Bonds and interest rates

FBL661 Corporate Finance

Lecture 6

Bonds and interest rates

  • Outline

  • Government Bonds
  • Term Structure of Interest Rates
  • Floating Interest Rates
  • Managing Interest Rate Risk
  • Futures
  • Forwards
  • Swaps

Government Bonds

  • Gilt Edged Securities, Gilts, in the UK
  • Nominal value £100
  • Regular interest payments, coupon.
  • Fixed repayment date
  • Tradable
  • Default risk free
  • Shorts – redeemable within 5 years
  • Medium –  redeemable within 5 – 15 years
  • Long – redeemable over 15 years
  • Undated
  • Index linked

Term Structure of Interest Rates

Risks faced by Investors

  • Unexpected change in interest rates
  • Unexpected change in inflation
  • Default

Fixed Interest Investment

  • Known, fixed, interest (coupon) rate
  • Known time to maturity (fixed repayment date)
  • Tradable
  • Market value changes with change in market rates of interest

Relationship between changes in interest rates and market price

  • Price moves inversely to change in interest rate
  • Longer the maturity greater the price change
  • Price changes  increase with maturity but at a decreasing rate
  • Lower the coupon rate the greater the change in price

Term Structure of Interest Rates

P0    I    +       I      + ……. +   I + 100

(1+r)      (1+r)2                  (1+r)n

if you increase the interest rate the discounted cash-flow will decrease

 

Where:

P0 = current market price

I    = interest paid

r  = constant discount rate each year

Term Structure of Interest Rates

P0    I    +       I      + ……. +   I + 100

          (1+s1)    (1+s2)2                  (1+sn)n

this is more practical as every year you have different interest rates

Where:

P0 = current market price

I    = interest paid

sn  = spot interest rate for each year

s1   s2   sn

Spot Interest Rates

discount rate to use to discount any future rate, it is know now

  • The interest rate required to give a future cash flow its present value
  • Fair rate of return between now and period ‘n’
  • Different spot rates for different periods
  • Calculated by using Government Bonds
  • Plotted to give yield curve
today i will invest money, (spot rate)
UK Yield Curve – November 2010

Forward Interest Rates

estimation of the future interest rate

expected

  • Required rate of return for an investment in period A that is repaid in period

AFB

  • Found from spot rates
  • To avoid arbitrage profits the return for a given period must equal the return for a shorter period followed by a reinvestment

Forward Interest Rates

calculation of forward rate from spot rates:

(1+SA)A*(1+AFB)B-A = (1+SB)B

Where:

SA    = spot rate for period A

SB    = spot rate for period B

AFB  = forward rate between periods A & B

Calculation of Spot & Forward Rates

Relationship between forward rates and future spot rates

  • Forward rates are best estimate of future spot rates
  • But are they biased?
  • Expectations
  • Liquidity premium <<
  • Inflation premium
  • Market segmentation, clientele effect <<

Floating Interest Rates

  • LIBOR <
  • London Inter Bank Offered Rate
  • Fixed daily for set periods – 6 months, 1 year, 1 month, overnight etc.
  • Average of 8, out of 16, leading London banks
  • LIBOR Rates – July 2010

Hedging interest rate risk

  • Hedging is important due to the size of the potential losses from adverse interest rate movements.
  • Interest rate risk depends on interest rate volatility, gearing and floating rate exposure.
  • Firms with significant floating rate debt are concerned about interest rate increases.
  • Firms with a lot of fixed rate debt may lose competitive advantage if interest rates fall.

Hedging techniques include:

  • Futures
  • Forwards
  • Swaps

Futures contracts

  • Futures are exchange-traded contracts to buy or sell a standard quantity of a financial instrument at an agreed price on an agreed date.
  • Company taking out futures contract places initial margin with the clearing house.
  • Contracts are marked to market so variation margin may be needed to meet the losses.
  • Hedging interest rate risk
  • Companies buy interest rate futures to hedge an interest rate fall and sell futures to hedge an interest rate rise.
  • Interest rate futures are priced by subtracting the interest rate from 100.
  • Gains and losses on interest rate changes are given in ticks (0.01% of contract price).
  • Futures position closed out by opposite trade.
  • Example of using interest rate futures
  • Company will borrow £0.5m for 3 months in 3 months time, interest rate now is 10%.
  • Company hedges by selling one £500 000 interest rate future at 90.
  • Assume interest rate in 3 months is 13% and that futures contract price has moved to 87.
  • Company closes out futures position by buying one interest rate future at 87.

