F3 CIMA Q & A! CIMA F3 Workbook Questions & Solutions

CIMA F3 Workbook Questions & s

Lecture 1 Financial Strategy

Shareholder Wealth - Illustration 1 Year Share Price Dividend Paid 2007 3.30 40c 2008 3.56 42c 2009 3.47 44c 2010 3.75 46c 2011 3.99 48c There are 2 million shares in issue.!!!!!!!!!!!! Calculate the increase in shareholder wealth for each year: II. Per share III. As a percentage IV. For the business as a whole Year Share Price Share Price Growth Div Paid Increase in S holder Wealth As a Percentage Total Shareholder Return 2007 3.30 40c 2008 3.56 (3.56-3.30) = 26c 42c (26 + 42) = 68c 2009 3.47 (3.47-3.56) = -9c 44c (-9 + 44) = 35c 2010 3.75 (3.75-3.47) = 28c 46c (28 + 46) = 74c 2011 3.99 (3.99-3.75) = 24c 48c (24 + 48) = 72c (68 / 330) = 20.6% (35 / 356) = 9.8% (74 / 347) = 21.3% (72 / 375) = 19.2% 2m x 68c = $1.36m 2m x 35c = $0.70m 2m x 74c = $1.48m 2m x 72c = $1.44m

EPS - Illustration 2 2010 $ 000 2011 $ 000 PBIT 2000 2100 Interest 200 300 Tax 300 400 Profit After Tax 1500 1400 Preference Dividend 300 400 Dividend 800 900 Retained Earnings 400 100 Share Capital (50c) 5000 5000 Reserves 3000 3100 Share Price $2.50 $2.80 Calculate the EPS for 2010 and 2011. 2010 2011 Profit After Tax 1500 1400 Preference Dividend 300 400 Earnings 1200 1000 No. Ordinary Shares (5000 / 0.50) 10,000 10,000 EPS (Earnings / No. Ordinary Shares) 12c 10c

Lecture 2 Performance Measurement

Performance Analysis Illustration X1 X2 X3 Non Current Assets 500 700 1000 Current Assets 150 200 300 650 900 1300 Ordinary Shares ($1) 300 300 300 Reserves 100 280 430 Loan Notes 150 200 300 Payables 100 120 270 650 900 1300 Revenue 3000 3500 4200 COS 2000 2400 3200 Gross Profit 1000 1100 1000 Admin Costs 300 350 400 Distribution Costs 200 250 300 PBIT 500 500 300 Interest 100 150 220 Tax 120 90 50 Profit After Tax 280 260 30 Dividends 100 110 30 Retained Earnings 180 150 0 Share Price $3.30 $4.00 $2.20 Using the information calculate and comment on the following Ratios: I. Return on Capital Employed II. Return on Equity III. Gross Margin IV. Net Margin V. Operating Margin VI. Revenue Growth VII. Gearing VIII. Interest Cover IX. Dividend Cover X. Dividend Yield XI. P/E Ratio

ROCE X1 X2 X3 Equity + LT Liabilities Shares 300 300 300 Reserves 100 280 430 LT Loan Notes 150 200 300 Capital Employed 550 780 1030 Non Current Assets + Net Current Assets Non Current Assets 500 700 1000 Net Current Assets (Current Assets - Current Liabilities) (150-100) = 50 (200-120) = 80 (300-270) = 30 Capital Employed 550 780 1030 Total Assets - Current Liabilities Total Assets 650 900 1300 Current Liabilities 100 120 270 Capital Employed 550 780 1030 PBIT 500 500 300 Return on Capital Employed PBIT / Capital Employed (500 / 550) = 90.91% (500 / 780) = 64.10% (300 / 1030) = 29.13%

X1 X2 X3 Return on Capital Employed (ROCE) 90.91% 64.10% 29.13% In the first year the ROCE was 90.91%. At first glance this would appear to be a good return, however without industry averages or prior period information we are unable to tell if this is the case. In year X2 the ROCE is 64.10%. This is a fall of 29.5% from the previous year indicating that the business in not able to make the same return on it s assets that it has previously been able to do. In the year X3 the ROCE is 29.13%. This is a fall of 54.55% indicating that there may be some serious underlying problems which are affecting the ability of the business to generate the return on capital previously generated. ROE X1 X2 X3 Profit After Tax 280 260 300 Ordinary Shares 300 300 300 Reserves 100 280 430 Total 400 580 730 Return on Equity (PAT / Ord Shares + Reserves) (280 / 400) = 70% (260 / 580) = 44.8% (300 / 730) = 41% In the first year the ROE was 70%. At first glance this would appear to be a good return, however without industry averages or prior period information we are unable to tell if this is the case. In year X2 the ROE is 44.8%. This is a fall of 36% from the previous year indicating thatt the business in not able to make the same return on the shareholders funds that it has previously been able to do. In the year X3 the ROE is 41%. This is a fall of 8.4% indicating thatt the business may be having difficulty generating the returns it was able to do previously.

Margins X1 X2 X3 Revenue 3000 3500 4200 Gross Profit 1000 1100 1000 PAT 280 260 30 PBIT 500 500 300 Gross Margin (Gross Profit / Revenue) (1000 / 3000) = 33.33% (1100 / 3500) = 31.42% (1000 / 4200) = 23.89% Net Margin (PAT / Revenue) (280 / 3000) = 9.3% (260 / 3500) = 7.4% (30 / 4200) = 0.7% Operating Margin (PBIT / Revenue) (500 / 3000) = 16.66% (500 / 3500) = 14.28% (300 / 4200) = 7.1% The Gross Margin is 33.33% in X1 and holds reasonably steady in X2 at 31.42%. However in X3 the Gross Margin falls to 23.89% indicating that the business has either had to cut prices to sell the greater volume it has, or the cost of it s purchases have gone up. The Net Margin is 9.3% in X1 but begins to falll in X2 with 7.4% achieved, before falling dramatically to 0.7% in X3. The main reason for this is the falll in Gross Profit as other costs have risen in line with expectations given the increase in sales. However another point to note is that interest costs have risen with the increase in long term loans. The extra interest costs have put pressure on the business. The Operating Margin dropped slightly in X2 to 14.28% from 16.66% the previous year - a fall of almost 15%. In X3 the Operating Margin fell away to 7.1%, a decrease of over 50%. This is due to the decreasing Gross Margin achieved as well as rises in the other expenses.

Gearing X1 X2 X3 Debt 150 200 300 Equity Number of Shares 300 300 300 Share Price 3.30 4 2.20 Market Value (300 x 3.30) = 990 (300 x 4) = 1200 (300 x 2.20) = 660 Gearing (Debt / Equity) (150 / 990) = 15% (200 / 1200) = 16.66% (300 / 660) = 45.45% Gearing levels in year X1 are 15%. Without industry averages or prior year data we are unable to assess this level although at first glance it does not seem excessive. In year X2 gearing increases slightly to 16.66%, an increase of 11% from year X1. This is due to debt levels increasing to 200 from 150, although this is offset by the increase in the share price from $3.30 to $4. In year X3 gearing increases dramatically to 45%, an increase of over 180%. This is due to debt levels rising to 300 from 200 and the share price dropping to $2.20 due to the deteriorating resultss of the business.

