Question

ABC Limited is a private company located in Nairobi County. The company manufactures and
sells various products. You have been tasked with the assignment of valuing the private firm
using discounted cash flow approach. You have been provided with the following information
for the company and that of ten similar firms in the industry.
(i) Data for ABC limited for the most recent period
YEAR 2019
Revenues Sh. 30 Million
Earnings Before Interest and Tax Sh. 10 Million
Capital Expenditure Sh. 4 Million
Working Capital Investment Sh. 2 Million
Depreciation Sh. 2 Million
(ii) Corporate tax rate relevant for ABC limited is 25%. The before tax cost of debt of ABC ltd.
is 10 %
(iii) Extracts from the statement of financial position of ABC limited is as shown below
YEAR 2019
Ordinary Share Capital (Sh. 1.5 Par value) Sh. 150 Million
Borrowings Sh. 75 Million
(iv) The average beta of ten comparable companies in the same industry as ABC limited is 1.5
based on market value of debt and equity.
(v) On average, market value of equity is twice the book value whereas market value of debt equals to the book value.
(vi) The average debt equity ratio of the industry is 0.45

(vii) Average return on market and risk free rate of return is 12 % and 7 % respectively.
Additional information:
The firm expects Revenues, Earnings before Interest and Taxes, Capital Expenditure, Investment
in Working Capital and Depreciation to grow at an annual rate of 6 % each year for 20 years.
After the twenty year growth period the growth in Revenues, Earnings before Interest and Taxes
and Investment in Working Capital will decline to stable 3 % each year into the foreseeable
future. During the steady state period, capital expenditure and Non-cash charges will offset each
other.
Required:
(a) Compute Free cash flow to ABC limited for year 2019
(b) Compute weighted average cost of Capital
(c) Compute Terminal value for ABC limited
(d) Compute the value of operations of ABC limited

Answer 1

a) Free cash flow (FCF2019) to ABC limited for year 2019:

FCF2019 = EBIT*(1-tax rate) + Depreciation - capital expenditure - Net working investment

= 10million*[1-0.25] - 4million + 2million - 2million = 10million*0.75 - 4million

= 7.5million - 4million

= 3.5million

b) Weighted average cost of Capital:

Average debt equity ratio of the industry = 0.45

Average beta of ten comparable companies in the same industry = 1.5

Beta (Unlevered) = 1.5/{1+[(1-0.25)*0.45/1]}

Beta (Unlevered) = 1.5/[1+(0.75*0.45)]

Beta (Unlevered) = 1.5/(1+0.3375)

Beta (Unlevered) = 1.5/1.3375

Beta (Unlevered) = 1.1215

For ABC limited, Market value of equity = Twice the book value = 2*150million = 300million

Market value of debt = book value = 75million

Debt-equity ratio = 75million/300million = 0.25

Beta (Levered) = Beta(Unlevered)*[1+(1-tax)Debt/equity]

Beta (Levered) = 1.1215*[1+(1-0.25)*0.25]

Beta (Levered) = 1.1215*[1+(0.75*0.25)]

Beta (Levered) = 1.1215*(1+0.1875)

Beta (Levered) = 1.1215*1.1875

Beta (Levered) = 1.33

Cost of equity = risk free rate +[(average return on market - risk free rate)*Beta of ABC limited]

Cost of equity = 7% +[(12%-7%)*1.33]

= 7%+(5%*1.33)

= 7%+6.65%

= 13.65%

Cost of debt after tax = Cost of debt*(1-tax) = 10%*(1-0.25) = 10%*0.75 = 7.5%

WACC = [(Cost of debt after tax*0.25)+(Cost of equity*1)]/1.25

WACC = [(7.5%*0.25)+(13.65%*1)]/1.25

WACC = [1.875%+13.65%]/1.25

WACC = 15.525%/1.25

WACC = 12.42%

c) Terminal value for ABC limited after 20years:

EBIT after 20years = 10million*(1+growthrate)^20

= 10million*(1+0.06)^20 = 10million*(1.06)^20 = 10million*3.2071354 = 32,071,354

Working capital after 20years = 2million*(1+growthrate)^20

= 2million*(1+0.06)^20 = 2million*(1.06)^20 = 2million*3.2071354 = 6,414,271

Note:After 20years capital expenditure & noncash expenditure offset each other, so no need to compute it for terminal value purpose.

Free cash flow after 20years = EBIT*(1-tax rate) - Working capital

= 32,071,354*(1-0.25) - 6,414,271

= 32,071,354*0.75 - 6,414,271

= 24,053,515.5 - 6,414,271

= 17,639,244.50

Terminal value = Free cash flow after 20years*(1+stable growthrate)/WACC

Terminal value = 17,639,244.50*(1+0.03)/0.1242

Terminal value = 17,639,244.50*1.03/0.1242

Terminal value = 18,168,421.84/0.1242

Terminal value = 146,283,589.70

d) Value of operation of ABC limited:

Note: For first 20years, free cash flow expected to grow 6% each year.

Year	FCF	Present value factor	Discounted FCF
1	3.5million*(1.06) = 3,710,000	0.8895	3,300,125
2	3.5million*(1.06)^2 = 3,932,600	0.7912	3,111,663
3	3.5million*(1.06)^3 = 4,168,556	0.7038	2,933,965
4	3.5million*(1.06)^4 = 4,418,669.36	0.6261	2,766,414
5	3.5million*(1.06)^5 = 4,683,789.52	0.5569	2,608,432
6	3.5million*(1.06)^6 = 4,964,816	0.4954	2,459,471
7	3.5million*(1.06)^7 = 5,262,705	0.4407	2,319,018
8	3.5million*(1.06)^8 = 5,578,468	0.3920	2,186,585
9	3.5million*(1.06)^9 = 5,913,176	0.3487	2,061,715
10	3.5million*(1.06)^10 = 6,267,966	0.3101	1,943,976
11	3.5million*(1.06)^11 = 6,644,044	0.2759	1,832,961
12	3.5million*(1.06)^12 = 7,042,687	0.2454	1,728,285
13	3.5million*(1.06)^13 = 7,465,248	0.2183	1,629,588
14	3.5million*(1.06)^14 = 7,913,163	0.1942	1,536,526
15	3.5million*(1.06)^15 = 8,387,953	0.1727	1,448,780
16	3.5million*(1.06)^16 = 8,891,230	0.1536	1,366,044
17	3.5million*(1.06)^17 = 9,424,704	0.1367	1,288,033
18	3.5million*(1.06)^18 = 9,990,187	0.1216	1,214,477
19	3.5million*(1.06)^19 = 10,589,598	0.1081	1,145,121
20	3.5million*(1.06)^20 = 11,224,974	0.0962	1,079,726
20	146,283,589.70	0.0962	14,072,481
	Value of the ABC limited		54,033,385