Example of using interest rate futures

  • One tick = 500 000 × 0.0001 × 3/12 = £12.50
  • Tick movement = (90 – 87)/0.01 = 300 ticks
  • Gain on futures = 300 × 12.50 = £3750
  • This compensates for higher borrowing cost of 500 000 × 0.03 × 3/12 = £3750
  • Perfect hedge, since the contract price change mirrors the cash market change and the contract is equal to the borrowing amount and the period.

Advantages

  • Returns ‘marked to market’
  • Readily tradable
  • Prices are  ‘transparent’
  • No up-front premium

Disadvantages

  • Imperfect hedge due to over-or under-hedging
  • Cannot take advantages of favourable rates
  •  Allows borrower/lender to lock into an agreed interest rate at a future date for an agreed period
  • Short term, usually under 1 year
  • Start date and end date specified
  • An  FRA starting in 3 months and lasting for 3 months
  • Rate is determined from future rate
  • Over The Counter (OTC)

Swaps

  • General definition of swap
  • An exchange of one stream of future cash flows for another stream of future cash flows with different characteristics.
  • Swaps are used extensively by banks and companies for hedging interest rate risk and exchange rate risk over long time periods.
  • Banks intermediate by warehousing swaps until counterparty is found.

Interest Rate Swaps

  • Started in 1980’s
  • Off balance sheet
  • Needed to find counterparty
  • Same principle and time period
  • OTC arrangement

Now arranged through bank

Interest Rate Swaps

  • Bank is counterparty – less risky
  • Any principle and time period
  • Bank will quote:
  • 5.25 – 5.62 against 6 month LIBOR
  • Company will either:
  • Pay bank 5.62% and receive LIBOR or
  • Pay bank LIBOR and receive 5.25%

Example of plain vanilla interest rate swap

  • Two companies A and B can borrow at:
  • Company A:     LIBOR   10% Fixed
  • Company B:      11% Fixed   LIBOR + 2%
  • A has a better credit rating than B
  • A wants floating rate debt, has comparative advantage in fixed rate debt
  • B wants fixed rate debt, has comparative advantage in floating rate debt.

Example of plain vanilla interest rate swap

  • A raises fixed rate loan at 10%
  • B raises floating rate loan at LIBOR + 0.2%
  • If servicing requirements are swapped, B is 1% better off and A is 0.2% worse off
  • Giving 0.2% of B’s 1% benefit to A makes A no worse off, giving half of remaining 0.8% benefit to A gives equal benefit to A and B
  • A pays LIBOR – 0.4%, B pays 10.6% fixed.

Interest Rate Swaps

Advantages:

  • Reduces cost of borrowing
  • Allows management of exposure to interest rate movements, hedging
  • Separates raising finance from cost of finance
  • Allows cash flows to be matched
  • Speculation

Disadvantages

  • Swap locks company into agreed rates so cannot benefit from favourable rate changes.
  • Counterparty risk exists, as legal liability for interest payments stays with loan signatory.
  • Company exposed to interest and exchange rate risk if counterparty defaults.

Gordon Growth Model

 1.      Plover Plc and Lapwing Plc are two companies in the same business sector.   Plover Plc is entirely equity financed with 800,000 ordinary shares (par value 25p) with a current market price of £1.20.  Lapwing plc is a geared company with 500,000 ordinary shares (par value 25p), with a current market value of £1.00, and £600,000 of 8% irredeemable bonds currently quoted at par.   Both companies generate annual earnings before interest and tax of £120,000 and it is the policy of both companies to distribute all available earnings as a dividend.  It is envisaged that neither company will be liable to Corporation Tax in the foreseeable future.

Robin owns 5,000 shares in Lapwing Plc.   His friend has recommended he sells these shares and borrow £6,000, at a rate of 8%, and use the money to buy ordinary shares in Plover Plc.

Definition of ‘Gordon Growth Model’

A model for determining the intrinsic value of a stock, based on a future series of dividends that grow at a constant rate. Given a dividend per share that is payable in one year, and the assumption that the dividend grows at a constant rate in perpetuity, the model solves for the present value of the infinite series of future dividends.