Interest Cover X1 X2 X3 PBIT 500 500 300 Interest 100 150 220 Interest Cover (PBIT / Interest) (500 / 100) = 5 times (500 / 150) = 3.33 times (300 / 220) = 1.36 times Interest coverage in year X1 is 5 times. Without industry averages or prior year data we are unable to assess this level although at first glance it does not seem unreasonable. In year X2 interest coverage falls to 3.33 times. This has occurred due to the interest charge increasing in the period while PBIT has remained constant. In year X3 interest coverage has decreasedd again to 1.36 times. This is caused by the PBIT achieved decreasing to 300 combined with the increase in the interest charge to 220. The increase in interest is caused by the increase in the long term debt of the company as shown by the gearing ratios calculated above. Dividend Cover X1 X2 X3 PAT 280 260 30 Dividends 100 110 30 Dividend Cover (PAT / Dividends) (280 / 100) = 2.8 times (260 / 110) = 2.36 times (30 / 30) = 1 time Dividend coverage in year X1 is 2.8 times. Without industry averages or prior year dataa we are unable to assess this level although at first glance it does not seem unreasonable. In year X2 dividend coverage falls to 2.36 times. This would not concern investors as although coverage has gone down slightly, the dividend paid this year is greater than last. In year X3 dividend coverage has decreased to 1 time. This is caused by the decreasee in profit achieved by the company restricting the level of dividend payable. This willl be of concern to investors and their concern is reflected in the fall in the share price from $4 in year X2 to $2.20 in year X3.

Dividend Yield X1 X2 X3 Number of Shares (300 / 1) 300 300 300 Dividends 100 110 30 Dividends Per Share (100 / 300) = 33c (110 / 300) = 36c (30 / 300) = 10c Dividend Yield (Dividends Per Share / Share Price) (33 / 330) = 10% (36 / 400) = 9% (10 / 220) = 4.5% The Dividend Yield is 10% in year X1. Whilst we do not have comparatives, this seems a reasonable return. In year X2 the Dividend Yield falls to 9%. This will not be overly concerning to investorss as the increase in share price over the year will have more than made up for the slightly lower yield. In year X3 the Dividend Yield has fallen to 4.5% which is 50% lower than the previous year. This, combined with the fall in share price and reduced profitability will be a major concern to investors. P/E Ratio X1 X2 X3 Share Price $3.30 $4 $2.20 Profit After Tax 280 260 30 No. Ordinary Shares 300 300 300 EPS (280 / 300) = 93c (260 / 300) = 86c (30 / 300) = 10c P/E Ratio (Share Price / EPS) (330 / 93) = 3.54 (400 / 86) = 4.65 (220 / 10) = 22 The P/E Ratio in year X1 is 3.54. We don not have industry comparatives or prior year information with which to compare this. In year X2 the P/E Ratio increases to 4.65. This indicates that the market expectations for this share have risen since X1 and that investors are now willing to pay 4.65 times what the business earns in a year to own the share. In year X4 the P/E ratio has increased dramatically to 22. This is unusual as the earnings have decreased to 12% of the previous year. The share price has fallen to reflect this, but not by as much as would be expected. This may indicate that the market feels that the resultss in year X3 were perhaps a one-off and that next years results will improve.

Lecture 3 Finance Sources

Rights Issue - Illustration 1 XYZ Ltd. intends to raise capital via a rights issue. The current share price is $8. They are offering a 1 for 4 issue at a price of $6. Calculate the Theoretical Ex-rights Price. Number of Shares Share Price Total 4 $8 (4 x $8) = 32 1 $6 (1 x $6) = 6 5 38 We now have 5 shares in issue at total value of $38 so the THERP is (38 / 5) = $7.60

Rights Issue - Illustration 2 ABC Ltd. has decided to raise capital via a rights issue. The share price is currently $5.50 and ABC intends to raise $5m. There are currently 6.25m shares in issue and ABC is offering a 1 for 5 rights issue. Calculate the Theoretical Ex-Rights Price. Amount of Capital to raise $5m No. of shares issued (6.25m / 5) 1.25m Share issue price ($5m / 1.25m) $4 Number of Shares Share Price Total 5 $5.50 (5 x 5.50) = 27.5 1 $4 (1 x 4) = 4 6 31.5 We now have 6 shares in issue at total value of $31.5 so the THERP is (31.5 / 6) = $5.25

Lecture 5 Investment Appraisal I

ARR - Illustration 1 ABC Ltd are considering expanding their internet cafe business by buying a business which will cost $275,000 to buy and a further $175,000 to refurbish. They expect the following cash to come in: Year Net Cash Profits ( ) 1 45,000 2 75,000 3 80,000 4 50,000 5 50,000 6 60,000 The equipment will be depreciated to a zero resale value over the same period and, after the sixth year, they can sell the business for $200,000 Calculate the ARR or ROCE of this investment

Total Profit over 6 years 45,000 + 75,000 + 80,000 + 50,000 + 50,000 + 60,000 360,000 Total Depreciation Equipment of $175,000 fully depreciated 175,000 Total Profits 185,000 Average Profits $185,000 / 6 years 30,833 Average Investment (Capital Investment + Residual Value) / 2 ROCE (Ave. Profit / Ave Investment) (450,000 + 200,000) / 2 325,000 30,833 / 325,000 9.5%

Relevant Cash Flow Criteria - Illustration 2 A business is considering investing in a new project. They have already spent $20,000 on a feasibility study which suggests that the project will be profitable. The headquarters of the company has spare floor space which will be allocated to the project with $7,000 of the current monthly rent allocated to the project. New equipment costing $2.5m will have to be bought and will be depreciated on a straight line basis over 10 years. A manager who earns $30,000 per year and currently runs a similar project will also manage the new project taking up 25% of his time. State whether each of the following items are relevant cash flows and explain your answer. I. The cost of the feasibility study. II. The rent charged to the project. III. The new equipment. IV. The depreciation on the new equipment. V. The Managers salary. Item Relevant Cash Flow? Explain Feasibility Study No This is a sunk cost as it has already been paid. Rent No The rent is not relevant as it must be paid whether the project goes ahead or not. It is not incremental. New Equipment Yes This is a relevant cash flow. Depreciation No Depreciation is not a cash-flow but an accounting entry. Managers Salary No The managers salary must be paid whether the project goes ahead or not so is not relevant.

Payback Period - Illustration 3 Initial Investment of $5.8m. Annual Cash Flows of $400,000. Calculate the Payback Period. Payback Period (Initial Investment / Annual Cash Flows) $5.8m / $400,000 14.5 years

Payback Period - Illustration 4 Initial Investment of $6.2m. Cash Flows of: Year 1:! $1,200,000 Year 2:! $2,200,000 Year 3:! $2,500,000 Year 4:! $1,700,000 Calculate the Payback Period. Year Cash Flows Cumulative Cash Flows 1 1,200,000 1,200,000 2 2,200,000 3,400,000 3 2,500,000 5,900,000 4 1,700,000 7,600,000 Payback period is between 3 and 4 years Additional amount required to return capital (6,200,000-5,900,000) = 300,000 Total cash flows in year 4 of 1,700,000 so it will take (300,000 / 1,700,000) x 12 = 2.11 months

Discounted Cash-flows - Illustration 5 An investor wants a real return of 10%. Inflation is 5% What is the MONEY/NOMINAL rate required? Use Formula: 1+m = (1+r) x (1+inf) We are looking for m, therefore: 1+m = (1+0.10) x (1+0.05) 1+m = 1.155 m = 0.155 = 15.5%

