Questions and Answers of Talk Finance

(b) Prove that the fair price at time n of a European contingent claim h is given by WnEW (h/WN |Fn) .
(a) Prove that the probability measure PW introduced in Question 4 is unique, and satises dPW/dP¤ =WN/S0N.
6. Assume that the market is viable and complete, and denote by P¤ the unique equivalent probability measure with respect to which ˜ S is a martingale.
5. Prove that, in a viable market, there is at most one deterministic numéraire.
4. Prove that the market is viable if and only if there exists a probability PW, equivalent to P, such that SW is a PW-martingale.
3. Prove that for any predictable sequence Á=(Án)n=0,...,N , with values in Rd+1 and any real number V0, there exists a self-nancing strategy ˆÁsuch thatˆÁn.SW n =V0 +Xn j=1Áj .¢SW j , n=0,
2. Prove that for n=1, . . . ,N, Pn j=1 µj .¢SW j =0.
1. Prove that a predictable sequence Á=(Án)n=0,...,N , with values in Rd+1, is a self-nancing strategy if and only if we have V W n (Á)=V0(Á) +Xn j=1Áj .¢SW j , n=1, . . . ,N, with the
2. Show that if F achieves a minimum at µ¤ 2Rd, we have EXeµ¤.X =0.
1. Show that if P(X =0)
7. We can now use the model to price a call or a put with maturity T on a single stock. In order to do that, we divide the interval [0, T] into N subintervals, so that we can refer to the N-period
(1 + r)n +HnSn−1u=c(n, Sn−1u).Subtracting one from the other, it turns out that¢(n, x)=c(n, xu) − c(n, xd)x(u − d).
(1 + r)n +HnSn−1d=c(n, Sn−1d)and
(1 + r)n +HnSn =c(n, Sn).Since H0n and Hn are Fn−1-measurable, they are functions of S1, . . . , Sn−1 only and, since Sn is equal to Sn−1d or Sn−1u, the previous equality implies H0n
6. Show that the replicating strategy of a call is characterized by a quantity Hn =¢(n, Sn−1) at time n, where ¢ will be expressed in terms of the function c.We denote by H0n the number of
By conditioning with respect to (Tn+2, . . . , TN) in (1.4.1), we have c(n, x)(1 + r)−(N−n) = pE¤xd NY i=n+2 Ti −K!++(1 − p)E¤xu NY i=n+2 Ti −K!+.
(c) Prove that the function c satises the recursive equations c(n, x)=(pc(n + 1, xd) + (1 − p)c(n + 1, xu))1 + r, n=0, . . . ,N − 1.
If the Ti's are independent and satisfy P(Ti =d)=p=1 − P(Ti =u), we have E(Tn+1|Fn)=E(Tn+1)=pd + (1 − p)u=1 + r, and thus ( ˜ Sn) is a P-martingale, according to Question 1.
4. From now on, we assume that r 2 (d − 1, u − 1) and we write p=(u − 1 − r)/(u − d). Show that ( ˜ Sn) is a P-martingale if and only if the random variables T1, T2, . . . , TN are
3. Give examples of arbitrage strategies if the no-arbitrage condition derived in Question 2 is not satised.Assume for instance that r ·u − 1. By borrowing an amount S0 at time 0, we can purchase
2. Deduce that r must belong to (d − 1, u − 1) for the market to be arbitrage-free.If the market is viable, there exists a probability P¤ equivalent to P, under which ( ˜ Sn) is a martingale.
1. Show that the discounted price ( ˜ Sn) is a martingale under P if and only if E(Tn+1|Fn)=1 + r, 8n 2 {0, 1, . . . ,N − 1}.The equality E( ˜ Sn+1|Fn)= ˜ Sn is equivalent to E( ˜ Sn+1/ ˜
List and explain three limitations of ratio analysis.
What is liquidity and how can it be measured?
What is ROCE?
What are the five key measures for a business?
Having done all of the analysis what is your assessment of the organisation’s current financial position and performance? Remember to couple your analysis with the director’s report and the
If you haven’t done so already follow the investment ratios and apply them to your company. What do your results tell you?
Are cash and profit the same thing?
What does the balance sheet show?
What is the BTA’s overall financial health?
What is the BTA’s financial position?
What is the BTA’s financial performance?
What is Net Profit?
What is Gross Profit and how is it calculated?