Where:
D = Expected dividend per share one year from now
k = Required rate of return for equity investor
G = Growth rate in dividends (in perpetuity)

Required:

a)        Calculate the cost of equity and weighted average cost of capital for each company.

b)        Suggest reasons why these costs differ for each company.

c)         Advise Robin as to whether the proposed transaction is worthwhile.  You should consider both the risk and the return to Robin in your answer.

d)        Assuming all other prices remained constant calculate the price of the ordinary shares of Plover Plc that would eliminate any arbitrage profits.

current income from lapwing 5000 (number of shares he has) /500,000(number of shares total) x 72,000 = £720 income

 

Sell Shares:
5,000 shares @ £1 per share = 5,000

if he borrows in the same capital structure 5,000 equity 6,000 debt totaling £11,000

 

 

income of robin from plover = 720 after interest rate £1200

 

Plover =1200,000/800,000 = 15p

 

1,200 divided by dividend per share of 15
number of shares he should own to achieve 1200 = 8,000 shares to make 1,200

 

Income = 11,000 << money he has / 800,000 (which is the value of plover) x 1.2

e)        Calculate the cost of equity and weighted average cost of capital for each firm using the price of Plovers shares calculated above.

2. Partridge Plc and Pheasant Plc are two companies operating in the charter airline business.  Both companies shares are traded on the London Stock Exchange where they are generally assigned similar risk ratings.   Partridge, the larger of the two companies, has 3 million 75p ordinary shares in issue which currently stand at 180p (ex div.) in the market.  In addition, some years ago the company issued £10 million of 6% undated bonds to help finance a new holiday route and these are currently quoted at 75% (ex int.).  Their competitor, Pheasant Plc, operates on an all equity basis of 25 million 5p ordinary shares that have a current ex div. market value of 32p each.

 

Partridge Plc has annual earnings before interest and tax of £1.4 million, this level is generally expected to be maintained in the future.  Pheasant Plc has annual earnings before interest and tax of £1 million and this too is expected to remain stable.  Both companies follow a strict policy of not retaining any of their after tax earnings.

Required:

a)        Calculate the cost of equity capital and the weighted average cost of capital for both companies.  Suggest reasons why these costs of capital differ between the two companies.  Taxation is to be ignored.

Where:

Es
The expected return for a security
Rf
The expected risk-free return in that market (government bond yield)
βs
The sensitivity to market risk for the security
RM
The historical return of the stock market/ equity market
(RM-Rf)
The risk premium of market assets over risk free assets.

MV o Share = 3m * 1.8 = 5.4m
MV of Debt  = £10m * 75% = 7.5m

Ke = D1 / MV

 

Company A

Ke = 1.4 – (6% * 10m) / 5.4 = 1.4 -0.6/5.4 = 14.8%

Kd = 0.6/7.5 = 8%
WACC = 14.8% * 5.4 / 12.9 + 8% * 7.5 / 12.9 = 8.8%

 

Company B

Ke = 1m / 32 * 25 = 12.5%

b)        Explain what action you might take, if any, if you were a shareholder owning 10% of the share capital of Partridge and why.  Produce calculations to illustrate the effects of your actions stating any assumptions that you have made.  Comment on what the effect would be if other shareholder in Partridge took similar action.

 

c)         Comment briefly on what effect the presence of taxation and other capital market imperfections would be likely to make on your answer to part (b) above.

 

3)          There is a controversial debate in the literature about the dividends. Does the dividend policy affect the firm value? Discuss different empirical evidence which support relevance or irrelevance arguments.

Security Analysis of Equities

Prof. Mohammed Elgammal

Outlines

  • Fundamental Analysis Technical Analysis
  • EMH
  • Market Anomalies
  • Active and Passive Management

Fundamental Analysis

  • Compare market price with “correct” price Determine “correct” price by using models
  • Ratio analysis
  • Gordon’s growth model
  • Market model
  • Capital asset pricing model
  • Cap M Model << to determine the expected return and if you have BETA
    R= P+ – P+ -1 / P+ -1
check with historical values to see if past values of the share price are correct

Technical Analysis

Study past share price movements to identify a pattern

Chartists

Economic analysis:

  •  Global economy – political risks, exchange rates, etc
  •  Domestic economy – GDP, employment, inflation, interest rates, budget deficit, consumer sentiment, etc
  •  Supply / demand shocks – government spend, tax rates, oil prices, foreign export demand, etc
  •  Government policy – fiscal policy, monetary policy, supply-­‐side policies
  • Business cycles – economic indicators
All decisions depend on expected cash flows for the firms, as market as a whole are not doing well e.g. middle east crises, government spendings. if the government does not spend it sends a signal that they might increase unemployment and investment in infrastructure.
 Industry analysis: 
  1.  Defining an industry
  2.  Sensitivity to the business cycle – types of good and service sold
  3.  Industry life cycles – stage of business development and sensitivity to economy
  4.  Industry structure and performance , competitive strategy and profitability (Porter’s five forces)

Firm-­‐specific analysis:

  • Financial statement analysis Future cash flows generated
  • Dividends
  • Profits
  • Liabilities

Technical analysis

  • Concentrate on recurrent and predictable patterns in share prices
  • Does not discount the importance of new information on future prospects of the firm
  • BUT, if prices respond slowly enough the analyst can identify a trend that may be exploited during an adjustment period
  • Such trends have been found to exist in equities, bonds, currencies, commodities, and other classes of financial assets

analysis believe that past events will happen again, this approach tries to identify a trend in a period of time because there is a delay in data coming in and out of the market and because of this delay it could be possible to beat the market.