Discounted Cash-flows - Illustration 6 A company undertakes a project with the following cash-flows: Year Cash-Flows 1 5,000 2 7,000 3 8,000 4 10,000 5 11,000 6 9,000 The company has a cost of capital of 10%. Calculate the present value of the cash flows for each of the six years and in total. Year Cash-Flows Discount Rate (From Tables) Present Value 1 5,000 0.909 4,545 2 7,000 0.826 5,782 3 8,000 0.751 6,008 4 10,000 0.683 6,830 5 11,000 0.621 6,831 6 9,000 0.564 5,076 Total 35,072

Discounted Cash-flows - Illustration 7 A company undertakes a project with the following cash-flows: Year Cash-Flows 1 5,000 2 5,000 3 5,000 4 5,000 5 5,000 6 5,000 The company has a cost of capital of 10%. Calculate the present value of the total cash flows for the six years Year Cash-Flows Discount Rate (From Tables) Present Value 1 5,000 0.909 4,545 2 5,000 0.826 4,130 3 5,000 0.751 3,755 4 5,000 0.683 3,415 5 5,000 0.621 3,105 6 5,000 0.564 2,820 Total 21,770 Years Cash-flow Discount Rate (Annuity Tables) Present Value 1-6 5,000 4.355 21,775

Discounted Cash-flows - Illustration 8 A company expects to receive $100,000 per year forever. Their cost of capital is 10%. Calculate the present value of the perpetuity. Annual Cash Flow $100,000 Cost of Capital (10%) 0.10 Perpetuity (Cash-Flow / Cost of Capital) 100,000 / 0.10 = $1m

Lecture 6 Investment Appraisal II

WDA - Illustration 1 A business buys a piece of equipment for $100. Capital allowances are available at 25% reducing balance. The tax rate is 30% After the 4 year project the equipment can be sold for $25. Period Balance 25% WDA 30% Tax Saving Period 1 100.00 25.00 7.50 2 2 75.00 18.75 5.63 3 3 56.25 14.06 4.22 4 4 42.19 Sale of Item -25.00 17.19 5.16 5 Period 0 1 2 3 4 5 Tax Saving - - 7.5 5.63 4.22 5.16

Working Capital - Illustration 2 A business requires the following working capital investment into a four year project: Initial Investment:!! 30,000 Year 1!!! 35,000 Year 2!!! 45,000 Year 3!!! 32,000 Show the working capital line in the NPV calculation. Period 0 1 2 3 4 Total Invested 30,000 35,000 45,000 32,000 Movement to NPV Calculation -30,000-5,000-10,000 13,000 32,000

NPV - Illustration 3 A business is evaluating a project for which the following information is relevant: I. Sales will be $100,000 in the first year and are expected to increase by 5% per year. II. Costs will be $50,000 and are expected to increase by 7% per year. III. Capital investment will be $200,000 and attracts tax allowable depreciation of the full value of the investment over the 5 year length of the project. IV. The tax rate is 30% and tax is payable in the following year. V. Working Capital invested will be 20% of projected sales for the following year. VI. General inflation is expected to be 3% over the course of the project and the business uses a real discount rate of 9%. Calculate the NPV for the project. Working 1 - WDAs Initial Investment WDAs Tax Saving Periods 200,000 (200,000 / 5) = 40,000 (40,000 x 30%) = 12,000 2-6

Working 2 - Inflation Period 1 2 3 4 5 Sales 100,000 100,000 100,000 100,000 100,000 Inflation - 1.05 1.05 to power of 2 1.05 to power of 3 1.05 to power of 4 Inflated Sales 100,000 105,000 110,250 115,763 121,551 Costs 50,000 50,000 50,000 50,000 50,000 Inflation - 1.07 1.07 to power of 2 1.07 to power of 3 1.07 to power of 4 Inflated Costs 50,000 53,500 57,245 61,252 65,540 Working 3 - Discount Rate Working Real Discount Rate In Question 9% Inflation In Question 3% Nominal Discount Rate 1 + m = (1 + 0.09) x (1 + 0.03) 1 + m = 1.12 m = 0.12 12%

Working 4 - Working Capital Period 0 1 2 3 4 5 Inflated Sales 100,000 105,000 110,250 115,763 121,551 Working Capital Required (20%) 20,000 21,000 22,050 23,153 24,310 Movement -20,000-1,000-1,050-1,103-1,158 24,310 NPV Period 0 1 2 3 4 5 6 Inflated Sales (W2) Inflated Costs (W2) 100,000 105,000 110,250 115,763 121,551-50,000-53,500-57,245-61,252-65,540 Profit 50,000 51,500 53,005 54,510 56,011 Tax at 30% -15,000-15,450-15,902-16,353-16,803 Tax Saving (W1) 12,000 12,000 12,000 12,000 12,000 Capital Investment Working Capital (W4) Total Cash Flows Discount Rate 12% (W3) Discounted Cash Flows -200,000-20,000-1,000-1,050-1,103-1,158 24,310-220,000 49,000 47,450 48,452 49,451 75,968-4,803 1 0.893 0.797 0.712 0.636 0.567 0.507-220,000 43,757 37,818 34,498 31,451 43,074-2,435 NPV -31,838

Lecture 7 - Investment Appraisal III

Illustration 1 ABC has evaluated a project and come to the following conclusions. At a discount rate of 10% the NPV will be $100,000 At a discount rate of 15% the NPV will be -$75,000 What is the IRR? 10 + (100,000/(100,000 +75,000) 5 = 12.85%

Illustration 2 Initial Investment (5,000) Period Cash Flows 1 2,000 2 (1,000) 3 3,500 4 3,800 Cost of Capital 10% NPV = 1,216 IRR = 19% Calculate the MIRR.

Terminal Value of Inflows Period Inflow Inflate Value 1 2,000 (1.10) 3 2,662 3 3,500 (1.10) 1 3,850 4 3,800 1.10 3,800 Terminal Value 10,312 Present Value Outflows Period Outflow Discount Rate PV 0 5,000 1 5,000 2 1,000 0.826 826 Present Value of Outflows 5,826 Discount Factor where 10,312 x DF (P4) = 5,826 5,826/10,312 = 0.565 Look at tables for Period 4 and find closest to 0.565. MIRR = 15%

Lecture 8 - Foreign NPV

Illustration 1 Item costs $1,000 /$ 1 : 2 However inflation in US is 5% and Eurozone 3% Calculate the exchange rate in one years time. Future exchange rate calculation Exchange rate now x 1+ Inf (counter) / 1 + inf (base) 2 x 1.05 / 1.03 = 2.039

Illustration 2 (i) US Interest rate = 10% UK Interest rate = 8% Exchange rate = /$ 1 : 2 Predict the exchange rate in 1 year Future exchange rate calculation Exchange rate now x 1+ Int (counter) / 1 + int (base) 2 x 1.10 / 1.08 = 2.037

Illustration 2 (ii) Current spot rate $/ 1 : 1 The dollar is expected to strengthen by 7% per anum Forecast the $: rate for the next 4 years. Period 0 1 2 3 4 FX Rate 1 1.07 1.145 1.225 1.310

Illustration 3 ABC Ltd. is a UK company intending to undertake a project in Foreignland where the currency is the Franc (FR). ABC uses a discount rate of 10% to evaluate projects in the UK and the current spot rate is / FR 2.000. The risk free rate of interest in Foreignland is 5% with the UK rate being 7%. The initial investment in the project will be FR 400,000 with net cash inflows over a 5 year project of FR 150,000 per year. Ignore Tax. Calculate the NPV of the project.

