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Finance I: Tutorial
Six
SOLUTIO
NS
[The internal rate of return on investments can be designated as i or k – these are
interchangeable. In these questions i is given as IRR]
Valuation Models
Q1. Gordon Model Given the Gordon constant rate of growth of dividends model:
P 0 =
Where b is the retention ratio
D 1
r − g
E 1 ( 1 −
b )
r − ib
i is the rate of return on new investment undertaken by the frm
D 1 the^ dividend^ per^ share^ expected^ in^ period^ one E 1 the^ earnings^ per^ share^ expected^ in^ period^ one a) What will be the value of a share if the next dividend is expected to be 40p, the dividends are expected to grow at 6 per cent per annum, and the shareholders’ required rate of return is 10 per cent.
Use the most basic form of the model
P = D
0 1 =^1 ,
r − g 0.10 − 0.06.
b) If the company retains 60 per cent of earnings what rate of return on the investment fnanced by retentions is necessary to produce an expected rate of growth of 6 per cent?
growth rate
G
retention rate times rate of return on
investment b x k
rate of
return
K
growth rate / retention rate
g/b
The rate of return on investment is being assumed (implicitly) to be
equal to 10 per cent.
2 c) Determine the price for the share that can be expected at the end of the frst year, and the capital gain yield that this implies.
At the end of the frst year the same basic model can be applied with
appropriate adjustments to the inputs: the next expected dividend will be
higher (D 2 > D 1 ) but the required rate of return (r) and the expected rate
of growth (g) will remain unchanged.
P 1 = D
2
r − g
P
= D
0 1 =^1 ,
r − g 0.10 − 0.05 0.
There is no change in the price despite the lower rate of growth. The
immediate increase in the dividend offsets the lower rate of growth of
dividends the short term increase in dividends balances off the longer
term fall in dividends.
0
g
= i
× b = 0.08 × 0.60 = 0.
P
Compare this price with that if the company pays out all of its earnings as dividends (P 0 = 1,000). Even though growth of 4.8 per cent is expected it adds nothing to value – indeed it destroys value. Achieving this rate of growth through investments yielding no more than 8 per cent reduces the share price by 23 per cent (from 1,00 0 p to 769p). Growth is not necessarily desirable: the critical factors in determining value are the rate of return on new investment and the level of this investment. h) The value of a share depends on the dividends that the company is expected to pay its shareholders. Can a company increase the value of its shares by increasing the proportion of its earnings paid out as dividends? Dividend policy is irrelevant to the extent that the frm can employ outside fnancing instead of retentions. The critical determinant of value are the earnings that the company is expected to produce from existing assets and the proftability and scale of its anticipated investment programme. Q2. RST Company The price earnings ratio for the RST company is well above average for the stock market, reflecting its market standing as a growth company. The earnings performance of the company in recent years has not disappointed its shareholders. Earnings have grown at an average rate of 20 per cent over the last fve years. Whilst this has been partly the result of the high level of retentions, the company has consistently reinvested 80 per cent of its earnings, the high proftability of new investment has also played a role. Now competition is intensifying and the rate of return on new assets is expected to fall over the next few years. Investments undertaken next year are expected to yield 22 per cent, those started in the following year 18 per cent, those in year three 12 per cent, and by year four investments are expected to generate no more than the minimum rate of return required by shareholders of 10 per cent. Earnings next year are expected to be £6 million and the company is expected to reinvest 80 per cent of earnings as in the past few years. After this, retentions will be reduced as investment opportunities diminish: 60 per cent in year two, 40 per cent in year three, and 20 per cent, which is expected to be the average in the longer term. a) Estimate the current value of the company. Year Earnings Payout Ratio Dividend Retention Rate of Return NPV Incremental E a r
nings Next Period Earnings 1 6 0.8 1.2 4.8 0. 22 5. 76 1. 056 7. 056 2 7. 056 0.6 2. 8224 4. 2336 0. 18 3. 38688 0. 762048 7. 818048 3 7. 818048 0.4 4. 690829 3. 1272192 0. 12 0. 62544
- 37526630 4 8. 193314 3 4
- 19331430 4 0.2 6. 554651 1. 6386629 0.1 0
- 16386628 6
- 3571805 9
- All investments are fnanced from retentions
- The rate of return on new investments and the proportion of
earnings retained is
constant from year 4 in perpetuity.
Q3. Cymru Mining Plc Cymru Mining Plc’s reserves of coal are being depleted, and its costs in recovering coal are increasing each year as it fnds it necessary to work more difficult seams. This implies that the company’s earnings are declining by 6 per cent per annum. Earnings for next year are anticipated to be about £8m. The required rate of return on minimum is 14 per cent. Determine a value for the company.
As the company’s business is being run down it is reasonable to assume that
all of the earnings are paid out as dividends. If dividends are falling over
time at a constant rate the share price can be shown to be given by
P = D
0 1
r + d
Where d is the rate of decline (and can be interpreted as negative growth).
V = P N = D
= £8 m^
0 0 0 1 =^ £4^0 m
(This assumes that the depreciation charge employed in calculating earnings
represents the sum required for replacement investment to maintain the
ability of the company to limit the rate of decline of earnings to 6 per cent).
The £40 million is a reasonable starting point for further analysis that could
take into account further details of the nature of the business. If the
company’s liquidation value – based on the sale of land, machinery, etc. less
redundancy payments is higher than £40 million a case can be made for its
immediate closure if management in the interests of the shareholders.