Dow Theory

Charles Dow is widely regarded as the grandfather of most technical analysis, the market is affected by:

  • Primary trend – the long-­‐term movement of prices, lasting for several months or years
  • Secondary / intermediate trend – caused by short-­‐term deviations of prices from the underlying trend line.Such deviations are eliminated via corrections when prices revert back to the trend value
  • Minor trends – daily fluctuations of little importance
There also tends to be a positive relationship between a trend and the volume of shares traded

The primary trend

Intermediate trend

Head and shoulders topping pattern:

Head and shoulders topping pattern:

  •  A head and shoulders pattern typically appears after an upward primary market trend
  •  By early February the neckline has been set at the previous low from mid-­‐December
  •  High trading volume in the decline of the right shoulder and low volume in the formation of the head are taken as signals of the pattern
  •  Once the neckline is broken the price is expected to further decline by the difference between the top of the head and the neckline

Trend/Tram Lines

  • The support trend line is formed when a share price decreases and rebounds at a pivot point that aligns with at least two previous support pivot points
  • A resistance trend line is formed when a share security price increases and then rebounds at a pivot point that aligns with at least two previous resistance pivot points

Moving average trading rules

  • Simple moving average trading rules are built on the basis of taking the arithmetic average of the share price over a specified number of days:
  • The market price is higher than the moving average price, so there is a momentum for it to further increase in the near future
  • The market price is lower than the moving average price therefore the trend is for the market price to reduce in the near future
As the price is lower then the moving average then sell

Efficient Market Hypotheses

Information efficiency

Identified by Fama in 1960’s

  • Three forms
  • Weak form
  • Semi-­‐strong form Strong form

Efficient Markets Hypothesis (EMH):

  •  The market price of a security reflects ‘all available information’ about the stock
  •  The expected return on the security is related to its risk
  •  So you can not make any abnormal returns in the long run.

Assumptions of EMH

There are a large number of profit-­‐maximizing market participants who, independently of one another, analyze and value stocks

New information on securities comes to the market in a random fashion

Profit maximizing investors adjust security prices rapidly to reflect the effect of new information

Random Walk

The outcome of the EMH is that share prices should follow a ‘random walk’

  •  Current prices reflect all available information
  •  Changes in prices occur in response to new information, which is random and unpredictable
  •  Under the random walk hypothesis, the best prediction for tomorrow price is today price.

Weak form market efficiency

Share prices reflect all information that can be derived by examining past market trading data: past share prices; trading volume, etc.

έt represents new information hitting the market, and is assumed to be random.

  •  Tradingstrategiesthataimtoexploitinformationonpast share price data cannot be used to make abnormal levels of profits
  •  Abnormalreturnscanonlybeearnedwhere:

Investors have public or private information about the firm’s present / future performance

Can be expressed as: Pt = Pt-­‐1 + έt

Semi-strong form market efficiency

  • Stock prices reflect all publicly available information about the company
  • Past share price data; trading data; financial statements; forecasts of future firm, industry and economic conditions
  • Trading strategies that aim to exploit information on past share price data AND publicly available data cannot be used to make abnormal profits
  • Abnormalreturnscanonlybeearnedwhere:
  • Investorshaveprivateinformationaboutthecompany’spresent/ future performance
  • Can be expressed as: Ωt-­‐1 represents the publicy available information set at t-­‐1

Pt = Pt-­‐1|Ωt-­‐1 + έt

Strong form market efficiency

Stock prices reflect all available information relevant to the firm, including private information

Past share price data; trading data; financial statements; forecasts of future firm, industry and economic conditions; insider information

  •  Trading strategies that aim to exploit information on past share price data, publicly available data, AND privately held data cannot be used to make abnormal profits
  •  Abnormal returns cannot be earned based on any of the information highlighted above:
  •  Even company directors left unregulated to trade would not be able to make abnormal profits in their

own company’s shares

Evidence on the EMH

Strong-­‐form market efficiency:

