Question $1$

DML Lifestyle Ple $($DMIL$),$ a listed company, employs an external growth strategy that involves acquiring new businesses in its industry. The directors of DML have identified a target company for acquisition: Wigs Lair

Ghana Ltd $($Wigs Lair$).$ Wigs Lair is a growing private company that deals in hair and beauty products.

You have been engaged to value the ordinary stock of Wigs Lair to inform the directors of DML of the appropriate consideration DML should offer for $45\%$ of the equity stake in Wigs Lair. You have gathered the information below for the valuation exercise:

Exhibit A: Financial results of DML and Wigs Lair

Sales revenue

Cost of sales

Gross margin

Operating expenses

Earings before interest and tax $($EBIT$)$

Less interest expense

Net income before tax

Tax

Net income

Noncurrent assets

Current assets

Total assets

Current liabilities

Long$-$term debt

Total liabilities

Stated capital

Retained earnings

Shareholders' fund

Total equity and liabilities

Shares outstanding $($in millions$)$

Depreciation $($GHS$\text{'}$m$)$

Amortisation $($GHS$\text{'}$m$)$

Capital expenditure $($GHS$\text{'}$m$)$

Net working capital as of $31$ Dec $2022($GHS$\text{'}$m$)$

Long$-$term debt as of $31$ Dec $2022($GHS$\text{'}$m$)$

Equity beta

DMIL

$31-$Dec$-23$

GHS$\text{'}$m

$720\mathrm{.}0$

$(396\mathrm{.}0)$

$324\mathrm{.}0$

$(112\mathrm{.}0)$

$212\mathrm{.}0$

$(57\mathrm{.}6)$

$154\mathrm{.}4$

$(38\mathrm{.}5)$

$115\mathrm{.}9$

$404\mathrm{.}0$

$77\mathrm{.}0$

$481\mathrm{.}0$

$19\mathrm{.}6$

$160\mathrm{.}0$

$179\mathrm{.}6$

$200\mathrm{.}0$

$101\mathrm{.}4$

$301\mathrm{.}4$

$481\mathrm{.}0$

$26\mathrm{.}0$

$13\mathrm{.}5$

$5\mathrm{.}5$

$18\mathrm{.}5$

$2\mathrm{.}5$

$200\mathrm{.}0$

$1\mathrm{.}5$

Wigs Lair

$31-$Dec$-23$

GHS$\text{'}$m

$379\mathrm{.}0$

$(214\mathrm{.}0)$

$165\mathrm{.}0$

$(58\mathrm{.}0)$

$107\mathrm{.}0$

$(22\mathrm{.}0)$

$85\mathrm{.}0$

$(21\mathrm{.}5)$

$63\mathrm{.}5$

$257\mathrm{.}0$

$16\mathrm{.}0$

$273\mathrm{.}0$

$13\mathrm{.}0$

$120\mathrm{.}0$

$133\mathrm{.}0$

$120\mathrm{.}0$

$20\mathrm{.}0$

$140\mathrm{.}0$

$273\mathrm{.}0$

$22\mathrm{.}0$

$13\mathrm{.}8$

$3\mathrm{.}2$

$11\mathrm{.}2$

$1\mathrm{.}5$

$150\mathrm{.}0$Exhibit B: Historical dividends ofDMIL and Wigs Lair

Year

DML

$2023$

GHS

Wigs Lair

$2022$

$1\mathrm{.}7955$

GHS

$1\mathrm{.}6415$

$1\mathrm{.}6980$

$2021$

$1\mathrm{.}6405$

$2020$

$1\mathrm{.}6118$

$1\mathrm{.}6255$

$2019$

$1\mathrm{.}5959$

$1\mathrm{.}5565$

$1\mathrm{.}6200$

$1\mathrm{.}5085$

Exhibit C: Historical market price of DIMIL

Year

Price per share

GHS

$2023$

$19\mathrm{.}12$

$2022$

$17\mathrm{.}14$

$2021$

$22\mathrm{.}25$

$2020$

$20\mathrm{.}35$

$2019$

$18\mathrm{.}14$

Additional information:

$1.$ The interest rate on the $10-$year government bond is $18\%.$

$2.$ The return on the market portfolio is expected to be $22\%.$

$3.$ The risk associated with the equity stock of Wigs Lair is higher than that of DML$.$ Consequently, the market would require an additional risk premium of $500$ basis points above that of DML to invest in the equity stock of Wigs Lair.

Required:

$($a$)$ Estimate the cost of equity for MIL using the capital asset pricing model. $(3$ marks$)$

$0)$ Derive an appropriat cost of debt for Wies Lain from that of ML$.(2$ marks$)$

$($c$)$ Estimate the after$-$ax cost of debt for Wigs Lair. $(4$ marks$)$

$($a$)$ Estimate the Atman's arge cost of capital for Wigs Lair. $(3$ marks$)$

$(0)$ Compute the rem premise mai: Based on the resul, would you advise that the company is valued on a going concern premise? $[6$ marks$)$

$(1)$

Calculate the valve per share of the equity stock of Wigs Lair using the following bases:

Net asset value. $[3$ marks$]$

$1)$

Discounted dividends assuming dividend will grow by $10\%$ over the next $3$ years, $7\%$ in the following two years; and $5\%$ thereafter to perpetuity. $[5$ marks$]$

Free cash flow to the firm, assuming cash flows will grow at $5\%$ to perpetuity. $[4$ marks$]$