FX Calculations Period 1 2 3 4 5 Rate at start of period 2.000 1.963 1.926 1.890 1.855 IRP (1.05 / 1.07) (1.05 / 1.07) (1.05 / 1.07) (1.05 / 1.07) (1.05 / 1.07) FX Rate to use 1.963 1.926 1.890 1.855 1.820 NPV Calculations Period 0 1 2 3 4 5 Investment -400 Cash Flows (FR) 150 150 150 150 150 FX Rate 2 1.963 1.926 1.890 1.855 1.820 Cash Flows ( ) -200.00 76.41 77.88 79.37 80.86 82.42 Discount Rate (10%) 1 0.909 0.826 0.751 0.663 0.621 PV Cash Flows ( ) -200.00 69.46 64.33 59.60 53.61 51.18 NPV 98.19

Illustration 4 ABC Ltd. is a UK company intending to undertake a project in Foreignland where the currency is the Franc (FR). ABC uses a discount rate of 16% to evaluate projects in the UK and the current spot rate is / FR 2.000. The risk free rate of interest in Foreignland is 7% with the UK rate being 9%. so... (1 + DRFoR) / (1 + 0.16) = (1 + 0.07) / (1 + 0.09) (1 + DRFoR) / (1 + 0.16) = 0.982 (1 + DRFoR) = (1.16 x 0.982) (1 + DRFoR) = 1.138 DRFoR = 13.8%

Illustration 5 ABC Ltd. is a UK company intending to undertake a project in Foreignland where the currency is the Franc (FR). ABC uses a discount rate of 20% to evaluate projects in the UK and the current spot rate is / FR 2.000. Sterling is expected to appreciate against the Franc by 10% per year. so... If appreciates by 10% it will be able to buy 10% more FR which makes one worth (2 x 1.1) = 2.2FR (1 + DRFoR) / (1 + 0.20) = 2.2 / 2 (1 + DRFoR) / (1 + 0.20) = 1.1 (1 + DRFoR) = (1.20 x 1.1) (1 + DRFoR) = 1.32 DRFoR = 32%

Illustration 6 ABC Ltd. is a UK company intending to undertake a project in Foreignland where the currency is the Franc (FR). ABC uses a discount rate of 10% to evaluate projects in the UK and the current spot rate is / FR 2.000. The risk free rate of interest in Foreignland is 5% with the UK rate being 7%. The initial investment in the project will be FR 400,000 with net cash inflows over a 5 year project of FR 150,000 per year. Ignore Tax. Calculate the NPV of the project by adjusting the discount rate.

(1 + DRFoR) / (1 + 0.10) = (1 + 0.05) / (1 + 0.07) (1 + DRFoR) / (1 + 0.10) = 0.981 (1 + DRFoR) = (1.10 x 0.982) (1 + DRFoR) = 1.079 DRFoR = 7.9%...say 8% NPV Calculations Period 0 1 2 3 4 5 Investment -400 Cash Flows (FR) 150 150 150 150 150 Discount Rate (8%) 1 0.926 0.857 0.794 0.735 0.681 PV Cash Flows (FR) -400.00 138.90 128.55 119.10 110.25 102.15 NPV (FR) 198.95 Spot Rate 2.00 NPV( ) 99.48 This is the same as the NPV in illustration 3 with a slight rounding difference.

Lecture 9 WACC I

Cost of Equity using DVM - Illustration 1 ABC Company has just paid a dividend of 35c. The current share price is $3.25. Calculate the Cost of Equity (Ke) using DVM. Dividend 35 Share Price 325 Cost of Equity (Dividend / Share Price) (35 / 325) = 10.76%

Cost of Equity using DVM - Illustration 2 ABC Company has just paid a dividend of 35c. The dividend paid has grown by 4% per year for the past 5 years. The current share price is $3.25. Calculate the Cost of Equity (Ke) using DVM. Dividend 35 Share Price 325 Dividend Growth 4% Cost of Equity (Dividend (1+g) / Share Price) +g ((35 x 1.04) / 325) + 0.04 = 0.152 = 15.2%

Cost of Equity using CAPM - Illustration 3 Company A has a Beta of 1.2. Government bonds are currently trading at 4%. The average return than investors in the market can expect is 15%. Calculate the Cost of Equity using CAPM. Rf (Risk Free Rate) 4 Rm (Ave Return on the Market) 15 Beta 1.2 Ke = Rf + β(rm - Rf) (4 + 1.2(15-4)) = 17.2%

Cost of Equity using CAPM - Illustration 4 Company A has a Beta of 1.2. Company B has a Beta of 1. Government bonds are currently trading at 5%. The average return than investors in the market can expect is 12%. Calculate the Cost of Equity using CAPM for each company. Company A Company B Rf (Risk Free Rate) 5 5 Rm (Ave Return on the Market) 12 12 Beta 1.2 1 Ke = Rf + β(rm - Rf) (5 + 1.2(12-5)) = 13.4% (5 + 1(12-5)) = 12% Notice that when Beta is 1 (Company B) Ke is 12% which is the same as the average return on the market. Also notice that a higher Beta of 1.2 gives a higher Ke of 13.4% showing that a higher Beta means higher risk.

Cost of Equity using CAPM Illustration 5 Company A has a Beta of 1.3. Company B has a Beta of 1.2. Government bonds are currently trading at 5%. The average market risk premium is 6%. Calculate the Cost of Equity using CAPM for each company. Company A Company B Rf (Risk Free Rate) 5 5 Rm - Rf (Ave Market Risk Premium) 6 6 Beta 1.3 1.2 Ke = Rf + β(rm - Rf) (5 + 1.3(6) = 12.8% (5 + 1.2(6)) = 12.2% Remember to look out for the market risk PREMIUM as this is always (Rm - Rf) rather than Rm (Average return on the market) Again notice that a higher Beta leads to a higher Ke i.e. more risk.

Lecture 10 WACC II

Irredeemable Debt - Illustration 1 A company has issued 10% irredeemable debt. The market value of the debt is $90. The tax rate is 30% Calculate the cost of debt (Kd). Interest paid (Per $100 nominal) $10 Tax Rate 30% After tax interest (Amount Paid (1 - t)) $10 x (1-0.30) = $7 Market Value of Debt (Per $100 nominal) $90 Cost of Debt (After tax interest / Market Value of Debt) (7 / 90) = 7.7%

Redeemable Debt - Illustration 2 A Company has issued debt which is redeemable in 5 years time. Interest is payable at 8%. The current market value of the debt is $102. Ignore taxation. Calculate the Cost of Debt (Kd). Perio d Item $ DR 5% PV DR 15% PV 1-5 Interest 8 4.329 34.63 3.352 26.82 5 Capital 100 0.784 78.40 0.497 49.70 Market Value -102-102 11.03-25.48 IRR Calculation: 5 + (11.03 / (11.03 - (25.48)) (15-5) = 8.02%

