Question

a) You are the owner of a firm that currently generates revenues of £1 million per year. Next year, revenues will either decrease by 8% with 60% probability or increase by 10% with 40% probability and then stay at that level for as long as you run the business. You own the firm outright. Also, you have annual costs of £700,000. If you decide to shut down the firm the cost is zero. In that case, you can always sell the firm for £600,000. What is the business worth today if the cost of capital is 12%? [15 marks]

b) Zweite Pharma is a fast-growing company. The company forecasts that in the next three years its growth rates will be 30%, 28% and 24% respectively. After three years, the company expects a more stable growth of 8% that will last forever. Last week it declared a dividend of £1.67. The required rate of return is 14%.

i) Compute the dividends for the next three years and find their present value.

ii) Calculate the price of the shares at the end of year 3 when the firm settles to a constant growth.

iii) What is the current price of the shares?

Answer 1

Answer (a):

Year 0: Current sale value = £600,000

Perpetual expected annual cash flow = 60%*(1000000 * (1- 8%) - 700000) + 40% * (1000000 * (1 + 10%) - 700000)

= 292000

Present value of perpetual expected cash flows = 292000 / 12% =  £2433333.33

Worth of business today = £2433333.33 - 600000 = £1,833,333.33

Worth of business today = £1,833,333.33

Answer (b):

(i)

D0 = £1.67

D1 =  £1.67 * (1 + 30%) = 2.171

D2 = 2.171 * (1 + 28%) = 2.77888

D3 = 2.77888 *(1 + 24%) = 3.4458112

Present value = 2.171 / (1 + 14%) + 2.77888 / (1 + 14%)^2 + 3.4458112 / (1 + 14%)^3 = 6.368468

Hence:

D1 =  £2.17

D2 =  £2.78

D3 =  £3.45

Their present value =  £6.37

(ii)

P3 = D4 / (Required rate of return - Constant growth rate) = 3.4458112 *(1 + 8%) / (14% - 8%) = £62.0246

Hence:

Price of the shares at the end of year 3 = £62.02

(iii)

Current price of the shares = PV of dividends of year 1, 2 and 3 + PV of Price of the shares at the end of year

= 6.368468 + 62.0246 / (1 + 14%)^3

= £48.23

Current price of the shares = £48.23