  • Insiders (such as company directors) have been found to make profits when they trade in their own company’s securities which rejects the notion that financial markets are strong-­‐form efficient

Semi-­‐strong and weak form market efficiency:

  • MIXED evidence that technical trading rules (weak form) and fundamental (semi-­‐strong) trading strategies have been used to make abnormal returns in the past

EMH forms and abnormal return

Market anomalies

  •  Overall, current evidence suggests that financial markets are less than strong form efficient. Markets are generally taken to be semi-­‐strong efficient, but with some anomalies to this.
  •  Anomalies to the EMH suggest a form of market inefficiency:Mainly relate to the semi-­‐strong form of the EMHTheoretically allow investors to systematically earn abnormally high returns from trading

Types of anomalies:

  • Firm anomalies
  •  Small firms Vs Bigfirms
  •  Value firms Vs Growth firms
  •  Winners Vs Losers Market anomalies
    Seasonal anomaliesJanuary or April
  • Event anomalies << Dividend before or after
  • Accounting anomalies
  • Earning momentum: Firms with reporting unexpectedly high earnings outperform firms reporting unexpectedly low earnings.
  • Accruals : firms with relatively high (low) levels of accruals to total assets experience negative (positive) future abnormal returns.

Active or passive fund management?

Passive Investment Management:

  •  Buy-­‐and-­‐hold management strategy
  •  No attempt to outsmart financial markets
  •  Setting up a well-­‐diversified portfolio with no attempt to identify mispricing of securities

Active Investment Management:

  •  Bottom-­‐up type approach to portfolio selection
  •  Regular trading of assets based on perception of under or overvaluation in financial markets
research as shown that passive approach is expected to gain more in the long term

EMH and asset management:

If the (semi-­‐strong) EMH holds then there is no value to active investment management

  • Regular trading incurs high transaction costs
  • Implications of Market Efficiency
  • The market cannot CONSISTENTLY be beaten
  • Market has no memory
  • All shares are the same
  • Correct return for given level of risk
  • Share price is good indicator of the future

Implications for Financial Manager

  •  There are no financial illusions
  •  Shares will be correctly priced by the market, nobetter time to issue new shares
  •  Current share price reflects current public knowledge
  •  To increase value of company undertake +NPV projects

What Makes Markets Efficient

  •  Large number of analysts
  •  Availability of information
  •  Company reports
  •  Legal, accounting and stock market requirements
  •  Credit agencies
Financial press, TV, internet, etc.

Cost of capital

Questions for Seminar 4

1.         In October of 2011 when Carlsberg were proposing to take over Scottish and Newcastle they planned to raise 2.8bn GBP through a rights issue.  Critically analyse a rights issue and three other methods that a company can use to issue additional shares to raise finance.

2.         Jackdaw Plc has an issued share capital of 1 million ordinary shares (nominal value £1 each); it has also issued £800,000 of 8% bonds.  The market price of ordinary shares is £4.76 per share and bonds are priced at 69%.  Dividends and interest are payable annually and have both been paid recently.  Bonds are redeemable at par in ten years time.

Total dividend payment over the last few years has been:

2006               £200,000

2007               £230,000

2008               £230,000

2009               £260,000

2010               £300,000

 

Jackdaw Plc currently pays Corporation Tax at 30%.

Required:

a)         Estimate the cost of capital which Jackdaw Plc should use as a discount rate for purposes of investment appraisal.

b)         Discuss any difficulties and uncertainties in your estimation.

 

 