Redeemable Debt - Illustration 3 A Company has issued debt which is redeemable in 5 years time. Interest is payable at 10%. The current market value of the debt is $104. Tax is payable at 30%. Calculate the Cost of Debt (Kd). Perio d Item $ DR 5% PV DR 15% PV 1-5 Interest (10 x (1-0.3) 7 4.329 30.30 3.352 23.46 5 Capital 100 0.784 78.40 0.497 49.70 Market Value -104-104 4.70-30.84 IRR Calculation: 5 + (4.7 / (4.7 - (30.84)) (15-5) = 6.32%

Convertible Debt - Illustration 4 A Company has issued debt which is convertible in 5 years time. Interest is payable at 10%. The current market value of the debt is $120. On conversion, investors will have a choice of either: I. Cash at a 15% premium; or II. 18 shares per loan note. The current share price is $6 and it is expected to grow in value by 4% per year. Tax is payable at 30%. Calculate the Cost of Debt (Kd). Working 1 - Cash or Convert? Working Cash (15% Premium) 100 x 1.15 $115 Shares Current Value $6 Value in 5 years with 4% growth 6 x (1.04 to the power of 5) $7.30 Number of shares per $100 18 Conversion Value 7.30 x 18 $131.40 The conversion value is higher than the cash so the investors will choose to convert. Do an IRR the same as for redeemable but filling $131.40 into the capital repaid

Cost of Debt Perio d Item $ DR 5% PV DR 15% PV 1-5 Interest (10 x (1-0.3) 7 4.329 30.30 3.352 23.46 5 Conversion Value 131.4 0.784 103.02 0.497 65.31 Market Value -120-120 13.32-31.23 IRR Calculation: 5 + (13.32 / (13.32 - (31.23)) (15-5) = 8% Preference Shares - Illustration 5 A company has issued 8% preference shares with a nominal value of $1. The market value of the shares is 80c. The tax rate is 30%. Calculate the cost of the preference shares (Kd). Interest Paid 8 Market Value of share 80 Cost (Kd) (Interest Paid / Market Value) (8 / 80) = 10%

Bank Debt - Illustration 6 A company has a bank loan of $2m at an interest rate of 10%. The tax rate is 30%. Calculate the cost of debt (Kd). Interest Rate before Tax 10 Tax Rate 30% After Tax Cost of Debt (10 x (1-0.3)) 7%

WACC - Illustration 7 Company A is funded as follows: Item Capital Structure Cost Equity 85% 15% Debt 15% 7% Calculate the Weighted Average Cost of Capital. Item Capital Structure Cost Ave Equity 85% 15 12.75 Debt 15% 7 1.05 WACC 13.8

WACC - Illustration 8 Company A is funded as follows: Balance Sheet Extract Ordinary Shares (50c) 3000 Loan Notes 2000 Bank Loan 1000 The cost to the company of each of the above items has been calculated as: Ordinary Shares 13% Loan Notes 8% Bank Loan 5% The Loan notes are currently trading at $94. The current share price is $1.50 Calculate the Weighted Average Cost of Capital. Working 1 - Calculate Cost of Capital for each item. Given in the Question Ordinary Shares 13% Loan Notes 8% Bank Loan 5%

Working 2 - Calculate the Market Value of Debt and Equity. Ordinary Shares (50c) SFP 3000 No. of shares (3000 / 0.50) = 6000 Share Price = $1.50 Market Value (6000 x $1.50) = 9000 Loan Notes 2000 Loan Notes nominal value (on SFP) = 100 Market Value = 94 Bank Loan 1000 No market for this so use SFP value (2000 x (94 / 100) = 1880 1000 Working 3 - Calculate the weighting of each item. Item Market Value Weighting Equity 9000 (9000 / 11,880) = 75.75% Loan Notes 1880 (1880 / 11,880) = 15.82% Bank Loan 1000 (1000 / 11,880) = 8.41% 11880 Working 4 - Weighted Average Cost of Capital Item Market Value Weighting Cost (W1) Ave Equity 9000 (9000 / 11,880) 13 (9000 / 11,880) x 13 = 9.85 Loan Notes 1880 (1880 / 11,880) 8 (1880 / 11,880) x 8 = 1.27 Bank Loan 1000 (1000 / 11,880) 5 (1000 / 11,880) x 5 = 0.42 11880 WACC 11.54%

WACC - Illustration 9 Company A is funded as follows: Balance Sheet Extract Ordinary Shares (50c) 2000 12% Loan Notes 1500 8% Preference Shares ($1) 500 Bank Loan 750 Details on these are as follows. The company has an equity beta of 1.2. Government bonds are currently trading at 6% and the average market risk premium is 7%. The Loan notes are currently trading at $106 and are redeemable at par in 5 years time. The preference shares are trading at 92c. The bank loan has an interest rate of 10%. The current share price is $1.25. The tax rate is 30%. Calculate the Weighted Average Cost of Capital.

Working 1 - Calculate Cost of Capital for each item. Cost of Equity using CAPM Rf (Risk Free Rate) 6 (Rm - Rf)(Ave market risk premium) 7 Beta 1.2 Ke = Rf + β(rm - Rf) (6 + 1.2(7)) = 14.4% Cost of 12% Loan Notes Perio d Item $ DR 5% PV DR 15% PV 1-5 Interest (12 x (1-0.3) 8.4 4.329 36.36 3.352 28.16 5 Capital 100 0.784 78.40 0.497 49.70 Market Value -106-106 8.76-28.14 IRR Calculation: 5 + (8.76 / (8.76 - (28.14)) (15-5) = 7.37% Cost of Preference Shares Interest Paid 8 Market Value of share 92 Cost (Kd) (Interest Paid / Market Value) (8 / 92) = 8.7%

Cost of Bank Debt Interest Rate before Tax 10 Tax Rate 30% After Tax Cost of Debt (10 x (1-0.3)) 7% Working 2 - Calculate the Market Value of Debt and Equity. Ordinary Shares (50c) 12% Loan Notes 8% Preference Shares ($1) SFP 2000 No. of shares (2000 / 0.50) = 4000 Share Price = $1.25 1500 Loan Notes nominal value (on SFP) = 100 Market Value = 106 500 Preference shares nominal value (on SFP) = $1 Market Value = 92c Market Value (4000 x $1.25) = 5000 (1500 x (106 / 100) = 1590 (500 x (92 / 1)) = 460 Bank Loan 750 No market for this so use SFP figure 750 Working 3 - Calculate the weighting of each item. Item Market Value Weighting Equity 5000 (5000 / 7800) Loan Notes 1590 (1590 / 7800) Preference Shares 460 (460 / 7800) Bank Loan 750 (750 / 7800) 7800

Working 4 - Weighting & Weighted Average Cost of Capital Item Market Value Weighting Cost (W1) Ave Equity 5000 (5000 / 7800) 14.4 (5000 / 7800) x 14.4 = 9.23 Loan Notes 1590 (1590 / 7800) 7.37 (1590 / 7800) x 7.37 = 1.50 Preference Shares 460 (460 / 7800) 8.7 (460 / 7800) x 8.7 = 0.51 Bank Loan 750 (750 / 7800) 7 (750 / 7800) x 7 = 0.67 7800 WACC 11.91%

