Revision exercise 1 solutions kho tài liệu bách khoa

Finance – Revision Exercise - solutions Finance – Revision Exercise - Solutions In the solutions: PV = Present value PVIF = Present Value interest factor (Table A.1) PVA = Present value of an annuity PVAIF = Present value of annuity interest factor (Table A.2) FV = Future value FVIF = Future Value interest factor (Table A.3) FVAIF = Future Value interest factor (Table A.4) CF = Cash Flow m = number of compounding periods per year n = number of years r = interest rate PV = What is the present value of £26,250 to be received at the end of years, if the relevant interest rate is 12%? FV (1 + r)n Or, using the tables PV = FV * PVIFr,n (Table A.1) PV = 26250 * 0.4523 FV = = £11,873 What is the future value of £1200 if it earns 14% compounded annually for 15 years? PV * (1 + r)n Or, using the tables FV = PV * FVIFr,n (Table A.3) FV = 1200 * 7.1379 APR = £8,565 What is the Annual Percentage Rate (APR, – or effective rate in USA) if a 10% annual rate is compounded monthly? = (1 + (r/m))m = (1 + (0.1/12))12 zfm1573208547.doc 2010 -1- Finance – Revision Exercise - solutions PVA FVA = 1.104713 = 10.47% What is the present value of a stream of cash flows of £500 per annum for years at 8% interest rate? = CF * PVAIFr,n (Table A.2) = 500 * 3.9927 = £1996 What is the future value of a stream of cash flows of £10,000 per annum for years at 11% interest? = CF * FVAIFr,n (Table A.4) = 10000 * 11.859 = £118,590 What is the return offered if you can invest £1200 now for years and obtain £1900 at the end of that time? FV = PV * FVIFr,n (Table A.3) FVIFr,n = FV PV = 1900 1200 = 1.5833 Look up table A.3, years and across until you get to the closest number to 1.583, then read up for the interest rate = 8% Using the calculator it will be 1.58331/6 = 1.0795979 (1 + R) = 7.96% If a company’s nominal cost of capital is 12% and inflation is 3%, what is the real cost of capital for the company? = zfm1573208547.doc 2010 (1 + N) (1 + I) -2- Finance – Revision Exercise - solutions (1 + R) R = 1.12 1.03 = 1.087378 = 8.738% What is the nominal return if the real return is 4% and the inflation rate is 3%? (1 + N) (1 + N) N = (1 +R) * (1 + I) = 1.04 * 1.03 = 1.0712 = 7.12% What would be the annualised return over two years, if in year two the real return remained the same, but the inflation rate rose to 5%? (1 + N) = (1 +R) * (1 + I) = 1.04 * 1.05 = 1.092 Two year return = (1.0712) * (1.092) (1 + N)2 = 1.16975 this is the year compound growth factor, we want the annualised return, so we need to take this return to the root of the number of years; = 1.169750.5 = 1.08155 Subtract to get the interest rate = 8.155% If a bond has a coupon of 7.5% and a nominal value of £100, and is priced at £110.22 in the market, what is the interest yield? Interest yield (or running yield) zfm1573208547.doc 2010 = Coupon Payment £ Market price = 7.5 110.22 -3- Finance – Revision Exercise - solutions = 0.068 = 6.8% 10 If you buy shares in BAe Systems today for 462p, sell them in three months time for 488p and receive a quarterly dividend of 6p, what is your holding period return? What is this return annualised? Holding period return = Div + selling price – buying price Buying price = + 488 – 462 462 = 0.069264 = 6.9264% To annualise, (1 + r)m where m = number of periods in a year annualised return = (1.069264)4 = 1.30719 = 30.719% 11 There is a 20% probability of getting a return of –8% (minus 8%), a 25% chance of getting a return of 2%, a 35% chance of getting a return of 9% and a return of 15% has a probability of 20% What is the expected return and standard deviation of this investment? rtn -0.08 0.02 0.09 0.15 prob 0.2 0.25 0.35 0.2 exp rtn = rtn * prob rtn - E( r ) rtn - E( r )^2 p* (rtn - E( r)^2 -0.016 -0.1305 0.0170303 0.00340605 0.005 -0.0305 0.0009303 0.00023256 0.0315 0.0395 0.0015603 0.00054609 0.03 0.0995 0.0099003 0.00198005 0.0505 Variance = 0.00616475 Std dev = 0.07851592 Expected return = 5.05% Standard deviation = 7.851% zfm1573208547.doc 2010 -4- Finance – Revision Exercise - solutions 12 What will a sum of £7000 at 8% compounded semi-annually be worth in 10 years time? FV = PV*(1 + (r/m))mn Where m = number of times compounded per year and n = number of years FV = 7000 * (1 + (0.08/2))2*10 = 7000 * (1.04)20 = 7000 * 2.1911 = £15,337.86 13 What will a sum of £12,000 at 12% compounded monthly be worth at the end of years? FV = PV * FVIFr,n (Table A.3) = 12,000 * FVIF0.01,24 = 12000 * 1.2697 = £15,236 or, FV = = PV * (1 + (r/m))mn PV * (1 + (0.12/12))12*2 14 If you were offered £10,000 four years from today, or £1000 a year for ten years and the return you can earn on your investments is 7%, which would you