CPA
Intermediate Leval
Financial-Management-November 2018
ANSWERS

(i). "Operating leverage" is the use of fixed operating costs to increase a company's profitability. It is measured using the degree of operating leverage (D.O.L)

D.O.L = % Change in EBIT / % change in sales

or

Contribution/(contribution-fixed cost)

"Financial leverage" refers to the use of fixed financing cost in order to improve earnings per share. It is measured using the Degree of Financial leverage (D.F.L)

D.F.L = (Q(SP - VC) - FC) / (Q(SP - VC) - FC - 1 - Pd / (1 - T))

or

D.F.L = EBIT / EBT - Pd ÷ (1 - t)

Where;

Q = units sold

SP = Selling price per unit

VC = Variable cost

FC = Fixed cost

I = interest

Pd = Preference dividends

T = corporate tax rate

(ii). The "Cum-right" Market Price allows registered shareholders to participate in a company's public rights issue. Eligible shareholders may purchase shares at a discount to the current market price per share.
The "ex-right" is the stock price after the right issue.

(iii). The "time value of money" refers to the idea that a shilling today is worth more than a shilling tomorrow.
"Time preference of money refers" to the desire for present consumption as compared to future compensation. Therefore, to induce people to save, high interest has to be charged for money not consumed today.

(i) Degree of operating leverage

Degree of operating leverage = Contribution / (Contribution - Fixed operating costs)

(1 - 0.2) x 8,000,000 = 6,400,000

D.O.L = 6,400,000 / (6,400,000 - 5,800,000) = 10.67

(ii) Degree of financial leverage





(iii). Degree of combined leverage

D.C.L = Degree of operating leverage x Degree of financial leverage

10.67 x 1.69 = 18.07

Depreciation per year alpha = (3,800,000 - 0) / 4 = sh. 950,000

Depreciation per year Beta = (800,000 - 0)/ 6 = sh. 1,333,333.33

For working capital it will be utilized in first year and recovered at end of project life.

Project Alpha
Year Pretax cash flows (000) Less: Depreciation (000) Profit before tax (000) Tax rate at 30% Profit after tax Add: Depreciation Add: Recovery working capital Cash flows	1 2,590 (950) 1,640 (492) 1,148 950 0 2,098	2 2,880 (950) 1,930 (579) 1,351 950 0 2,301	3 3,050 (950) 2,100 (630) 1,470 950 0 2,420	4 2,950 (950) 2,000 (600) 1,400 950 825 3,175

Discount payback period
Year 1 2 3 4	Cashflows "000" 2,098 2,301 2,420 3,175	DF 12% 0.8929 0.7972 0.7118 0.6355	Discounted cashflows "000" 1,873.30 1,834.36 1,722.56 2,017.71	Cumulative cashflows "000" 1,873.30 3,707.66 5,430.22 7,447.93

Initial outlay project Alpha

3,800,000 + 825,000 = 4,625,000

Discount payback period

2yrs + (4,625 - 3,707.66) / 1,722.56 x 12months

2yrs6.39months

Project Beta
Year PBDT Less: Depreciation PBT Less tax PAT Add: Depreciation Add: Recovery WC Cashflows	1 "000" 4300 (1,333.333) 2,966.667 (890.000) 2,076.667 1,333.333 0 3,409.333	2 "000" 3,290 (1,333.333) 1,956.667 (587.000) 1,369.667 1,333.333 0 2,703	3 "000" 3,200 (1,333.333) 1,866.667 (560.000) 1,306.667 1,333.333 0 2,640	4 "000" 3,700 1,333.333 2,366.667 (710.000) 1,656.667 1,333.333 0 2,990	5 "000" 4,850 (1,333.333) 3,516.667 (1,055.000) 2,461.667 1,333.333 0 3,795	6 "000" 4,420 (1,333.333) 3,086.667 (926.000) 2,160.667 1,333.333 825 4,319