Lecture 11 Capital Structure

Capital Structure - Illustration 1 A company has total capital of $1,000 with debt making up $300 and equity making up $700 of the total. The company s cost of debt is 5% and cost of equity is 14%. I. Calculate the company s current WACC. II. Calculate the WACC if the company substitutes $200 of equity for $200 of debt causing their cost of equity to rise to 16%. III. Calculate the WACC if the company substitutes $300 of equity for $300 of debt causing their cost of equity to rise to 25%. I. Item Market Value Weighting Cost WACC Debt 300 300 / 1000 5% 1.5 Equity 700 700 / 1000 14% 9.8 1000 11.3 II. Item Market Value Weighting Cost WACC Debt 500 500 / 1000 5% 2.5 Equity 500 500 / 1000 16% 8 1000 10.5 III. Item Market Value Weighting Cost WACC Debt 600 600 / 1000 5% 3 Equity 400 400 / 1000 25% 10 1000 13

Lecture 12 M & M Formulae

Illustration 1 ABC Ltd has a share price of 350c and 1m shares in issue. It currently has no debt. Current cost of capital is 13%. The directors have decided to replace $2m of equity with 10% debt. The tax rate is 30%. Required (i) Calculate the new value of the geared firm. (ii)calculate the value of the Equity in the geared firm. Value of Ungeared Firm (1m x 350c) 3,500 Market Value of Debt 2,000 Tax Rate 30% Fill into Formula (Vg = Vu + TB) Vg = (3500 x (30% x 2000) 4,100 Value of Debt (In Question) 2,000 Value of Equity (4,100-2,000) 2,100

Illustration 2 ABC Co. and CD Co. operate in the same industry and are identical in their ability to generate cash flows. ABC Co. is financed by Equity only of 3m shares with current value of $1 and has a cost of equity calculated at 15%. CD Co. has the same total capital but within it has irredeemable debt with a market value of $0.9m. The tax rate is 33%. Required (i) Calculate the value of CD Co. (ii)calculate the value of the Equity in CD Co. Value of Ungeared Firm (3m x 100c) 3,000 Market Value of Debt 900 Tax Rate 33% Fill into Formula (Vg = Vu + TB) Vg = (3,000 x (33% x 900) 3,297 Value of Debt (In Question) 900 Value of Equity (3,297-900) 2,397

Illustration 3 ABC Co. and CD Co. operate in the same industry and are identical in their ability to generate cash flows. ABC Co. is financed by Equity only of 3m shares with current value of $1 and has a cost of equity calculated at 15%. CD Co. has the same total capital but within it has irredeemable debt with a market value of $0.9m and cost of debt of 8%. The tax rate is 33%. Required (i) Calculate the Cost of Equity for CD Co. Keg = Keu + (Keu - Kd) Vd(1-t)/Ve Keg = 15 + (15-8) 900(1-0.33) / 3297 Keg = 16.76%

Illustration 4 ABC Co. and CD Co. operate in the same industry and are identical in their ability to generate cash flows. ABC Co. is financed by Equity only of 3m shares with current value of $1 and has a cost of equity calculated at 15%. CD Co. has the same total capital but within it has irredeemable debt with a market value of $0.9m and cost of debt of 8%. The tax rate is 33%. Required (i) Calculate the WACC for CD Co. Kadj = Keu (1 - tl) Kadj = 15 (1 - (0.33 x (900 / 3,297))) Kadj = 13.65

Lecture 13 Risk Adjusted WACC

Risk Adjusted WACC - Illustration 1 Company A intends to undertake a project in an unrelated industry. The following details are relevant: Item Company A Proxy Company Equity Beta (βe) 1.2 1.4 Value of Equity 1000 800 Value of Debt 400 500 The risk free rate is 4%. The average return on the market is 12%. The post tax cost of debt is 7%. Calculate the risk adjusted WACC to be used in evaluating the project. Ignore Tax Working 1 - Un-gear the proxy βe to get βa. Proxy Equity Beta 1.4 Value of Equity of Proxy 800 Value of Debt of Proxy 500 βu = βg(ve / (Ve + Vd)) 1.4 (800 / (800 + 500)) = 0.86

Working 2 - Re-gear βa with our capital structure βa 0.86 Value of Equity of Company A 1000 Value of Debt of Company A 400 βg = βu + (βu -βd) (Vd / Ve) 0.86 + (0.86 x (400 / 1000) = 1.20 Working 3 - Fill into CAPM Rf (Risk Free Rate) 4 Rm (Ave return on the market) 12 Beta 1.2 Ke = Rf + β(rm - Rf) (4 + 1.2(12-4)) = 13.6% Working 4 - Risk Adjusted WACC Item Market Value Weighting Cost Ave Equity 1000 (1000 / 1400) 13.6 9.71 Debt 400 (400 / 1400) 7 2.00 1400 WACC 11.71

Risk Adjusted WACC - Illustration 2 Company A intends to undertake a project in an unrelated industry. The following details are relevant: Item Company A Proxy Company Equity Beta (βe) 1.1 1.3 Value of Equity 1200 900 Value of Debt 500 450 The risk free rate is 4%. The average return on the market is 12%. The tax rate is 30%. The post tax cost of debt is 8%. Calculate the risk adjusted WACC to be used in evaluating the project. Working 1 - Un-gear the proxy βe to get βa. Proxy Equity Beta 1.3 Value of Equity of Proxy 900 Value of Debt of Proxy 450 βu = βg(ve / (Ve + Vd x 1-t)) 1.3 (900 / (900 + (450 x 0.7)) = 0.96

Working 2 - Re-gear βa with our capital structure βa 0.96 Value of Equity of Company A 1200 Value of Debt of Company A 500 βg = βu + (βu -βd) (Vd (1-t)/ Ve) 0.96 + (0.96 x 500/1200) = 1.24 Working 3 - Fill into CAPM Rf (Risk Free Rate) 4 Rm (Ave return on the market) 12 Beta 1.24 Ke = Rf + β(rm - Rf) (4 + 1.24(12-4)) = 13.92% Working 4 - Risk Adjusted WACC Item Market Value Weighting Cost Ave Equity 1200 (1200 / 1700) 13.92 9.83 Debt 500 (500 / 1700) 8 2.35 1700 WACC 12.18

Illustration 3 Company A Company B Debt/Equity 1/3 1/4 Equity Beta 1.2 Debt Beta 0.3 Assume that the Asset Beta and the Debt Beta of each firm is the same. Calculate the Equity Beta for Company B. Ungear Equity Beta Company A: Ba = (1.2 (3/4)) + (0.3 (1/4) = 0.9 + 0.075 = 0.975 Regear Asset Beta for Company B: Be = 0.975 + ((0.975-0.3) 1/4) = 1.14 or 0.975 = Be (4/5) + 0.3 (1/5) 0.975 - (0.3 x 1/5) = Be (4/5) 0.915 = Be (4/5) Be = 0.915 x 5/4 Be = 1.14

Lecture 14 APV

Illustration 1 Cost of Equity in Geared Firm = 12% Cost of Debt = 8% Debt/Equity ratio = 1/2 Tax rate = 30% Calculate the cost of equity in an ungeared firm. 12% = Keu + (Keu - 8%) (1(1-0.3) / 2) 12% = Keu + 0.35Keu - 2.8% 14.8% = 1.35 Keu Keu = 10.96%

Illustration 2 Company AB has used $5m of 10% debentures to finance a project lasting for 4 years. The tax rate is 35%. Issue costs are 3% and are tax deductible. What is the PV of the issue costs for APV purposes? Issue Costs:! $5m x 3% = $150,000 Tax Relief:!! $150,000 x 35% = $52,500 Post Tax Cost:! $150,000 - $52,500 = $97,500