prefer? PV PVA = FV * PVIF0.07,4 = 10000 * 0.7629 = £7,629 = CF * PVAIF0.07,10 = 1000 * 7.0236 = £7,023.60 You would prefer £10,000 in four years time zfm1573208547.doc 2010 -5- Finance – Revision Exercise - solutions 15 How long does it take £14,500 to grow into £23,352 at 10% interest? FVIFr,n = FV PV = 23352 14500 = 1.6105 Look up future value factors table (A.3), down the 10% column until you come to 1.6105 and read across for the number of years = 16 A company is expecting £4000 a year from a contract for the next years (first cash flow at the end of year 1) What is the present value of this contract if the interest rate is 7%? PVA = CF * PVAIFr,n (Table A.2) = 4000 * 5.9713 = £23,885 17 A company wants to redeem a bond at the end of five years time The amount outstanding is £250m If the company can earn 7% on its cash, how much must it save each year to have the £250m in years time to pay off the bond? FVA = CF * FVAIFr,n (Table A.4) CF = FVA FVAIFr,n = 250 5.7507 = £43.473m per year 18 If you can borrow at 9% compounded daily, what is your effective rate of interest (your true borrowing rate that reflects the daily compounding? The true borrowing rate will be higher than the annual quoted rate The calculation is; (1 + (i/m))m – 1, zfm1573208547.doc 2010 -6- Finance – Revision Exercise - solutions where i is the annual interest rate and m is the number of compounding periods per year Here we have; (1 + (0.09/365))365 -1 = (1 + 0.000246575)365 – = 1.09416 – = 9.416% If you borrowed £15,000 for years, how much would you pay back? You will use the same formula, but you don’t need to subtract the at the end This will give you a compound growth factor that you can multiply your cash sum by The formula becomes; CF * (1 + (i/m))mn where n is the number of years £15,000 * (1 + (0.09/365)365*5 = £15,000 * (1.000246575)1825 = £15,000 * 1.568225 = £23,523 You borrow £15,000 over years, at an interest rate of 9% compounded daily, which means that you will repay £23,523 over the life of the loan This compares to repaying £23,079 if the interest was compounded annually (£15k * 1.095) 19 If you were charged 3% interest per month, how much would you pay back over the life of a £5,000, two year loan? Using the framework from Q.18, we have; CF * (1 + (i/m))mn where n is the number of years = £5000 * (1 + 0.03)12*2 = £5000 * (2.03279) = £10,163.97 Here, we don’t need to calculate the i/m rate (the per period interest rate), because it is already given in the question (3% per month – it is not expressed as the annual rate zfm1573208547.doc 2010 -7- Finance – Revision Exercise - solutions here) We are not working out the true annual interest rate, just the amount we need to repay The true annual interest rate is 42.576%, which sounds a lot worse than 3% per month 20 You have twins that are five years old just now You estimate that you will need a fund of £80,000 at the end of six years to be able to fund their schooling A financial product is offering a saving rate of return of 6% per annum i) How much you have to deposit now to grow to £80,000 over the six years? PV = FV * PVIF0.06,6 (Table A.1) = 80000 * 0.7050 = £56,400 or, PV = ii) FV (1 + 0.06)6 How much would you have to save each year for it to grow to £80,000 at the end of six years? FVA = CF * FVAIFr,n CF = FVA FVAIF0.06,6 = 80000 6.9753 = £11,469 needs to be saved each year 21 Assume HSBC has a required rate of return of 8%, it has earnings per share (eps) for fiscal year 2009 of 22.32p How long will it take for the eps to double at that required rate of return? FVIFr,n here is 2.0 (eps doubling), so we just need to look up Table A.3 and 8%, read down for 2.0 and read off the year = years Compound growth of 8% annually will double the value of money in years 22 Tesco had a total capital expenditure in 1998 of £841m, in 2002 this was £2027m, in 2006 it was £2.8bn, in 2009 it was £3.1bn and in 2011 it was £3.7bn zfm1573208547.doc 2010 -8- Finance – Revision Exercise - solutions What was the annualised growth rate in capex at Tesco from ’98-02, 02-06, 06-09, 09-11, and for the entire period? For 1998 – 2002, the growth was; FV = PV * FVIFr, n 2027 = 841 * FVIFr,4 FVIFr,4 = 2027 841 = 2.4102 To find out the annualised growth rate, take to the power of over the number of periods, = 1/4 = 0.25 = 2.41020.25 = 1.24599 = 24.599% compound growth per annum Tesco 1998 2002 2006 2009 2011 Capex 841 2027 2800 3100 3700 eps dividend 8.64 3.87 11.86 5.60 20.2 8.63 27.5 11.96 33.1 14.96 Tesco growth rates 1998 2002 2006 2009 2011 whole period growth: Capex 841 2027 2800 3100 3700 growth 24.60% 8.41% 3.45% 9.25% 12.07% Eps 8.64 11.86 20.20 27.50 33.10 growth 8.24% 14.24% 10.83% 9.71% 10.88% dividend 