Revision exercise 1 solutions kho tài liệu bách khoa

What is the Annual Percentage Rate APR, – or effective rate in USA if a 10% annual rate is compounded monthly?... If a company’s nominal cost of capital is 12% and inflation is 3%, wha

Finance – Revision Exercise 1 - Solutions

In the solutions:

1 What is the present value of £26,250 to be received at the end of 7

years, if the relevant interest rate is 12%?

(1 + r)n

Or, using the tables

2 What is the future value of £1200 if it earns 14% compounded

annually for 15 years?

Or, using the tables

3 What is the Annual Percentage Rate (APR, – or effective rate in USA)

if a 10% annual rate is compounded monthly?

= 1.104713

4 What is the present value of a stream of cash flows of £500 per annum

for 5 years at 8% interest rate?

5 What is the future value of a stream of cash flows of £10,000 per

annum for 8 years at 11% interest?

6 What is the return offered if you can invest £1200 now for 6 years and

obtain £1900 at the end of that time?

PV

1200

Look up table A.3, 6 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 = 7.96%

7 If a company’s nominal cost of capital is 12% and inflation is 3%,

what is the real cost of capital for the company?

= 1.12

1.03

8 What is the nominal return if the real return is 4% and the inflation

rate is 3%?

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%?

Two year return = (1.0712) * (1.092)

want the annualised return, so we need to take this return to the root of the number of years;

Subtract 1 to get the interest rate = 8.155%

9 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?

Market price

110.22

= 0.068

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

462

To annualise, (1 + r)m where m = number of periods in a year

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 prob rtn * prob rtn - E( r ) rtn - E( r )^2 p* (rtn - E( r)^2

Expected return = 5.05%

12 What will a sum of £7000 at 8% compounded semi-annually be worth in

10 years time?

Where m = number of times compounded per year and n = number of years

13 What will a sum of £12,000 at 12% compounded monthly be worth at the end of 2 years?

FV = PV * FVIFr,n (Table A.3)

or,

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?

You would prefer £10,000 in four years time

15 How long does it take £14,500 to grow into £23,352 at 10% interest?

PV

14500

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 = 5

16 A company is expecting £4000 a year from a contract for the next 8 years (first cash flow at the end of year 1) What is the present value of this contract if the interest rate is 7%?

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 5 years time to pay off the bond?

FVAIFr,n

5.7507

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,

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

= 1.09416 – 1

= 9.416%

If you borrowed £15,000 for 5 years, how much would you pay back?

You will use the same formula, but you don’t need to subtract the 1 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

You borrow £15,000 over 5 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

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 do you have to deposit now to grow to £80,000 over the six

years?

or,

(1 + 0.06)6

ii) How much would you have to save each year for it to grow to £80,000

at the end of six years?

FVAIF0.06,6

6.9753

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 = 9 years Compound growth of 8% annually will double the value of money in 9 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

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;

841

To find out the annualised growth rate, take to the power of 1 over the number of periods, = 1/4 = 0.25

Tesco

Capex eps dividend

Tesco growth

rates

Capex growth Eps growth dividend growth

whole period

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

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?

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);

r (formula from the top of Table A.2)

= 1 – [1/(1 + 0.04)20 ]

0.04

26 A company has borrowed £100,000 to buy new machinery It has to repay the loan in equal instalments over a 5 year period If the borrowing rate

is 12 %, what is the annual repayment?

3.6048

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?

4649.72

Look up table A.2, 30 periods until you get to 25.808, = 1% per month

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 4 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 £5m *( PVAIF0.08,7 - PVAIF0.08,3)

£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 5 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 5 so we use the discount rate for the end of year 4 = 0.683, multiply the 213.1 by this = £145,550 – don’t accept the contract

Or (17 year annuity – 4 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 6 years time.

The relevant interest rate is 8%.

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 6 years as a result of lower labour costs If the opportunity cost of capital is 9%, should you buy the machine?

-£350000 = £314,013

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, do you accept or reject?

A fair price today for the prize would be:

PVA = CF * PVAIF0.08,10 * (1 + r) [as the annuity starts today] (Table A.2)

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

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 do 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 do 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