Sources of capital

Questions for Seminar 3
1. In January 2010 Tawny Owl Plc issued a 1 for 11 rights issue. At the time the
market price of the shares was 54.5 pence each, the rights price was set at
45p per share. Calculate the theoretical share price after the rights issue and
the value of the right.
2. Raven Plc is a geared company with a debt to equity ratio of 1:2. Its cost of
equity is 15% and the pre-tax cost of debt is 8%. Corporation tax is 30%.
Calculate the current weighted average cost of capital.
3. Rook Plc is financed by the following three types of capital:
• 1 million ordinary shares (nominal value 50p) with a current market value
of £5.20 cum. div. The current dividend of 20p per share is due to be
paid shortly. The dividend has grown steadily in the past at a compound
annual rate of 15% and this is expected to continue indefinitely
• 200,000 £1 preference shares paying an 8% dividend. The current exdiv market price of the preference shares is 50p each.
• £2m of company bonds. The bonds are redeemable in 10 years time
and have a coupon rate of 10%. The bonds are currently trading at a
discount of 36% of their nominal value..
Rook is considering a new project having the same risk characteristics as
existing projects, which would require an immediate outlay of £150,000 and
would produce annual after tax cash inflows of £30,000 indefinitely.
Rook Plc pays Corporation Tax at 30%. (This rate is not expected to change.)
Required:
Calculate the cost of capital of Rook and advise whether the new project is
worthwhile.
4. Company C has just paid a dividend of 17.5p per share. If the ex-dividend
market price of the share is 162p, the return on a treasury bond is 5.25% and
the market risk premium 4.70% calculate the beta of Company C.
5. The following extracts are from the most recent financial statements for Unicorn Plc.
£
Ordinary Shares (25p) 1,000,000
6.5% Preference Shares (£1) 800,000
7% Debentures 2010 2,500,000
Dividends per share:
2003 2002 2001 2000 1999
3.0p 3.0p 2.8p 2.75p 2.5p
The 2003 ordinary dividend has just been paid and the current market price of the shares is 230p, the current market price of the preference shares is 110p
and the debentures are currently trading at par. Unicorn is liable to corporation
tax at the rate of 30%. The current return on Government Bonds is 4.5% and
the market risk premium is 4.25%. The beta of Unicorn Plc is 0.78.
Required:
a] Calculate the cost of equity using the dividend growth model.
b] Calculate the required rate of return on equity using the CAPM.
c] Calculate the WACC of the company using the cost of equity calculated in
[a].
d] Calculate the WACC of the company using the required rate of return on
equity calculated in [b] as the cost of equity.
e] Explain the reasons for any difference in the two WACCs you have
calculated and explain which of the two you would recommend the
company to use as the discount rate in project appraisal.
6. Fully explain the theory on capital structure that he presented, along with
Merton Miller, in 1961. Your answer should include the original assumptions
and the subsequent adaptations they made to the model.
7. Explain Myer’s pecking order theory of capital structure.

Maximise the shareholders wealth

Questions for Seminar 2

 

1.         The main objective of corporate finance is to maximise the shareholders wealth, discuss how this objective is consistent with other public limited company’s objectives?

 

  1. Why can’t a Company be funded entirely by debt capital?

 

3.         Gander Plc has the following capital structure:

 

Ordinary Shares                                           £500,000

9% Cumulative Preference Shares                      £200,000

6% Bonds                                                      £100,000

 

EBIT (Earnings Before Interest and Tax) for the past five years has been:

 

2010               £30,000

2009               £40,000

2008               £20,000

2007               £50,000

2006               £25,000

 

It is company policy to distribute half of the available income after paying the debt interest and the preference dividends to the ordinary shareholders as dividends.  The retained amounts are reinvested in the company in the following year and not available for the payment of dividends.

 

Required:

 

Calculate and comment on the amounts paid to each class of investor for each year.  You may ignore tax.

 

  1. A Company is raising £500,000 by issuing Convertible bonds.  Explain the advantages off this form of finance to both the company and the investor.  If the conversion rate is three ordinary shares for each £5 worth of bonds would you expect the investor to convert the bond if the market price of the share on the conversion date is 186p?

 

  1. Company C wishes to issue 750,000 new shares by a tender offer.  By the closing date the issuing house had received the following bids:

 

No. of shares Bid price per share
60,500 234p
281,350 218p
408,150 201p
503,000 190p

 

Calculate and justify the price that the shares would be issued at and the amount the company would receive (you may ignore any transaction costs).

 

  1. Company D has offered their existing shareholders a 3 for 5 rights issue.  If the current market price of the shares is 375p each and the rights price is 300p calculate the theoretical ex-rights share price and the value of the right.

 

 

 

Present value of an individual cash flow

Present Value Table

 

 

Present value ofanindividual cash flow of £1 received at the end of the period.

 

 

 

 

Periods                                     Discount rates (r)

 

(n)           1%          2%            3%         4%          5%           6%           7%           8%           9%          10%

1          0.990       0.980       0.971        0.962       0.952        0.943       0.935       0.926       0.917       0.909

2          0.980       0.961       0.943        0.925       0.907        0.890       0.873       0.857       0.842       0.826

3          0.971       0.942       0.915        0.889       0.864        0.840       0.816       0.794       0.772       0.751

4          0.961       0.924       0.888        0.855       0.823        0.792       0.763       0.735       0.708       0.683

5          0.951       0.906       0.863        0.822       0.784        0.747       0.713       0.681       0.650       0.621

6          0.942       0.888       0.837        0.790       0.746        0.705       0.666       0.630       0.596       0.564

7          0.933       0.871       0.813        0.760       0.711        0.665       0.623       0.583       0.547       0.513