3.87 5.60 8.63 11.96 14.96 growth 9.68% 11.42% 11.49% 11.84% 10.96% Dividend and eps growth have picked up considerably in the second period Tesco continue to invest heavily in capex to drive the business forward (capex zfm1573208547.doc 2010 -9- Finance – Revision Exercise - solutions continues to grow although at a slower pace) The rapid growth in capex in the early period has delivered faster earnings and dividend growth in the second period In the more recent times (2006-2009), capex growth has slowed to only 3.45% per annum, this may already be slowing the growth of eps (down from 14.24% growth to 10.83% growth), which ultimately will affect the ability of the company to grow dividends at the current rate Through to the 2011 period capex has picked up again (international investments), but in early 2012, Tesco warned of a poor UK trading performance, which sent the shares down by almost 20% Results out in April 2012 The dividend payout ratio (div/eps) fluctuates around 45% It looks like the firm is very good at generating strong returns from its investment 23 Tesco’s eps in 1998 was 8.64p, in 2002 it was 11.86, in 2006 it was 20.20p, in 2009 it was 27.50p and in 2011 it was 33.1p What was the growth rate in eps from ’98-02, 02-06, 06-09, 09-11, and for the entire period? Same process as Q.22, see table for answer 24 Tesco’s dividend was 3.87p in 1998 and in 2002 it was 5.60p, in 2006 it was 8.63p, in 2009 it was 11.96p, and in 2011 it was 14.46p What was the dividend growth rate from ’98-02, 02-06, 06-09, 09-11, and for the entire period? Same process as Q.22 , see table for answer 25 What would you pay for an asset that produces a level cash stream of £50,000 every six months for the next 10 years, if your opportunity cost of capital is 8% (annual rate), compounded per period? PVA = CF * PVAIFr,n (Table A.2) = 50000 * PVAIF4,20 = 50000 * 13.590 = £679,500 or, working out the 20 period annuity factor using the formula (the method you would use if the interest rate was not a whole number); PVA = 1- [1/(1 + r)n] r (formula from the top of Table A.2) zfm1573208547.doc 2010 - 10 - Finance – Revision Exercise - solutions = – [1/(1 + 0.04)20] 0.04 = £679,516 26 A company has borrowed £100,000 to buy new machinery It has to repay the loan in equal instalments over a year period If the borrowing rate is 12 %, what is the annual repayment? PVA = CF * PVAIFr,n (Table A.2) 100000 = CF * 3.6048 CF = 100000 3.6048 = £27,740.80 27 You run a small business and you buy a fleet of four delivery vans You arrange the deal through a finance company They lend you £120,000, but you have to repay the loan in equal repayments over the next 30 months The payments are £4649.72 per month, what is the annualised interest rate being charged? PVA = CF * PVAIFr,n (Table A.2) 120000 = 4649.72 * PVAIFr,30 PVAIFr,30 = = 120000 4649.72 25.808 Look up table A.2, 30 periods until you get to 25.808, = 1% per month Annualised: = (1.01)12 12.6825% 28 Bryan Griggs is a world renowned corporate guru and has signed a £34m contract with Mckenzies the giant Scottish consulting firm The contract will entail Griggs being paid £2m per annum for three years and then £5m per annum for the next years, and assuming he makes it to the end of the contract, he will be paid a bonus of £8m If the opportunity cost of capital is 8%, what is the present value of the contract? PVA £2m * PVAIF0.08,3 zfm1573208547.doc 2010 = £5.1542m - 11 - Finance – Revision Exercise - solutions PVA £5m *( PVAIF0.08,7 - PVAIF0.08,3) = £5m * 2.6293 = £13.1465m PV £8m * PVIF0.08,7 = £4.668m £22.9687m 29 A rival company in your sector is offering you a joint venture deal – if you pay £200,000 to the other company today, it will pay you a cash flow of £30,000 per annum at the end of year and then for a further 12 years If your cost of capital is 10%, would you sign the contract? There is a 13 year annuity at 10% = 7.1034 (Table A.2), multiply £30,000 cash flow by this = £213.1 The cash flow starts from the end of year 5, the annuity will bring the value back to the start of year so we use the discount rate for the end of year = 0.683, multiply the 213.1 by this = £145,550 – don’t accept the contract Or (17 year annuity – year annuity) * 30,000 = £145,550 30 Your company has the following four options: - sell the division today for £10m cash accept an earn out with four fixed payments of £3.25m each, with the first payment today accept royalties of £1m per annum for the next 20 years with the first payment today accept £5m now and £10m in years time The relevant interest rate is 8% = = = = £10m £3.25 * PVAIF0.08,4*1.08 (PVAIF0.08,20)*1.08 £5m + (PVIF0.08,6 * £10m) = = = = £10m £11.625m £10.6035m £11.302m