Year 1 2 3 4 5 6

cashflows(000) 3,409,333 2,703,000 2,640,000 2,990,000 3,795,000 4,319,000

D.F 12% 0.8929 0.7972 0.7118 0.6355 0.5674 0.5066

PV 3,044,193.44 2,154,831.60 1,879,152.00 1,900,145.00 2,153,283.00 2,188,005.40

Project Beta Discounted payback period
Year 1 2 3 4 5 6	Discount Cashflows 3,044,193.44 2,154,831.60 1,879,152.00 1,900,145.00 2,153,283.00 2,188,005.40	Cumulative Cashflows (000) 3,044,193.44 5,199,025.04 7,078,177.04 8,978,322.04 11,131,605.04 13,319,610.44

Discount payback period

3yrs + (8,825,000 - 7,078,177.04) / 1,900,145 = 3.92yrs

Advise:
Management of Bundaaho limited should undertake project Alpha because it has the lowest discounted payback period"

g = [(Dn / Do)^1/n - 1] x 100

Where:

Dn = 1.8

Do = 1
n = 4years

g = [(1.8 / 1)^1/4 - 1] x 100

(1.1583 - 1) x 100 = 15.83%

Theoretical value of shares

V = Do(1 + g) / (r - g)

Where

Do = 1.8 , r = 20% , g = 15.83%

(1.8(1 + 0.1583)) / (0.2 - 0.1583) = 50

Advice:

Investor should not buy shares of Maraba limited since they are over-valued. Current market price of 55 is more than the intrinsic value of 50 shillings

Year 1 2 3 4 4 ∞

4 x 1.21 = 4.8 4 x 1.22 = 5.76 5.76 x 1.11 = 6.336 5.76 x 1.12 = 6.970 (6.970(1.06)) / (0.16 - 0.06) = 73.88

Discount factor 16% 0.8621 0.7432 0.6407 0.5523 0.5523

PV 4.14 4.28 4.06 3.85 40.80 Sh.57.13

Theoretical value of company's shares = Sh. 57.13

New sales

120 / 100 x 6,000,000 = sh.7,200,000

Average debtors:

Average collection period / 360 x credit sales

Average debtors new policy

60 / 360 x 7,200,000 = sh. 1,200,000

Average debtors old policy:

45 / 360 x 6,000,000 = sh. 750,000

Opportunity cost:

Debtors new policy

12 / 100 x 1,200,000 = sh.144,000

Debtors old policy

12 / 100 x 750,000 = sh.90,000

Bad debts:

New policy

2.5 / 100 x 7,200,000 = sh.180,000

Old policy:

2 / 100 x 6,000,000 = sh.120,000

Variable cost:

New policy

75 x 7,200,000 = sh. 5,400,000

Old policy

75 / 100 x 6,000,000 = sh.4,500,000

Details Sales Less: variable costs Contribution Less: Bad debts Less: opportunity cost Less: collection cost Profit before tax Less: tax Profit after tax

New policy 7,200,000 (5,400,000) 1,800,000 (180,000) (144,000) (84,000) 1,392,000 (417,600) 974,400

Old Policy 6,000,000 (4,500,000) 1,500,000 (120,000) (90,000) 0 1,290,000 (387,000) 903,000

Change 1,200,000 (900,000) 300,000 (60,000) (54,000) (84,000) 102,000 (30,600) 71,400

The management of Bahati enterprises should adopt new policy

(i) Vertical common size statements of income for the year ended 30 September 2018

W1

ABC LTD Common size income statement For year ended 30 September 2018
Revenue Cost of sales Gross profit Expenses: Distribution costs Administrative expenses Finance costs Profit before tax Tax paid Profit after tax Dividend paid Retained profit for the year Retained profit brought forward Retained profit carried forward	Sh "Million" 4,000 (3,000) 1,000 200 290 10 500 120 380 150 230 220 450	As % sales 4,000/4000 x100% = 100% 3,000/4000 x100% = 75% 1000/4000 x100% = 25% 200/4,000 x100% = 5% 290/4000 x100% = 7.25% 10/4000x100% = 0.25% 500/4000 x100% = 12.5% 120/ 4,000 x100% = 3% 380/4000 x100% = 9.5% 150/ 4,000 x100% =3.75% 230/ 4,000 x100%= 5.75% 220/ 4,000 x100% = 5.5% 450/4,000 x100%= 11.25%