Illustration 3 Company AB has used $5m of 10% debentures to finance a project lasting for 4 years. The tax rate is 35%. Issue costs are 3% and are tax deductible. These are to be raised along with the finance. What is the PV of the issue costs for APV purposes? Required Finance:! $5m is 97% of total to raise!!!!...so ($5m / 0.97) $5,154,639 must be raised. Issue Costs:!! $5,154,639 x 3% = $154,639 Tax Relief:!!! $154,639 x 35% = $54,124 Post Tax Cost:!! $154,639 - $54,124 = $100,515

Illustration 4 Company AB has used $5m of 10% debentures to finance a project lasting for 4 years. The tax rate is 35%. What is the PV of the tax relief available for APV purposes? Annual Interest = $5m x 10% = $500,000 Annual Tax relief = $500,000 x 35% = $175,000 PV Tax relief = $175,000 x 3.170 = $554, 750

Illustration 5 Company AC needs to raise $10m in debt finance for 4 years. Company AB has raised $7m of 10% debentures and the rest is provided by a subsidised government loan of $3m at 5%. The tax rate is 30%. Calculate the financing effects of the debt for APV purposes. PV Tax Shield Annual Interest = ($7m x 10%) + ($3m x 5%) = $850,000 Annual Tax relief = $850,000 x 30% = $255,000 PV Tax relief = $255,000 x 3.170 = $808,350 Cheap Loan Interest Saved = ($3m x (10% - 5%)) = $150,000 Tax Relief Lost = ($150,000 x 30%) = $45,000 Net Saving = ($150,000 - $45,000) = $105,000 Discount at the cost of debt as even though discounted it has the same risk as a normal loan... PV Interest Saved = ($105,000 x 3.170) = $332,850

Illustration 6 ABC Co. is considering a project which is expected to generate cash inflows of $500,000 per year for 5 years and cost $500,000 of initial investment. Costs have been estimated at $350,000 per year. ABC has a current cost of equity of 14% and a cost of debt of 7% and a current debt to equity ratio of 1/3. To undertake the the project the $500,000 will be raised through a bond issue of 8% with issue costs of 4% to be raised in addition to the finance. The tax rate is 30%. Un-gear the cost of equity 14% = Keu + (Keu - 7%) (1(1-0.3) / 3) 14% = Keu + 0.23Keu - 1.63% 15.63% = 1.23 Keu Keu = 12.71% say 13% Base Case NPV Discount at un-geared Ke of 13% PV Cash Inflows = ($500,000 x 3.517) = $1,758,500 PV Outflows = ($350,000 x 3.517) = $1,230,950 Net Cash Inflow = $527,550 Initial Investment = $500,000 Base Case NPV = ($527,550 - $500,000) = $27,550

Issue Costs Required Finance:! $500,000 is 96% of total to raise!!!!...so ($500,000 / 0.96) $520,833 must be raised. Issue Costs:!! $520,833 x 4% = $20,833 Tax Relief:!!! $20,833 x 30% = $6,250 Post Tax Cost:!! $20,833 - $6,250 = $14,583 PV Tax Shield Annual Interest = ($520,833 x 8%) = $41,666 Annual Tax relief = $41,666 x 30% = $12,500 PV Tax relief = $12,500 x 3.993 = $49,912 APV Base Case NPV! =! $27,550 PV Issue Costs! = ($14,583) PV Tax Shield! = $38,040 APV!!! = $51,007

Lecture 15 More Risk

Illustration 1 ABC Ltd is undertaking a project costing $900m with expected net cash flows of $400m in years 1 & 2 then $600m in year 3. The FD considers that these cash flows may be overestimated by as much as 10% in year 1, 15% in year 2 and 20% in year 3. The risk free rate is 5% Required Using certainty equivalents calculate the expected NPV of the project. 0 1 2 3 Cash Flows -900 400 400 600 Certainty Equivalents 1 0.9 0.85 0.80 CE Cash Flows -900 360 340 480 Discount Rate (5%) 1 0.952 0.907 0.864 Present Value -900 343 308 415 NPV 166

Lecture 16 Further Appraisal

Expected Values - Illustration 1 A business is considering 2 different projects. The likely profit made from each project is outlined below: Project A Project B Projected Profit Percentage Likely-hood Projected Profit Percentage Likely-hood $10,000 10% $10,000 15% $15,000 30% $15,000 25% $20,000 40% $20,000 30% $23,000 20% $23,000 30% Calculate the expected value for each of the projects. Project A Project B Project ed Profit Percent age Likelyhood Working EV Project ed Profit Percent age Likelyhood Working EV $10,000 0.1 (10,000 x 0.1) $15,000 0.3 (15,000 x 0.3) $20,000 0.4 (20,000 x 0.4) $23,000 0.2 (23,000 x 0.2) $1,000 $10,000 0.15 (10,000 x 0.15) $4,500 $15,000 0.25 (15,000 x 0.25 $8,000 $20,000 0.3 (20,000 x 0.3) $4,600 $23,000 0.3 (23,000 x 0.3) $1,500 $3,750 $6,000 $6,900 1 EV $18,100 1 EV $18,150

Sensitivity Margin - Illustration 2 A business is considering a project which will cost them an initial 20,000 The sales expected for the 2 year duration are 20,000pa. The variable costs are 2,000pa Cost of capital 10% Calculate the sensitivity margin of: I. The initial investment. II. III. The variable costs of the projects. The sales of the project. Working 1 - NPV of Project Period 0 1 2 Capital Investment -20,000 Cash-Flows 20,000 20,000 Variable Cost -2,000-2,000 Total Cash Flows -20,000 18,000 18,000 Discount Rate 10% 1 0.909 0.826 PV Cash Flows -20,000 16,362 14,868 NPV 11,230

Working 2 - PV of each item Period 0 1 2 Variable Costs -2,000-2,000 Discount Rate 10% 0.909 0.826 Total -1,818-1,652 Present Value of Variable Costs (1,818 + 1,652) = $3,470 Sales 20,000 20,000 Discount Rate 10% 0.909 0.826 Total 18,180 16,520 Present Value of Sales (18,180 + 16,520) = $34,700 Present Value of Initial Investment = $20,000 Sensitivity Margins Item Working Sensitivity Margin Explanation Initial Investmen t Variable Costs NPV / PV Initial Investment (11,230 / 20,000) NPV / PV Variable Costs (11,230 / 3470) 56% The NPV is 56% of the initial investment. 323% The Variable costs would need to rise by 323% to create a negative NPV Sales NPV / PV Sales (11,230 / 34,700) 32% Sales would need to drop by 32% before the NPV would be negative.

