Question

Big plc is planning on making a bid to takeover Small Ltd. They are both in the same industry and have similar gearing levels of 20% (where gearing is debt as a percentage of total finance).

Big plc has estimated that the takeover will increase its annual cash flows by the following amounts:

Year After-tax (but before interest) cash flows£m

2015 6.4

2016 9.1

2017 11.5

2018 onwards 12.5

Small Ltd has 7% irredeemable debentures of £21 million trading at par.

The risk-free rate is 7% and the market rate is 12%. Big plc’s equity beta is 2.3 and the corporation tax rate is 30%.

what is the value of equity for Small Ltd using the Free Cash Flow to Firm methodology？

Answer 1

Computation of Value of Equity by FCFF methodology

Step 1- Computation of Discount rate

Discount rate that should be used for valuing Small Ltd. is the Weighted Average Cost of capital

WACC = Weight of Debt x Cost of Debt (after tax) + Weight of Equity x Cost of Equity (refer note 1)

= 0.20 x 7 x (1-0.30) + 0.80 x 18.5

= 15.78%

Step 2- Computation of Present Value of Free Cash Flow for Firm

Year	Free cash flow	Discounting Factor @ 15.78%	Present Value
2015	6.4 m	0.863	5.5232 m
2016	9.1 m	0.746	6.7886 m
2017	11.5m	0.644	7.406 m
		Total	19.7178 m

Cash Flow From 2018 onwards = 12.5 m

Value of Cash Flows From 2018 onwards at the end of 2017 = 12,5/0.1578

= 79.2142 m

Present value of 79.2142 m = 79.2142/(1.1578)3

  = 51.0390 m

Step 3 - Computation of Value of Firm

Value of firm = 19.7178 + 51.0390

= 70.7568 m

Step 4 - Computation of Value of Equity

Value of Equity

= Value of Firm - Value of Debt

= 70.7568 - 21

= 49.7568 m

Note 1

Cost of Equity (as per CAPM model)

= Risk Free Interest Rate + (Market Rate - Risk Free Interest Rate) x Beta of Firm

= 7+ (12-7) x 2.3

= 18.5%

Note 2

As both the firms have same gearing levels, so they both shall have the same beta.