Valuing shares, earnings and dividends

Corporate Finance 33

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

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

Valuation using net asset value (NAV)

Source: Pearson plc, Annual Review 2006.

Net asset values and total capitalisation of some firms

Source: Annual reports and accounts; www.advfn.com 7.5.07.

What creates value for shareholders?

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

The dividend valuation models

•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 gainP0 = –––––– + ––––––

d1 P1

1 + kE 1 + kE

Worked example

•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.

P0 = –––––– + –––––– d1 P1

1 + kE 1 + kE

P0 = –––––– + –––––– = 221p 22 243

1 + 0.2 1 + 0.2

The dividend valuation model to infinity

P1 = –––––– + –––––– d2 P2

1 + kE 1 + kE

P0 = –––––– + –––––– d1 P1

1 + kE 1 + kE

P0 = –––––– + –––––– + ––––––– d1 d2 P2

1 + kE (1 + kE)2 (1 + kE)2

P0 = –––––– + –––––– + ––––––– + … + ––––––– d1 d2 d3 dn

1 + kE (1 + kE)2 (1 + kE)3 (1 + kE)n

Worked example

•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:

P0 = –––––– + –––––––– + –––––––– + … + ––––––– 20 20 20 20

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:

P0 = –––––– = –––––– = 166.67pd1 20

kE 0.12

The dividend growth model

•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 = 11.45pd0 (1 + g) d0 (1 + g)2 d0 (1 + g)3 d0 (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

kE – g kE – g 0.11 – 0.07

d1 d0 (1 + g) 10.7P0 = –––––– + –––––––– = –––––––––– = 267.50p

Pearson plc

Ö29.3––––– – 1 = 0.062 or 6.2%16.1

g =10

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

kE – g 0.10 – 0.062

d1 29.3 (1 + 0.062)P0 = –––––– = ––––––––––––– = 819p

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

Noruce

Stage 2 Calculate share price at time 3 when the dividend growth rate shifts to the new permanent rate.

kE – g kE – g 0.16 – 0.07

d4 d3 (1+g) 21.1 (1 + 0.07)P3 = –––––– + –––––––– = ––––––––––––– = 250.9

Stage 3 Discount and sum the amounts calculated in Stages 1 and 2.

1 + kE 1 + 0.16

d1 16.8 –––––––– = ––––––––– = 14.5

(1 + kE)2 (1 + 0.16)2

d2 18.8 + –––––––– = ––––––––– = 14.0

(1 + kE)3 (1 + 0.16)3

d3 21.1 + –––––––– = ––––––––– = 13.5

(1 + kE)3 (1 + 0.16)3

P3 250.9 + –––––––– = ––––––––– = 160.7

202.7p

Issues with DGM

•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

kE – g 0.095 – 0.08

d0 (1 + g) 24.2 (1 + 0.08)P0 = ––––––––– = ––––––––––––– = 1,742p

– 2 The quality of input data is often poor

– 3 If g exceeds kE a nonsensical result occurs

e.g. Pearson:

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

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

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.

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

The crude and the sophisticated use of the PER model

•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

kE – g

d0 P0 = –––––––

kE – g

d1/E1 = –––––––

P0

E1

Ridge plc

•Payout ratio of 48 per cent of earnings•Discount rate 14 per cent •Expected growth rate 6 per cent

kE – g

d1/E1 = –––––––

P0

E1

0.14 – 0.06

0.48 = –––––––––––– = 6

P0

E1

• Now assume a kE of 12 per cent and g of 8 per cent

0.12 – 0.08

0.48 = –––––––––––– = 12

P0

E1

• If kE becomes 16 per cent and g 4 per cent then the PER reduces to two-thirds of its former value:

0.16 – 0.04

0.48 = –––––––––––– = 4

P0

E1

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%

kE – g 0.16 – 0.10

d1/ E1 0.5 = –––––– = ––––––––––––– = 8.33

P0

E1

Prospective PERs for various risk classes and dividend growth rates

A comparison of the crude PER and the more complete model

Lecture review

•Valuation using NAV

•The dividend valuation models

•Growth rate

•Price-earnings ratio model