Corporate(Finance(

( 2(

Issues(for(Financial(Managers((

• The(Capital(Budgeting(Decision(! How(much(to(invest(and(in(which(assets?(

• The(Capital(Structure(Decision(! How(should(the(cash(required(for(investments(be(raised?(

• Working(Capital(Management(Decision(! How(should(the(dayMtoMday(financial(matters(be(managed?(

((Legal(Forms(of(Business(Organisation((Sole%Trader%

; The(simplest(form(of(business(to(start(and(the(least(regulated(; All(business(income(is(taxed(as(personal(income(; A( sole( trader( has( unlimited( liability( for( all( business( debts( and(other(

obligations(of(the(firm(%Partnership(

; Has(the(same(basic(advantages(and(disadvantages(of(a(sole(trader(; When(there(is(a(transfer(of(ownership,(the(partnership(is(terminated(

and(a(new(partnership(is(formed(; The( problem( of( unlimited( liability( can( be( avoided( with( a( limited(

partnership((Company(

; A(company(is(a(separate(legal(entity(from(its(owners(; The(owner’s(of(a(company(are(its(shareholders(; The( major( advantage( of( the( company( form( of( business( is( that(

shareholders(gave(limited(liability(; Public(companies(can(sell(their(debt(or(equity(in(the(public(securities(

market(((The(Firm’s(Financial(Objectives((The(firm’s(primary(objective(is(to(maximise(shareholders’(wealth.((Why(not(maximise(profits?(Accounting( profits( are( not( necessarily( the( same( as( cash( flows.( Profit(maximisation( does( not( tell( us( when( cash( flows( are( to( be( received.( Profit(maximisation(ignores(the(uncertainty(or(risk(associated(with(cash(flows.((Maximising( shareholder( wealth:( When( analysts( and( investors( determine( the(value(of(a(company’s(share(price,(they(consider:(

; size(of(the(expected(cash(flows(; timing(of(the(cash(flows(; riskiness(of(the(cash(flows(

(

Corporate(Finance(

( 4(

Time(Value(of(Money((A%dollar%today%is%worth%more%than%a%dollar%tomorrow.((Cash(flows(that(occur(at(different(points(in(time(cannot(simply(be(added(together(or(subtracted.(Why?(; Money(received(now(can(be(invested(to(earn(interest.(; A(significant(amount(of(time(may(elapse(between(the(outflow(of(cash(and(the(subsequent(inflows.(

(The(concept(of(present(value(and(future(value:(Present(Value(–( the(dollar( amount(payable( today( that( is( equivalent( to( a( stated(future(cash(flow.(Discounting( –( the( process( of( converting( an( expected( future( cash( flow( to( its(equivalent(value(now.(Future(Value(–(the(value(of(an(investment(after(it(earns(interest(for(one(or(more(periods.(Compounding( –( the(process( of( converting( a(dollar( value(now( into( an( expected(future(cash(flow.(((Simple(Interest((Simple(interest(is(typically(used(when(there(is(only(a(single(time(period.(Interest(is(calculated(on(the(original(sum(invested.(

!"#$%$&# = !"#$%#&'(! ! !×!!"#$%&'! ! !×!!"#$!(!)((Future(value(is(the(lump(sum(payable:(!" = !"(!+ !")((The(present(value(can(also(be(calculated:(!" = !"

!!!"(((Compound(Interest((“The(most(powerful(force(in(the(universe(is(compound(interest.”(

M(Albert(Einstein((Compounding( involves( accumulating( interest( on( previous( interest( payments.(Therefore,( in( the( case( of( compound( interest,( previous( interest( payments( will(generate(further(interest.((

!" = !"(!+ !)!((The(FV(and(PV(formulas(are(the(inverse(of(each(other.((The(more(frequent(interest(compounds,(the(more(‘wealth’(there(is.(((

Corporate(Finance(

( 5(

Nominal(and(Effective(Interest(Rates((• Nominal(Rate(

Quoted(interest(rate(where(interest(is(charged(or(calculated(more(frequently(than(the(time(period(specified(in(the(interest(rate.((

• Effective(Rate(Interest( rate(where( interest( is( charged( is( charged(at( the(same( frequency(as(the(interest(rate(quoted.((Used(to(convert(different(nominal(rates(so(that(they(are(comparable.((

The(effective(interest(rate(can(be(calculated(as:((

! = ! !+ !!