W2

XYZ LTD Common size income statement For year ended 30 September 2018
Revenue Cost of sales Gross profit Expenses: Distribution costs Administrative expenses Finance costs Profit before tax Tax paid Profit after tax Dividend paid Retained profit for the year Retained profit brought forward Retained profit carried forward	Sh "Million" 6,000 4,800 1,200 150 250 400 400 90 310 100 210 2,480 2,690	As % sales 6,000/6000x100% = 100% 4800/6000 x100% = 80% 1,200/6000 x100% = 20% 150/6000 x100% = 2.5% 250/6000 x100% = 4.17% 400/6000 x100% = 6.67% 400/6000 x100% = 6.67% 90/6000 x100% = 1.5% 310/6000 x100% = 5.17% 100/ 6,000 x100% = 1.67% 210/6,000 x100% = 3.5% 2,480/6000 x100% = 41.33% 2,690/ 6,000 x100% = 44.83%

Common size income statement For year ended 30 September 2018
Revenue Cost of sales Gross profit Expenses: Distribution costs Administrative expenses Finance costs Profit before tax Tax paid Profit after tax Dividend paid Retained profit for the year Retained profit brought forward Retained profit carried forward	ABC LTD 100% 75% 25% 5% 7.25% 0.25% 12.50% 3% 9.5% 3.75% 5.75% 5.5% 11.25%	XYZ LTD 100% 80% 2.5% 6.67% 4.17% 1.5% 5.17% 1.5% 5.17% 1.67% 3.5% 41.33% 44.83%

(ii) Vertical common size statements of financial position as at 30 September 2018

W1

Common size Balance sheet For year ended 30 September 2018
Non-current Assets: Land and buildings Furniture and fittings Total non-current assets Current assets: Inventories Trade receivables Financial assets Cash at Bank Total current assets Financed by: Equity and liabilities: Ordinary share capital Retained profits Total equity Non-Current liabilities: Bank loan Current Liabilities: Trade payables Bank overdraft Total current liabilities	ABC Ltd Sh"million" 1,200 600 1800 400 850 100 0 1350 1000 450 1450 500 1080 120 200	%Total assets 1200 / 4950 x 100% = 24.24% 600 / 4950 x 100% = 12.12% 1,800 / 4,950 x 100% = 36.60% 400 / 4,950 x 100% = 8.08% 850 / 4,950 x 100% = 7.17% 100 / 4,950 x 100% = 2.02% 0 / 4,950 x 100% = 0% 1,350 / 4,950 x 100% = 27.27% 1,000 / 4,950 x 100% = 20.20% 450 / 4,950 x 100% = 9.09% 1,450 / 4,950 x 100% = 29.29% 500 / 4,950 x 100% = 10.10% 1,080 / 4,950 x 100% = 21.82% 120 / 4,950 x 100% = 2.42% 200 / 4,950 x 100% = 24.24%	XYZ Ltd Sh."million" 5,000 1,000 6,000 800 750 230 100 1,880 1,600 2,690 4,290 3,000 590 590	% Total Assets 5,000 / 13,880 x 100% = 36.02% 1,000 / 13,880 x 100% = 7.20% 6,000 / 13,880 x 100% = 43.23% 800 / 13,880 x 100% = 5.76% 750 / 13,880 x 100% = 5.40% 230 / 13,880 x 100% = 1.66% 100 / 13,880 x 100% = 0.72% 1,880 / 13,880 x 100% = 13.54% 1,600 / 13,880 x 100% = 11.53% 2,690 / 13,880 x 100% = 19.38% 4,290 / 13,880 x 100% = 30.91% 3,000 / 13,880 x 100% = 21.61% 590 / 13,880 x 100% = 4.25% 590 / 13,880 x 100% = 4.25%

Vertical Common size Balance sheet For year ended 30 September 2018
Non-current Assets: Land and buildings Furniture and fittings Total non-current assets Current assets: Inventories Trade receivables Financial assets Cash at Bank Total current assets Financed by: Equity and liabilities: Ordinary share capital Retained profits Total equity Non-Current liabilities: Bank loan Current Liabilities: Trade payables Bank overdraft Total current liabilities	ABC Ltd 24.24% 12.12% 36.6% 8.08% 7.17% 2.02% 0% 27.27% 20.20% 9.09% 29.29% 10.10% 21.82% 2.42% 24.24%	XYZ Ltd 36.02% 7.20% 43.23% 5.76% 5.40% 1.66% 0.72% 13.54% 11.53% 19.38% 30.91% 21.61% 4.25% 4.25%