Choose the second option 31 Your company can buy a machine for £350,000 that will generate cash savings of £70,000 per annum for the next years as a result of lower labour costs If the opportunity cost of capital is 9%, should you buy the machine? PVA = - £350000 = zfm1573208547.doc 2010 CF * PVAIF0.09,6 (Table A.2) 70000 * 4.4859 - 12 - Finance – Revision Exercise - solutions -£350000 = £314,013 NPV -£35,987 = Don’t buy the machine 32 You have gone on ‘Who wants to be a millionaire anyway’ and won the star prize of £1m, but find out that your prize will be paid in equal annual instalments of £100,000 starting today You were so confident of winning that you have already spent £500,000 You are contacted by a financial company who are willing to buy your stream of cash flows off you for a single payment today Your opportunity cost of capital is 8% They offer you £700,000, you accept or reject? A fair price today for the prize would be: PVA A.2) = CF * PVAIF0.08,10 * (1 + r) [as the annuity starts today] = 100000 * 6.7101 * 1.08 = £724,690.80 (Table You should be able to sell the prize for that amount today, so you would reject the offer of £700,000 33 What is a convertible bond and what are the advantages and disadvantages of it? It is a bond (usually with a lower coupon than a straight bond would have) which is convertible into shares at some point in the future It is a means of raising finance for companies, at the current time companies are raising cash this way because they don’t want to sell shares at low current valuations If the convertible goes well the shares will rise above the conversion price, and the bondholders will convert into equity This will save the company having to find the cash to redeem the bond The downside is that there are now more shareholders – the original shareholders have been diluted The convertible is a way of resolving some of the agency problems If the managers enter a risky project and it pays off, the shareholders would get all the benefits – with the convertible the project is still undertaken, but part of the upside will be shared with the bondholders zfm1573208547.doc 2010 - 13 - Finance – Revision Exercise - solutions 34 What are the agency problems between shareholders and managers and how are they resolved? How effective are the resolution techniques you have identified? The dangers that managers expropriate too much of the company’s wealth for their own use See the black class folder cuttings from FT and Business Week focussing on the problems that stock options have caused They are a useful tool but they are being misused by managers Agency problems can range from J Messier at Vivendi getting the company to buy him a $17m apartment for him to live in New York, to the rewarding of managers to the tune of hundreds of millions of dollars for a miserable performance The banks took huge risks to generate higher returns that would result in higher bonuses for themselves – at the expense of the shareholders (and taxpayers) Managers and shareholders should have their interests aligned so they are moving towards the same goal Executive options were supposed to achieve that The institutional shareholders need to be stronger in the face of managers In the UK for more and more companies, the directors are obliged to buy a significant number of shares This means they are more aligned with ordinary shareholders When the shares go down, they will feel the pain in the same way that shareholders This wasn’t the case with options 35 What justification is there for shareholder wealth maximisation being the main corporate aim, why not any of the other common goals? It is the shareholders who own the company, they have put the money in, the customers haven’t, the community hasn’t, the government hasn’t The shareholders are risking their capital in the company and the company has to operate on the basis that they aim to maximise the shareholder’s return If the managers don’t it – get someone who will, or the company may be taken over That doesn’t mean the company puts shareholder wealth absolutely above everything else Companies can suffer if they get a bad reputation in the wider marketplace Consumers are quick to castigate companies for behaviour that is lacking in any thought for the wider community So, in recent years Nike have been lambasted for having no factories in the US, but continuing to charge huge price for their products BP is accused of cutting back on safety standards Other companies are caught up in bribery and corruption scandals Companies want to be perceived as good corporate citizens and will work to try and maintain that image If this means that some extra costs are incurred then