Lease V Buy - Illustration 3 Machine cost $10,000 The Machine has a useful economic life of 5 years with no scrap value Capital allowances available at 25% reducing balance Finance choices 1) 5 year loan 14.28% pre tax cost 2) 5 year Finance Lease @ $2,200 pa in advance If the machine is purchased then maintenance costs of $100 per year will be incurred. The tax rate is 30%. The leasing company will maintain the machine if it is leased. Should the company lease or buy the machine. Buy Working 1 - Capital Allowances Period Balance 25% WDA 30% Tax Saving Period 1 10000.00 2500.00 750.00 2 2 7500.00 1875.00 562.50 3 3 5625.00 1406.25 421.88 4 4 4218.75 1054.69 316.41 5 5 3164.06 3,164.06 949.22 6

Working 2 - Maintenance Amount Tax Saving $100 per Year (100 x 30%) = $30 Working 3 - Discount Rate Pre-tax Borrowing Rate 14.28% Tax Rate 30% Post Tax Borrowing Rate 14.28 x (1-0.3) = 10% Working 4 - NPV Period 0 1 2 3 4 5 6 Capital -10,000 WDA Tax Saving (W1) 750 562 422 316 949 Maintenance -100-100 -100-100 -100 Maintenance Tax Saving (W2) 30 30 30 30 30 Total Cash Flows -10,000-100 680 492 352 246 979 Discount Rate 10% (W3) 1 0.909 0.826 0.751 0.683 0.621 0.564 PV Cash Flows -10,000-91 562 369 240 153 552 NPV -8,214

Lease Period 0 1 2 3 4 5 6 Capital -2200-2200 -2200-2200 -2200 Tax Saving on Lease Payment 660 660 660 660 660 Total Cash Flows -2200-2200 -1540-1540 -1540 660 660 Discount Rate 10% (W3) 1 0.909 0.826 0.751 0.683 0.621 0.564 PV Cash Flows -2,200-2000 -1272-1157 -1052 410 372 NPV -6,898 Based on the above, the company should lease the machine.

Equivalent Annual Cost - Illustration 4 Machine Cost 30,000 Running costs Year 1 10,000 Year 2 11,500 Residual Value (if sold after..) Year 1 19,000 Year 2 16,000 Cost of capital = 10% Is it better to replace the machine every year or to replace it every 2 years?

NPV for replacement after one year Period 0 1 Capital Investment -30,000 Running Costs -10,000 Residual Value 19,000 Cash Flows -30,000 9,000 Discount Rate 10% 1 0.909 PV Cash Flows -30,000 8,181 NPV -21,819 Annuity Factor from tables (1yr at 10%) 0.909 Equivalent Annual Cost (NPV / Annuity Factor) = (-21,819 / 0.909) = -$24,003 NPV for replacement after two years Period 0 1 2 Capital Investment -30,000 Running Costs -10,000-11,500 Residual Value - 16,000 Cash Flows -30,000-10,000 4,500 Discount Rate 10% 1 0.909 0.826 PV Cash Flows -30,000-9,090 3,717 NPV -35,373 Annuity Factor from tables (2yrs at 10%) 1.736 Equivalent Annual Cost (NPV / Annuity Factor) = (-35,373 / 1.736) = -$20,376

Lecture 17 Further Appraisal II

Profitability Index - Illustration 1 A business has identified the following projects. They have $200,000 to invest and the projects are divisible. Project Investment NPV A 90,000 15,000 B 110,000 25,000 C 50,000 10,000 D 75,000 22,000 E 70,000-8,000 Which projects should the business undertake? Project Investment NPV PI (NPV / Investment) Rank A 90,000 15,000 17% 4% B 110,000 25,000 23% 2% C 50,000 10,000 20% 3% D 75,000 22,000 29% 1% E 70,000-8,000 - Investment Project Investment All of D 75,000 All of B 110,000 30% of C (50,000 x 0.3) 15,000 Total Investment 200,000

Investment Choices - Illustration 2 A business has identified the following projects. They have $200,000 to invest and the projects are non-divisible. Project Investment NPV A 90,000 15,000 B 110,000 25,000 C 50,000 10,000 D 75,000 22,000 Which projects should the business undertake? Project Investment NPV Rank A + B 90,000 + 110,000 = 200,000 15,000 + 25,000 = 40,000 2 A + C 90,000 + 50,000 = 140,000 15,000 + 10,000 = 25,000 6 A + D 90,000 + 75,000 = 165,000 15,000 + 22,000 = 37,000 3 B + C 110,000 + 50,000 = 160,000 25,000 + 10,000 = 35,000 4 B + D 110,000 + 75,000 = 185,000 25,000 + 22,000 = 47,000 1 C + D 50,000 + 75,000 = 125,000 10,000 + 22,000 = 32,000 5 The business should undertake projects B and D as these will yield the highest NPV.

Equivalent Annual Annuity - Illustration 3!!!! NPV Duration Project 1 300 5 yrs Project 2 200 3 yrs Project 3 350 6 yrs Calculate the EEA of each project given a cost of capital of 10% Project NPV Annuity Factor Working (NPV / Annuity Factor) EAA 1 300 3.791 300 / 3.791 79.13 2 200 2.487 200 / 2.487 80.42 3 350 4.355 350 / 4.355 80.37 Project 3 has the highest EAA.

Lecture18 Working Capital

Working Capital Illustration Balance Sheet $ 000 ASSETS Non Current Assets 1000 Inventory 300 Receivables 200 Cash 300 1800 LIABILITIES Ordinary Shares 800 Reserves 200 Long term Liabilities 700 Payables 100 Overdraft - 1800 Income Statement $ 000 Revenue 1000 COS 800 Gross Profit 200 Other Costs 100 Net Profit 100 Other Information: All sales are made on credit. Required: Calculate the Cash Operating Cycle for Inter Ltd.

Item Working Days Inventory Period 300/800 x 365 137 Collection Period 200/1000 x 365 73 Less: Payables Period 100/800 x 365 46 164

Working Capital Illustration Part II Show the journal entries and calculate the Revised Balance sheet if the operating cycle changes to: Item Days Inventory Period 200 Collection Period 100 Less: Payables Period 30 270

Item New Days Old Days Old Balance Working New Balance Movem t Inventory 200 137 300 300 x 200/137 438 138 Receivabl es Less: 100 73 200 200 x 100/73 274 74 Payables 30 46 100 100 x 30/46 65-35 270 164 Entries Dr Cr Dr Inventory 138 Cr Cash 138 Dr Receivables 74 Cr Cash 74 Dr Payables 35 Cr Cash 35

Revised Balance Sheet $ 000 Movement $ 000 ASSETS Non Current Assets 1000 1000 Inventory 300 138 438 Receivables 200 74 274 Cash 300-247 53 1800 1765 LIABILITIES Ordinary Shares 800 800 Reserves 200 200 Long term Liabilities 700 700 Payables 100-35 65 Overdraft 0 0 1800 1765

Working Capital Illustration Part III Show the journal entries and calculate the Revised Balance sheet if the operating cycle changes to: Item Days Inventory Period 90 Collection Period 30 Less: Payables Period 60 60 Item New Days Old Days Old Balance Working New Balance Movem t Inventory 90 200 438 438 x 90/200 197-241 Receivabl es Less: 30 100 274 274 x 30/100 82-192 Payables 60 30 65 65 x 60/30 130 65 60 270

Entries Dr Cr Dr Cash 241 Cr Inventory 241 Dr Cash 192 Cr Receivables 192 Dr Cash 65 Cr Payables 65 498 498 Revised Balance Sheet $ 000 Movement $ 000 ASSETS Non Current Assets 1000 1000 Inventory 438-241 197 Receivables 274-192 82 Cash 53 498 551 1765 1830 LIABILITIES Ordinary Shares 800 800 Reserves 200 200 Long term Liabilities 700 700 Payables 65 65 130 Overdraft 0 0 1765 1830