Question

4. Tiny plc is a stable growth, publicly traded company, expected to grow 2% a year in perpetuity. It has a cost of equity of 10% and is expected to pay out a. Estimate the "intrinsic" PE ratio for the company. (2.5 marks) b. The company has 100 million shares and 10 million management options outstanding; the options have a value of £5 per option. If the firm is expected to earn £50 million in net income next year, estimate the fair value per share, based upon the PE ratio you estimated in part a. (2.5 marks) 5. A firm is offered the right to manufacture a widget. The factory can be built instantaneously at a cost of $2,000 and will produce 1 widget per year in perpetuity. There are no operating costs and current price of widget is $200. The discount rate is 10%. Next year, the price will either be $300 or $100 with equal probabilities and will remain there forever. What is the maximum price the firm would be willing to pay for this right? (5 marks)

Answer 1

Values given are:

D/E(Dividend Payout Ratio) = 80%

k(Cost of Equity/Required rate of return on stock) = 10%

g(growth rate) = 2%

a. As per the Gordon growth valuation model

P D/E -9 0.8 (0.1 -0.02) E k -0.02) = 10

b.

Outstanding shares = 100 million

Earnings = 50 million

EPS( Earnings per share) = Earnings / Outstanding Shares = 50 / 100 = 0.5

Now as per the P/E ratio calculated above

P/E = Price / EPS

Therefore, Price = (P/E) * EPS = 10 * 0.5 = 5

5.

Given values are

Initial Outlay cost = $ 2000

Income from the Widget in year 1 = $ 200

Discount Rate = 10%

Now we will have two scenarios with the price either becoming $100 or $300

The perpetuity value can be calculated using Gordon Growth Model

Income Cost – Growth Rate

Growth rate is Zero as only one equipment can only be made for every year for remaining time frame and price will also remain constant

Value when price is $ 100

Value = 100/0.1 = $ 1000

Value when price is $ 300

Value = 300/0.1 = $ 3000

Now we will discount the future cash flows using the discounting factors to calculate the present value

Present Value when price is $ 100

PV = -2000 + 100 1. 1 1000 + 100 1 .12

PV = -2000 + 90.9 + 909 = -1000

Present Value when price is $ 100

300 PV = -2000 + 3000 + 300 1.12

PV = -2000 + 272.72 + 2727.27 = 1000

Hence as we can see the Maximum price the firm should be willing to pay for this widget should be $ 1000 considering the price to be $ 300 after one year