so be it, this is a price the companies are willing to pay, not to suffer in the court of public opinion So this means that shareholder wealth maximisation will be followed but with a softer face zfm1573208547.doc 2010 - 14 - Finance – Revision Exercise - solutions 36 How would you describe the key differences between shareholders in a company and bondholders in a company? Shareholders can only lose what they put in, they can’t be pursued for the debts of the company They have a vote in the running of the company They are last in line to receive cash from the company and will usually get nothing if the bondholders put the company into liquidation The shareholder’s return will be in the form of a dividend (not guaranteed) and a capital gain (risky – they have to realise the gain) The bondholders not have any say in the running of the company – they have no vote They receive a fixed annual return and their capital back at the end of the bond’s life 37 What is the usual order of preference for financing a company and why is this the case? Retained earnings, then debt finance, then equity finance Retained earnings is top because the finance is available for use without the scrutiny of the financial markets It is ‘internal’ finance Debt and equity finance is ‘external’ finance as it has to be raised on the capital markets and the company will face scrutiny because they have to publish a prospectus detailing the use of the cash Debt is preferred to equity because there is a tax break on the interest payments – debt is cheaper The markets will usually look at a company that is selling equity as having problems with the debt markets and this is something of a last resort (the equity market) 38 How far listed company responsibilities go? Any further than the shareholders? How ethical does a company need to be? Nike used to manufacture all their shoes outside the US in very cheap labour factories Consumer pressure (rather than shareholder pressure) forced the company to shift some production to the US Does the company owe the extended community anything? – No, why should shareholders cash be spent in this way if it doesn’t have to – Yes, it is an investment by the company in being recognised as a ‘good corporate citizen’ which will be rewarded by loyalty and good feelings from customers and other stakeholders Tesco is a giant corporation making £2 billion in profits but it is still in touch with its customers (and a larger supporter of schools and local charities) and is valued and respected [The big banks in the UK are perceived as not making a similar effort and don’t instil the same trust in their customers.] 39 How should chief executives be rewarded? Is Larry Ellison worth $700m a year? Should Stan O’Neal have been given $160m for what he did at Merrill Lynch? Should the average remuneration package of a top S&P 500 or FTSE 100 CEO run into the tens of millions of dollars per year? What risks are they taking? zfm1573208547.doc 2010 - 15 - Finance – Revision Exercise - solutions BP in January 2005 announced that it was stopping rewarding its staff with share options, instead shares would form part of their compensation Shares give an ownership in the company, options not Executives can simply exercise the options and sell at the same time, pocketing any gain If options are ‘under the water’ ie, the share price is well below the option exercise price, then they may not be much use in motivating the executives Shares will have a value, even if there has been a fall As far as the level of remuneration is concerned that is up to the shareholders But they should devise a system that rewards good performance with increases in remuneration and poor performance with reductions in remuneration Too many bosses remuneration goes up whether the company does well or does poorly Poor performance should not be rewarded as it has been at a number of banks in the past year There is a mismatch between risk and reward for the executives, they have all the rewards and the shareholders have all the risks zfm1573208547.doc 2010 - 16 - ... = 1/ 4 = 0.25 = 2. 410 20.25 = 1. 24599 = 24.599% compound growth per annum Tesco 19 98 2002 2006 2009 2 011 Capex 8 41 2027 2800 310 0 3700 eps dividend 8.64 3.87 11 .86 5.60 20.2 8.63 27.5 11 .96 33 .1. .. Eps 8.64 11 .86 20.20 27.50 33 .10 growth 8.24% 14 .24% 10 .83% 9. 71% 10 .88% dividend 3.87 5.60 8.63 11 .96 14 .96 growth 9.68% 11 .42% 11 .49% 11 .84% 10 .96% Dividend and eps growth have picked up considerably... = 1- [1/ (1 + r)n] r (formula from the top of Table A.2) zfm1573208547.doc 2 010 - 10 - Finance – Revision Exercise - solutions = – [1/ (1 + 0.04)20] 0.04 = £679, 516 26 A company has borrowed 10 0,000