FCF and FCFE method

Question

Wmart Co plans to make a bid for the entire share capital of Ada Co, a company in the same
industry. It is expected that a bid of $75m for the entire share capital of Ada Co will be successful.
The acquisition will generate the following after-tax operating cash flows (ie pre-interest) over the
next few years by:
Year $m
1 5.6
2 7.4
3 8.3
4 onwards 12.1
Both companies have similar gearing levels of 16.7% (debt as a % of total finance).
Ada Co has a $15 million bank loan paying a fixed rate of 5.75%.
Wmart Co has an equity beta of 2.178, the risk-free rate is 5.75% and the market rate is 10%.
Corporation tax is at 30%.
Required
Assess whether the acquisition will enhance shareholder wealth in Wmart Co. (Use both Approach 1
and Approach 2.)

Answer –
Approach 1

Time 1 2 3 4 onwards
$m 5.6 7.4 8.3 12.1
Annuity (1/0.13) 7.692
Value at time 3 93.1
@ 13% 0.885 0.783 0.693 0.693

PV 5.0 5.8 5.8 64.5

Total PV 81.1
Less debt (15.0)

Value of equity 66.1 This suggests that the target is not worth $75m

Ke (using CAPM) 5.75 + 2.178 (10 – 5.75) = 15.0%
Kd ? (1 – t) 5.75% ? 0.7 = 4.03%
WACC = (15 ? 0.833) + (4.03 ? 0.167) = 13.2% (rounded to 13%)

Approach 2
Interest p.a. = $0.6m after tax ($15m ? 0.0575 ? 0.7)
Time 1 2 3 4 onwards
$m after interest 5.0 6.8 7.7 11.5
Annuity (1/0.15) 6.667
Value at time 3 76.7
Ke = 15% 0.870 0.756 0.658 0.658

PV 4.4 5.1 5.1 50.5

Value of equity 65.1

(as Approach 1 except for a small rounding difference) since we used 13.0%
in Approach 1 instead of 13.2%

How did we get 0.833 in the calculation of WACC ?