Source Ordinary shares 12% preference shares 18% debentures Loan

Market Value 200,000 x 16 = 3,200,000 75,000 x 18 = 1,350,000 50,000 x 80 = 4,000,000 5,000,000 13,550,000

Floatation 200,000 x 1 = 200,000 75,000 x 2 = 150,000 0 200,000 550,000

Net float 3,000,000 1,200,000 4,000,000 4,800,000 13,000,000

Cost of OS(Ke)

Ke = (Do(1 + g)) / (Po - f) + g x 100%

Do = 28 / (100 x 10) = 2.8

g = 4% ,Po = 16 , f = 1

[(2.8(1 + 0.04)) / (16 - 1) + 0.04] x 100

[2.912 / 15 + 0.04] x 100 = 23.41%

Cost of preference shares (Kp)

Kp = Dp / (Po - f) x 100

Where

Dp = 12% x 20 = 2.4

Po = 18

f = 150,000 / 75,000 = 2

Kp = 2.4 / (18 - 2) x 100% = 15%

Cost of debenture (Kd)

Where

Kd = I(1 - 0.3) / (Po - f) x 100

I = 18 / 100 x 100 = 18

t = 30% , Po = 80 , f = 0

Kd = (18(1 - 0.3)) / (80 - 0) x 100 = 15.75%

Cost of longterm loan (Kl)

Kl = (I(1 - t)) / Mv x 100

I = 18 / 100 x 5,000,000 = 900,000

Kl =(900,000(1 - 0.3)) / 4,800,000 x 100% = 13.125%

Source Ordinary shares 12% preference shares 18% debentures 18% Loan

Amount 3,000,000 1,200,000 4,000,000 4,800,000 13,000,000

Weight 3,000 ÷ 13,000 = 0.23 1,200 ÷ 13,000 = 0.09 4,000 ÷ 13,000 = 0.31 4,800 ÷ 13,000 = 0.37

Cost of capital 23.41% 15% 15.75% 13.125%

Weighted Cost 5.38% 1.35% 4.88% 4.86% 16.47%

WMC = 16.47%

Annual interest paid = 12 / 100 x 100 = sh.12

Year 1 - 10 10

Cashflows 100 1000

DF 18% 4.4941 0.1911

PV 449.41 191.10 640.51

Since current market price of sh.80 is less than intrinsic value of
debenture of shs.104.9728, then William Mgunya should invest in the debentures.

(i). The expected return for each security.

➪ Expected return A = (Ā)

A = 0.3 x 12 + 0.4 x 15 + 0.3 x 10

3.6 + 6 + 3 = 12.6%

➪ Expected return B = (B̄)

B = 0.3 x 6 + 0.4 x 7.5 + 0.3 x 5

1.8 + 3 + 1.5 = 6.3%

(ii) Standard deviation of A

δ_A = √(12² x 0.3 + 15² x 0.4 + 10² x 0.3) - 12.6²

√(43.2 + 90 + 30) - 158.76²

√4.44 = 2.11

Standard deviation of B

δ_B =√(6² x 0.3 + 7.5² x 0.4 + 5² x 0.3) - 6.3²

√(10.8 + 22.5 + 7.5) - 39.69

√1.11 = 1.05

(iii) Coefficient of correlation

P 0.30 0.40 0.30

A 12 15 10

Ā 12.6 12.6 12.6

(A-Ā) -0.6 2.4 -2.6

B 6 7.5 5

B̄ 6.3 6.3 6.3

(B-B̄) -0.3 1.2 -1.3

(A-Ā)(B-B̄) 0.18 2.88 3.38 6.44

(iv) Portfolio return

0.6 x 12.6 + 0.4 x 6.3 = 10.08%

(v) Portfolio risk

δ_p =√W_A²δ_A² + W_B²δ_B² + 2(W_A W_BCOV_A&B)

√0.6² x 2.11² + 0.4² x 1.05² + 2[0.6 x 0.4 x 6.44]

2.2069