Suggested solution to case study – ACC7008
a) Find the appropriate cost of capital for the proposed combined firm. Clearly show all
calculations and state any assumptions you may have relied on for the calculation. (10 marks)
Answer a)
To value the acquisition, students need to estimate the appropriate weighted average cost of
capital (WACC) .
Calculation of WACC is straightforward using the following formula:
𝑅𝑤𝑎𝑐𝑐 =
𝐸
𝐷
𝑅𝐸 +
𝑅 (1 − 𝑇𝑐 )
𝐸+𝐷
𝐸+𝐷 𝐷
𝑅𝐷 is given as 5.0% in the question; most of the other elements of the above equation are also
given in the question including the corporate tax rate (Tc). However, one key element that
needs to be figured out is 𝑅𝐸 and this can be calculated using CAPM with beta for a levered
firm.
The question provides information on unlevered beta (1.21) and this can be used to find out
the levered beta (as applicable) using the following formula:
Beta_levered = 1.21 * [1+(1-0.27)]*(35/100)]
= 1.52
Now, finding cost of Equity using CAPM,
Cost of equity (using CAPM) = 3.5% + 1.52(8.5%)
= 16.41% appx
Students may also suggest using the capital structure of the target firm or the capital structure
of the combined firm immediately after the acquisition financing. They are free to assume
any other reasonable D/E ratio, with clear justifications, if they want.
Now WACC, can be calculated as follows
𝑅𝑤𝑎𝑐𝑐 =
𝐸
𝐷
𝑅𝐸 +
𝑅 (1 − 𝑇𝑐 )
𝐸+𝐷
𝐸+𝐷 𝐷
WACC = [(100/135)*16.41%] + [(35/135)*5%*(1-0.27)]
= 12.16% + 0.95%
= 13.1%
Alternatively, students could use the unlevered cost of equity, with clear justifications, if they
so desire. If TrueClean’s debt to equity ratio is used, the levered beta and cost of equity, and
in turn, WACC will be slightly different. This approach assumes that the book value and
market value of equity (and debt) is the same.
b) Assuming that the acquisition does not take place, calculate the present value of both the
firms. Clearly show all calculations and state any assumptions you may have relied on for the
calculation.
(20 marks)
Answer b
Find the free cash flows (FCF) of both the firms from the given tables, and then calculate the
PV at the WACC, as follows:
GREENCITY’s FCF:
Net sales
Operating profit
Net income
Depreciation and amortization
Change in net working capital
Capital expenditure
Total FCF
FCF
Terminal value
PV (GREENCITY)
3.7
$61.1
2024
1,246.4
22.4
16.4
6.6
6.8
12.5
3.7
2025
1,322.4
23.8
17.4
7.0
5.7
13.2
5.5
5.5
5.8
2026
1,403.0
25.3
18.4
7.5
6.0
14.0
5.8
6.2
2027
1,488.6
26.8
19.6
7.9
6.4
14.9
6.2
6.5
$78.2
2028
1,579.4
28.4
20.8
8.4
6.8
15.8
6.5
6.8
4.4% growth in FCF
TrueClean’s FCF:
2022
2023
2024
2025
2026
Net sales
578.5
608.0
639.0
671.6
705.9
Operating profit
29.5
31.0
32.6
34.3
36.0
Interest expense
0.6
0.6
0.6
0.6
0.6
Net income
21.1
22.2
23.4
24.6
25.8
Depreciation and amortization
10.2
10.5
10.8
11.1
11.4
Change in net working capital
2.3
1.6
1.7
1.8
1.8
Capital expenditure
14.5
15.2
16.0
16.8
17.6
Total FCF*
14.9
16.3
16.9
17.5
18.1
* note that interest expense (after tax) is added back as it will be accounted for by WACC
FCF (without acquisition)
14.9
Terminal value (without acquisition)
PV (TrueClean without acquisition)
$175.7
16.3
16.9
17.5
18.1
18.9
4.4% growth
$217.6
c) Assuming that the acquisition does take place, calculate the present value of both the firms.
Clearly show all calculations and state any assumptions you may have relied on for the
calculation.
(60 marks)
Take into account the information about the change in cash flows if the acquisition goes
ahead, for both the firms.
WACC
Revenue growth
Operating margin
Net WC
Capex
Revenue
Operating profits
Taxes
NOPAT
Depreciation and amortization
Net WC
Chg in net WC
Capex
FCF
Terminal value
PV (GreenCity)
Revenue growth
Gross margin
Operating expenses
Capex
Revenue
2024
2025
2026
2027
2028
13.10%
13.10%
13.10%
13.10%
13.10%
6.1%
3.5%
6.0%
1.0%
1246.4
43.6
11.8
31.8
6.6
74.8
-11.9
12.5
37.9
6.1%
3.5%
6.0%
1.0%
1322.4
46.3
12.5
33.8
7.0
79.3
4.6
13.2
23.0
6.1%
3.5%
6.0%
1.0%
1403.0
49.1
13.3
35.8
7.5
84.2
4.8
14.0
24.4
6.1%
3.5%
6.0%
1.0%
1488.6
52.1
14.1
38.0
7.9
89.3
5.1
14.9
25.9
6.1%
3.5%
5.5%
1.0%
1579.4
55.3
14.9
40.4
8.4
86.9
-2.4
15.8
35.4
4.0% growth per year
$404.2
$321.7
-5.0%
9.0%
1.8%
2.0%
522.9
-5.0%
9.0%
1.8%
2.0%
496.8
10.0%
9.0%
1.8%
2.0%
546.5
10.0%
9.0%
1.8%
2.0%
601.1
10.0%
9.0%
1.8%
2.0%
661.2
Gross profits
Operating profit
Taxes
NOPAT
Depreciation and amortization
Chg in net WC
Capex
FCF (with acquisition)
47.1
27.5
7.4
20.1
10.2
2.3
10.5
17.4
Terminal value (with acquisition)
PV (TrueClean with acquisition)
$207.6
44.7
25.3
6.8
18.5
10.5
1.6
9.9
17.4
49.2
28.6
7.7
20.9
10.8
1.7
10.9
19.0
54.1
32.2
8.7
23.5
11.1
1.8
12.0
20.8
59.5
36.2
9.8
26.5
11.4
1.8
13.2
22.7
4.0% growth
$259.9
d) Evaluate the attractiveness of the proposed acquisition to the shareholders of both the
companies - based on your calculations - and make a recommendation to Qiang if the
acquisition should go ahead.
(10 marks)
This answer should be based on the answers of the previous questions. Based on the
following summary table, the acquisition seems to add value to shareholders:
a PV of GreenCity's CF after acquisition
b Less: PV of GreenCity's CF pre-acquisition
c Value created in acquisition
321.7
61.1
260.6
d PV of TrueClean's CF after acquisition
e Less: PV of TrueClean's CF pre-acquisition
f Value created in acquisition
207.6
175.7
31.9
g Total value created in acquisition (c + f)
292.5
h Share of value allocated to GreenCity's s/h ($250 - b)
188.9
i Share of value allocated to TrueClean's s/h (g - h)
103.6
Comments are expected on how the value is allocated to shareholders of both the companies.
As is normal in acquisition transactions, most of the value created in the target company goes
to the shareholders of the target company.