8          0.923       0.853       0.789        0.731       0.677        0.627       0.582       0.540       0.502       0.467

9          0.914       0.837       0.766        0.703       0.645        0.592       0.544       0.500       0.460       0.414

10          0.905       0.820       0.744        0.676       0.614        0.558       0.508       0.463       0.422       0.386

11          0.896       0.804       0.722        0.650       0.585        0.527       0.475       0.429       0.388       0.350

12          0.887       0.788       0.701        0.625       0.557        0.497       0.444       0.397       0.356       0.319

13          0.879       0.773       0.681        0.601       0.530        0.469       0.415       0.368       0.326       0.290

14          0.870       0.758       0.661        0.577       0.505        0.442       0.388       0.340       0.299       0.263

15          0.861       0.743       0.642        0.555       0.481        0.417       0.362       0.315       0.275       0.239

(n)          11%         12%         13%        14%         15%         16%         17%         18%         19%         20%

1          0.901       0.893       0.885        0.877       0.870        0.862       0.855       0.847       0.840       0.833

2          0.812       0.797       0.783        0.769       0.756        0.743       0.731       0.718       0.706       0.694

3          0.731       0.712       0.693        0.675       0.658        0.641       0.624       0.609       0.593       0.579

4          0.659       0.636       0.613        0.592       0.572        0.552       0.534       0.516       0.499       0.482

5          0.593       0.567       0.543        0.519       0.497        0.476       0.456       0.437       0.419       0.402

6          0.535       0.507       0.480        0.456       0.432        0.410       0.390       0.370       0.352       0.335

7          0.482       0.452       0.425        0.400       0.376        0.354       0.333       0.314       0.296       0.279

8          0.434       0.404       0.376        0.351       0.327        0.305       0.285       0.266       0.249       0.233

9          0.391       0.361       0.333        0.308       0.284        0.263       0.243       0.225       0.209       0.194

10          0.352       0.322       0.295        0.270       0.247        0.227       0.208       0.191       0.176       0.162

11          0.317       0.287       0.261        0.237       0.215        0.195       0.178       0.162       0.148       0.135

12          0.286       0.257       0.231        0.208       0.187        0.168       0.152       0.137       0.124       0.112

13          0.258       0.229       0.204        0.182       0.163        0.145       0.130       0.116       0.104       0.093

14          0.232       0.205       0.181        0.160       0.141        0.125       0.111       0.099       0.088       0.078

15          0.209       0.183       0.160        0.140       0.123        0.108       0.095       0.084       0.074       0.065

 

 

These values are calculated by using the formula:  1/(1 + r)n.   Where r is the discount rate and n is the number of periods in years until payment.  You should be able to use this formula to calculate the discount factor for any interest rate and any time period.
Cumulative Present Value (Annuity) Table

 

 

Present value of an annuity of £1.   i.e. a series of identical cash flows received at the end of the period.  These values are calculated by using the formula:  a [(1-(1 + r)-n)/r].  Where a is the amount of the annuity, r is the discount rate and n is the period in years.

 

 

 

Periods                                     Discount rates (r)

 

 

(n)            1%           2%            3%         4%           5%           6%           7%           8%             9%        10%

1          0.990       0.980       0.971        0.962        0.952        0.943        0.935        0.926          0.917      0.909

2          1.970       1.942       1.913        1.886        1.859        1.833        1.808        1.783          1.759      1.736

3          2.941       2.884       2.829        2.775        2.723        2.673        2.624        2.577          2.531      2.487

4          3.902       3.808       3.717        3.630        3.546        3.465        3.387        3.312          3.240      3.170

5          4.853       4.713       4.580        4.452        4.329        4.212        4.100        3.993          3.890      3.791

6          5.795       5.601       5.417        5.242        5.076        4.917        4.767        4.623          4.486      4.355

7          6.728       6.472       6.230        6.002        5.786        5.582        5.389        5.206          5.033      4.868

8          7.652       7.325       7.020        6.733        6.463        6.210        5.971        5.747          5.535      5.335

9          8.566       8.162       7.786        7.435        7.108        6.802        6.515        6.247          5.995      5.759

10          9.471       8.983       8.530        8.111        7.722        7.360        7.024        6.710          6.418      6.145

11          10.37       9.787       9.253        8.760        8.306        7.887        7.499        7.139          6.805      6.495

12          11.26       10.58       9.954        9.385        8.863        8.384        7.943        7.536          7.161      6.814

13          12.13       11.35       10.63        9.986        9.394        8.853        8.358        7.904          7.487      7.103

