With shares there is no guaranteed annual payment and no promise of capital repayment

4. Valuation using net asset value (NAV) Source: Pearson plc, Annual Review 2006.

5. Net asset values and total capitalisation of some firms Source: Annual reports and accounts; www.advfn.com 7.5.07.

6. What creates value for shareholders?

7. When asset values are particularly useful • Firms in financial difficulty • Takeover bids • When discounted income flow techniques are difficult to apply • 1 Property investment companies • 2 Investment trusts • 3 Resource-based companies

8. The dividend valuation models d1P1 P0 = –––––– + –––––– 1 + kE 1 + kE • The market value of ordinary shares represents the sum of the expected future dividend flows, to infinity, discounted to present value • The only cash flows that investors ever receive from a company are dividends. • An individual holder of shares will expect two types of return: • (a) income from dividends • (b) a capital gain

9. Worked example 22 243 P0 = –––––– + –––––– = 221p 1 + 0.2 1 + 0.2 • At the end of one year a dividend of 22p will be paid and the shares are expected to be sold for £2.43 • The rate of return required on a financial security of this risk class is 20 per cent. d1P1 P0 = –––––– + –––––– 1 + kE 1 + kE

10. The dividend valuation model to infinity d2P2 d1P1 P1 = –––––– + –––––– P0 = –––––– + –––––– d1d2 P2 d1d2 d3 dn P0 = –––––– + –––––– + ––––––– P0 = –––––– + –––––– + ––––––– + … + ––––––– 1 + kE 1 + kE 1 + kE 1 + kE 1 + kE (1 + kE)2 (1 + kE)2 1 + kE (1 + kE)2 (1 + kE)3 (1 + kE)n

11. Worked example d1 20 P0 = –––––– = –––––– = 166.67p kE 0.12 • If a firm is expected to pay dividends of 20p per year to infinity and the rate of return required on a share of this risk class is 12 per cent then: 20 202020 P0 = –––––– + –––––––– + –––––––– + … + ––––––– 1 + 0.12 (1 + 0.12)2 (1 + 0.12)3 (1 + 0.12)n P0 = 17.86 + 15.94 + 14.24 + ... + ... + Given this is a perpetuity there is a simpler approach:

12. The dividend growth model d1d0 (1 + g) 10.7 P0 = –––––– + –––––––– = –––––––––– = 267.50p kE – gkE – g 0.11 – 0.07 • If the last dividend paid was d0 and the next is due in one year, d1, then this will amount to d0 (1 + g). Shhh plc has just paid a dividend of 10p and the growth rate is 7 per cent then: d1 will equal d0 (1 + g) = 10 (1 + 0.07) = 10.7p d2 will be d0 (1 + g)2 = 10 (1 + 0.07)2 = 11.45p d0 (1 + g) d0 (1 + g)2d0 (1 + g)3d0 (1 + g)n P0 = ––––––-- + –––––––– + –––––––– + … + –––––––– (1 + kE) (1 + kE)2 (1 + kE)3 (1 + kE)n 10 (1 + 0.07) 10 (1 + 0.07)2 10 (1 + 0.07)3 10(1 + 0.07)n P0 = –––––––––– + –––––––––– + –––––––––– + … + –––––––––– 1 + 0.11 (1 + 0.11)2 (1 + 0.11)3 (1 + 0.11)n

13. Pearson plc Ö 10 29.3 g = ––––– – 1 = 0.062 or 6.2% 16.1 If it is assumed that this historic growth rate will continue into the future (a big if) and 10 per cent is taken as the required rate of return d1 29.3 (1 + 0.062) P0 = –––––– = ––––––––––––– = 819p kE – g 0.10 – 0.062

14. Non-constant growth • Noruce plc has just paid an annual dividend of 15p per share and the next is due in one year • For the next three years dividends are expected to grow at 12 per cent per year • After the third year the dividend will grow at only 7 per cent per annum • Expected return of 16 per cent per annum Stage 1 Calculate dividends for the super-normal growth phase. d1 = 15 (1 + 0.12) = 16.8 d2 = 15 (1 + 0.12)2 = 18.8 d3 = 15 (1 + 0.12)3 = 21.1