!− !(

%j%=%nominal%rate%per%period%m%=%number%of%compounding%periods%which%occur%during%a%single%nominal%period%((Real(Interest(Rates((Nominal(Interest(Rate(–(The(interest(rate(before(adjusting(the(effects(of(inflation.(Real(Interest(Rate(M(The(interest(Rate(after(adjusting(for(the(effects(of(inflation.((The(real(interest(rate,(i*,(where(p(equals(the(expected(inflation(rate,(can(be(found(as(follows((

!∗ = ! !+ !!+ ! − !(((Continuous(Interest(Rates((A(method(of(calculating(interest(in(which(it(is(charged(so(frequently(that(the(time(period(between(each(charge(approaches(zero.(Continuously(compounded(interest(is(an(example(of(exponential(growth.((

((

FV(=(future(sum(PV(=(principal(j(((((=(continuously(compounding(interest(rate(per(period(n((((=(number(of(periods(e((((=(2.718(281(828(46((Euler’s(number)(

(((

jnePVFV ×=

Corporate(Finance(

( 6(

Geometric(Rates(of(Return((Also(referred(to(as(the(average(compound(rate(of(return.((

! = !!!!

!! − 1(

(Pn(=(Final(Value(or(Price(P0(=(Initial(Value(or(Price(((Multiple(Cash(Flows((• Cash( flows( occurring( at( different( times( cannot( be( validly( added( without(

accounting(for(timing.(• It( is( therefore( necessary( to( convert( multiple( cash( flows( into( a( single(

equivalent( cash( flow.( Cash( flows( can( either( be( carried( forward( in( time((accumulated)(or(back(in(time((discounted).(

((Annuities((An(annuity(is(a(stream(of(equal(cash(flows(that(are(equally(spaced(in(time.((The(three(major(types(of(annuities(are:(

1. Ordinary(Annuities(2. Annuity(Due(3. Deferred(Annuity(

((Ordinary(Annuity((Annuities(in(which(the(time(period(from(the(date(of(valuation(to(the(date(of(the(first(cash(flow(is(equal(to(the(time(period(between(each(subsequent(cash(flow.((Valuing(Ordinary(Annuities:(Present(Value:(

!" = !"! 1− 1

1+ ! ! (CF%=%annuity%cash%flow%i%=%interest%rate%per%compound%period%n%=%number%of%annuity%cash%flows%(Valuing(Ordinary(Annuities:(Future(Value:(

!" = !"! 1+ ! ! − 1 (

(((

Corporate(Finance(

( 7(

Annuity(Due((An(annuity(where(the(first(cash(flow(is(to(occur(immediately.((An(annuity(due(of(cash(flows(is(simply(an(ordinary(annuity(of((n(–(1)(cash(flows,(plus(an(immediate(cash(flow(of(CF.((

!" = !" + !"! 1− 11+ ! !!! (

(((Deferred(Annuity((An( annuity( in( which( the( first( cash( flow( is( to( occur( after( a( time( period( that(exceeds(the(time(period(between(each(subsequent(cash(flow.((The(present(value(of(a(deferred(annuity(involves(taking(the(present(value(of(an(ordinary(annuity.((

!" =!"! 1− 1

1+ ! !

1+ ! !!! (CF%=%annuity%cash%flow%i%=%interest%rate%per%compound%period%n%=%number%of%annuity%cash%flows%k%=%number%of%time%periods%until%the%first%cash%flow(((Ordinary(Perpetuity((An(ordinary(annuity(where(the(cash(flows(are(to(continue(forever.((

!" = !"! (

((PrincipalMandMInterest(Loans((• PrincipalMandMInterest(Loans(are(an(important(application(of(annuities(• They(are(loans(involving:(

" A(sequence(of(equal(cash(flows(" Each(of(which(is(sufficient(enough(to(cover(the(interest(accrued(since(

the(previous(payment(and(to(reduce(current(owing(balance(• Balance(owing(at(a(given(date(equals(the(present(value(of(the(thenMremaining(

repayments(• Solving(n(finds(the(loan(term(required(((