14          13.00       12.11       11.30        10.56        9.899        9.295        8.745        8.244          7.786      7.367

15          13.87       12.85       11.94        11.12        10.38        9.712        9.108        8.559          8.061      7.606

 

(n)          11 %        12%          13%        14%         15%         16%         17%         18%           19%       20%

1          0.901       0.893       0.885        0.877        0.870        0.862        0.855        0.847          0.840      0.833

2          1.713       1.690       1.668        1.647        1.626        1.605        1.585        1.566          1.547      1.528

3          2.444       2.402       2.361        2.322        2.283        2.246        2.210        2.174          2.140      2.106

4          3.102       3.037       2.974        2.914        2.855        2.798        2.743        2.690          2.639      2.589

5          3.696       3.605       3.517        3.433        3.352        3.274        3.199        3.127          3.058      2.991

6          4.231       4.111       3.998        3.889        3.784        3.685        3.589        3.498          3.410      3.326

7          4.712       4.564       4.423        4.288        4.160        4.039        3.922        3.812          3.706      3.605

8          5.146       4.968       4.799        4.639        4.487        4.344        4.207        4.078          3.954      3.837

9          5.537       5.328       5.132        4.946        4.772        4.607        4.451        4.303          4.163      4.031

10          5.889       5.650       5.426        5.216        5.019        4.833        4.659        4.494          4.339      4.192

11          6.207       5.938       5.687        5.453        5.234        5.029        4.836        4.656          4.486      4.327

12          6.492       6.194       5.918        5.660        5.421        5.197        4.988        4.793          4.611      4.439

13          6.750       6.424       6.122        5.842        5.583        5.342        5.118        4.910          4.715      4.533

14          6.982       6.628       6.302        6.002        5.724        5.468        5.229        5.008          4.802      4.611

15          7.191       6.811       6.462        6.142        5.847        5.575        5.324        5.092          4.876      4.675

 

 

 


Part 1 Revision Questions for Seminar 1

 

These questions are based on topics and techniques already covered in level four and five modules.  They form the basis of calculations you will meet in the following weeks.  If you are not familiar with, or have forgotten, how to do the calculations you should consult your earlier notes, or consult an appropriate textbook. If you have difficulty with these calculations you might want to consider changing modules

 

Discount tables and notes on the calculation of roots and powers and IRR can be downloaded from the module documents page.

 

 

1.         Calculate the total interest that you would receive if you invested £1,200 for a period of five years at a compound interest rate of 8%.

 

  1. Calculate the annual growth rate of a three year investment that is currently worth £250 if its original value was £230.

 

  1. Solve the following quadratic equation.

 

x2 + 6x – 5  = 0

 

4.         Mrs Jay has just won the first prize in a competition run by the “Daily News”.  The prize is a regular annual payment of £2,000 for a period of 10 years.  As an alternative Mrs Jay can receive a lump sum today that would give her the same present value as the annual payments. Calculate the amount of the lump sum that Mrs Jay would require if the annual payments were received as below.  The current interest rate is 10% per annum.

 

i)          The first annual payment is in 12 months time.

ii)         The first annual payment is in 24 months time.

iii)        The first annual payment is today.

5.         Crow Plc has just issued a ten-year bond (nominal value £100) with an annual coupon (interest) rate of 8% at a price of £90.  Calculate the Internal Rate of Return (IRR) of this bond.

 

Part 2

 

1. Discuss ways in which the shareholders of a company can encourage its managers to act in a way which is consistent with the objective of maximization of share holder wealth?

2. Critically discuss the advantage and disadvantage of different types of capitals.  If you are a financial manager what source of capital you will use and why? ( you may need to read sections1.5 and 1.6 of chapter 1 of Watson and Head before answering)

 

ESN & Policy

  1. which of these guidelines is the easiest to follow

The being smart about who you allow to become part of your network and youhave a direct intervention of who will see your profile. the problem with this is that some of you common friends will have share options such as friends of friends and this would mean that everything that your friend posts about you other people which are a friend of a friend of yours will gain access.

More must be done on these social networking websites just like google+ has done to create circuls and not allowing an interaction between the two, it is also important to keep your friend list private to ensure that at least some information regarding you is not

Professional:

  1. Which is the toughest

Its hard to protect your privacy while you are trying to be headhunted online as with linked in you have to give personal information and this information can be used to gain access to other websites such as with HMRC which askes for information relation to your past work experiance, this information could be eaisly accessed via linkedin, not to mention family relations on Facebook and how that information could be used for password verificion questions.

  1. Explain why, using examples as appropriate