15. Noruce 202.7p d2 18.8 P3 250.9 d3 21.1 d1 16.8 + –––––––– = ––––––––– = 160.7 + –––––––– = ––––––––– = 14.0 + –––––––– = ––––––––– = 13.5 –––––––– = ––––––––– = 14.5 (1 + kE)3 (1 + 0.16)3 (1 + kE)3 (1 + 0.16)3 (1 + kE)2 (1 + 0.16)2 1 + kE 1 + 0.16 d4d3 (1+g) 21.1 (1 + 0.07) P3 = –––––– + –––––––– = ––––––––––––– = 250.9 kE – gkE – g 0.16 – 0.07 Stage 2 Calculate share price at time 3 when the dividend growth rate shifts to the new permanent rate. Stage 3 Discount and sum the amounts calculated in Stages 1 and 2.

16. Issues with DGM d0 (1 + g) 24.2 (1 + 0.08) P0 = ––––––––– = ––––––––––––– = 1,742p kE – g 0.095 – 0.08 • What is a normal growth rate? • Companies that do not pay dividends • Problems with dividend valuation models • 1 They are highly sensitive to the assumptions e.g. Pearson: • 2 The quality of input data is often poor • 3 If g exceeds kE a nonsensical result occurs

17. Forecasting dividend growth rates – g • Determinants of growth • 1 The quantity of resources retained and reinvested within the business • 2 The rate of return earned on those retained resources • 3 Rate of return earned on existing assets

18. Growth • Focus on the firm • 1 Strategic analysis • 2 Evaluation of management • 3 Using the historical growth rate of dividends • 4 Financial statement evaluation and ratio analysis • Accounts have three drawbacks: (a) they are based in the past (b) the fundamental value-creating processes within the firm are not identified and measured in conventional accounts, (c) they are frequently based on guesses, estimates and judgements • Focus on the economy

19. The price-earnings ratio (PER) model Current market price of share 200p Historic PER = ––––––––––––––––––––––––––– = ––––– = 20 Last year’s earnings per share 10p Source: Financial Times, 5 May 2007. Reprinted with permission.

20. PERs for the UK and US (S&P 500) stock markets, 1964–2007

21. The crude and the sophisticated use of the PER model d0 d1/E1 P0 = ––––––– = ––––––– kE – g kE – g P0 E1 • Some analysts use the historic PER (P0/E0), to make comparisons between firms • Analysing through comparisons lacks intellectual rigour • The assumption that the ‘comparable’ companies are correctly priced is a bold one • It fails to provide a framework for the analyst to test the important implicit input assumptions

22. Ridge plc d1/E1 = ––––––– kE – g P0 P0 P0 0.48 0.48 0.48 = –––––––––––– = 12 = –––––––––––– = 6 = –––––––––––– = 4 E1 E1 E1 0.14 – 0.06 0.16 – 0.04 0.12 – 0.08 P0 E1 • Payout ratio of 48 per cent of earnings • Discount rate 14 per cent • Expected growth rate 6 per cent • Now assume a kE of 12 per cent and g of 8 per cent • If kE becomes 16 per cent and g 4 per cent then the PER reduces to two-thirds of its former value:

23. Whizz plc • Earnings per share rise by 10 per cent per annum • Prospective price earnings ratio (PER) of 25 • Beta of 1.8, Risk premium 5 per cent, Current risk-free rate of return is 7 per cent kE = rf + β (rm – rf) kE = 7 + 1.8 (5) = 16% P0 d1/E1 0.5 = –––––– = ––––––––––––– = 8.33 E1 kE – g 0.16 – 0.10

24. Prospective PERs for various risk classes and dividend growth rates

25. A comparison of the crude PER and the more complete model

26. Lecture review • Valuation using NAV • The dividend valuation models • Growth rate • Price-earnings ratio model