A business paid its annual rent of £12,000 in August. The business has an accounting period that ends in March. Explain the accounting entries that would be needed for the rent.
How do accruals and prepayments affect the trial balance?
Explain what is meant by (i) an accrued expense and (ii) a prepaid expense?
Does a trial balance list all the transactions made by the business?
years. It depreciates the van by£2,000 each year. What would be in the trial balance at the end of the second year for the van and its depreciation?
A company has owned a van worth £10,000 for
A company takes out a loan to pay for a new van. Is the loan an asset?
What effect does profit have on capital?
Should the cost of equipment we have purchased be shown in the income statement?
Indicate where each of the following items will be shown (in the trading income statement or balance sheet):■ Trade Debtors■ Cash and Bank■ Bank Loans■ Rent■ Wages■ Loan interest paid■
List the five circumstances in which a trial balance might balance even though some of the balances are incorrect.■■■■■
Would ‘discounts allowed’ be shown as an expense?
Explain the difference between ‘interest payments’ and ‘capital repayments’ on a loan.
Would ‘interest receivable’ be shown as an expense?
per cent per year, how much extra cash would leave the company in the second year of the machine’s usage?
per cent per annum. If the depreciation rate was changed to
A machine cost £50,000 and was being depreciated at
What is the net book value of an asset?
What are the accounting entries for question 4?
the company decides to sell the machine for £3,000. What is the profit/loss for the machine?
At the end of year
What will be the NBV of the machine at the end of year 5?
What will be the accumulated depreciation by the end of year 5?
What will be the annual depreciation charge for the machine? (Assume the straight line method for depreciation.)
The company returns goods to one of its suppliers and receives a credit note(i.e. does not obtain a cash refund)?
Customers return goods and obtain a cash refund immediately?
What impact will the discount have on the profit on the period?
What accounting entries will be required to record the discounted payment(ignore the original purchase)?
What is the amount of the discount?
Will this be ‘discount allowed’ or ‘discount received’ in Kitlocker’s accounts?
What will the net book value of the machine be at the end of year 6?
What will be the balance on the Provision for Depreciation of Machinery account at the end of year 4?
What will be the annual percentage rate of depreciation?
How much is the depreciation charge per annum?
per cent per annum.■ Calculate the interest payable in the third year of the loan.■ What is the balance on the loan account at the end of the third year.
A business takes out a 5-year ‘interest only’ loan of £250,000, at an interest rate of
What is the percentage rate of interest per annum on a loan of £25,000 where the interest payable for the year is £1,250?
per cent?
What is the amount of interest payable for the year on a loan of £50,000 at an annual rate of interest of
Which of the following items are shown under the wrong headings?
Complete the ‘T’ accounts for the following examples:a The owner of the firm introduces capital of £15,000 in cash.b Goods for re-sale are purchased, by cash, for £6,000.c The rent bill arrives
Are these statements true or false?a Assets are items or resources that have a value to the business and things that are used by the business and for the business.b Liabilities are amounts owed to
Identify three of the regulatory bodies that oversee accounting.
For the following statements fill in the blanks.a The concept recognises that each transaction conducted by a business will affect two items within the business.b The concept dictates that
List the accounting concepts and principles that you can remember from this chapter.
Is your favourite sport team listed?
Which sector, sport or leisure, is represented the most on the UK Stock Exchange?
How many leisure organisations are listed?
How many sport organisations are listed?
True or False: The balance sheet helps us determine the profit of an organisation?
What type of information does financial accounting examine?
What are the four main company types?
List three users of financial information (ignoring managers).
Why do managers use financial information?
The strategy to buy players was the Chairman’s idea but what other things could Leeds have done to improve on-the-field success?
Do you think that there is a right level of borrowing and if so how do you think that it could be calculated?
Do you think that the Leeds United model suggests that football clubs, or any sport organisation, should avoid borrowing?
Appraise an organisation’s financial position and performance through the application of ratio analysis and interpretation of the Annual Report.
Explain the purpose of analysing financial statements.
Understand the reporting and measurement of financial performance and position. Understand and explain the accounts of non-trading organisations.
Understand and explain the information needed to construct the financial statements.
Make adjustments to the trial balance (cost of sales, mispostings, accruals and prepayments, and others).
Construct an outline income statement and balance sheet.
Determine balances on ‘T’ accounts and construct a trial balance.
Understand and communicate the interrelationship between ‘T’ accounts and financial statements.

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