Finance for managers - Lecture notes All PDF

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Finance for managersWeek 1 – firm objectives and time value of moneyBusiness corporations: - A separate legal entity - Separation of ownership and control - Unlimited life (because shareholders can sell shares) - Easy transfer of ownership - Easy to raise capital - Limited liabilityThe firm overridi...

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Finance for managers Week 1 – firm objectives and time value of money Business corporations: - A separate legal entity - Separation of ownership and control - Unlimited life (because shareholders can sell shares) - Easy transfer of ownership - Easy to raise capital - Limited liability The firm overriding objectives: - Clear decision requires clear objectives - Shareholders are the owners of firms - In competitive market economies, it’s assumed that business corporations exist for one overriding objective: to benefit shareholders and to strive to maximize that benefit (in other words, the primary objective is to maximise shareholder wealth) Wealth maximization • Wealth is the market value (current market price) of ordinary shares, as these reflect the future returns shareholders will expect to receive, taking into account the level of risk. • Hence, corporation managers try to increase the share price. As the share price increases, the shareholders’ wealth increases. • A business corporation can maximise shareholder wealth by accepting all projects with positive net present values, as this will maximise the market share price (see later). The role of accounting profit • Accounting profit is a reporting device, not a decision-making device. • Wealth, worth and value are all concepts related to the future but profit is related to the past. • Financial decisions are evaluated in terms of their cash flow impact. But profit cannot be ignored: • A major criterion by which investors judge a company’s success. • Retained profit form a maximum barrier to an annual dividend payment. In the longer run, good cash flows will result in good reported profits Shareholder vs. Shareholder view (but is shareholder wealth the only objective that should matter? Or should we also consider stakeholder view) • Typical stakeholders for an organisation (in addition to shareholders) would include: – Employees, Suppliers, Customers, The Community etc. • Many argue that a business must adopt the stakeholder view, which involves: – balancing the competing claims of a wide range of stakeholders, and – taking account of broader economic and social responsibilities. – Studies show that corporations with good business ethics and good corporate governance generally generate higher stock returns. One overriding objective - Still, maximising shareholder wealth is the overriding objective for most corporations. - By focusing on a single objective clear decisions can be made. - This objective leads to the development of products that consumers need, new technology, new jobs, efficient service etc. - Looking after shareholders does not mean overlooking at other stakeholders.

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In BEA3008 we assume that primary objective of a business corporation is to maximise shareholder wealth.

Agency relationships • Agency relationships occur when one party, the principal, employs another party, the agent, to perform a task on their behalf. • Examples of agency relationships: – Managers can be seen as the agents of shareholders. – Employees as the agents of managers. – Managers and shareholders as the agents of creditors. • In most of these principal-agent relationship, conflicts of interest will exist.. • The most important conflict is that between the interest of shareholders and managers. The costs of agency problem • Shareholders are reliant upon the management of the company to understand and pursue the objectives set for them. • Although shareholders can intervene via resolutions at general meeting, the managers are usually left alone on a day-to-day basis. • Management are uniquely placed to make decisions to maximise their own wealth or happiness rather than the wealth of the shareholders. • Losses in value from agency problems – or costs incurred to mitigate the problems – are called agency costs. • Jensen and Meckling (1976) define agency costs as the sum of: monitoring expenditures by the principal, bonding expenditures by the agent, and residual loss. How to potentially fix the problem? Managerial reward schemes (e.g., executive share option scheme) • Managerial compensation can be used to align management and shareholder interests. • The incentive need to be structured carefully to make sure that they achieve their intended goal. Corporate Governance Codes • Non-executive directors, • Executive directors, • Annual General Meeting. Takeovers • The threat of a takeover may result in better management. Information requirements • Greater presentation requirements for corporations.

TIME VALUE OF MONEY Decision making and valuation The overriding objective: maximise shareholder wealth through value creation • Decisions are based on the comparison of alternatives. • Alternatives have to be valued in order to be compared.

PV =

CF1

(1+ r )

1

+

CF2

(1+ r )

2

+…

CF n

( 1+r )n

NPV =- CF 0+ • •

CF 1 CF 2 CF n . . . + + 1 2 n (1 + r ) (1 + r ) (1 + r )

What is the value of the stream of future cash flows today? We link this value to the time value of money (TVM).

We need to understand the time value of money because - Potential for earning interest - Impact of inflation - Effect of risk Comparing cash flowsIf we know money is worth different amounts at different times, it will affect our decisions. Hence we need a way of restating these investment options so that we are comparing it right -

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-

Cash flows that occur at different points in time can be compared only by transforming them through compounding or discounting into equivalent flows with reference to a particular point in time. Compounding specifies how a given amount of money grows over time at a particular rate of interest. By compounding at a rate that represents the time value of money, we can calculate future values of current cash flows (see later). Discounting is the inverse of compounding; it allows us to calculate present values of future cash flows (see later).

Cash flows: • Single cash flows • Multiple cash flows – Uneven cash flows – Regular cash flows – Infinite regular cash flows • Annual cash flows, more frequent cash flows etc. • A conventional cash flow for a project is typically structured as an initial outlay or outflow, followed by a number of inflows over a period of time. • Non-conventional cash flows – cash flows that change signs more than once during the project’s life. Timeline • A graphical representation which shows the timing of cash flows.

•

The tick marks represent end of periods (often years), so time 0 is today; time 1 is the end of the first year, or 1 year from today; and so on. A lump sum is a single flow; for example, a £100 inflow in year 2. Annuity: •

Annuity: a series of equal payments or receipts that occur at evenly spaced intervals.

–

•

•

Examples include: rental payment, regular deposits to a savings account, monthly home mortgage payment etc. Constant Annuity Timeline:

An annuity can occur at the end of each period, as in this time line, or at the beginning of each period.

Ordinary (Standard) Annuity The payment or receipt occurs at the end of each period. – Example: interest payments on debt and mortgages. Annuity Due The payment or receipt occurs at the beginning of each period. – Example: leasing arrangements. Delayed Annuity An annuity with the first payment or receipt starting after year 1. – Example: an annuity with the first payment in four years from now. Growing Annuity The payment or receipt increases each period at a constant percentage ( g). Perpetuity • • •

Perpetuity: an annuity that continues indefinitely (i.e. a constant stream of identical cash flows with no end). The concept of perpetuity is used often in financial theory, such as the dividend discount model (DDM), by Gordon Growth, used for stock valuation. Constant Perpetuity Timeline:

Ordinary (Standard) Perpetuity A regular perpetual stream of payments starting one period from now. Delayed Perpetuity A perpetuity with the first payment starting after year 1. – Example: a perpetuity with the first payment in four years from now. Growing Perpetuity A perpetuity where the annual payment increases each year at a constant percentage ( g).

Future value (single cash flow) FV – the one-period case

F V = C F 0 ´ (1 + r )

In the one-period case, the formula for FV can be written as: where: FV = Future value. CFo = Initial or Present value (cash flow at date 0). r = the appropriate interest rate. • The term (1+r) is the future value interest factor, also called future value factor.

Simple interest • Simple interest is the amount paid on the original principal (or initial investment) only. • The principal is the amount of money on which interest is paid. For example, an investor has £500 to invest at an interest rate of 5%. – In one year, they will have earned: £500 x 5% = £25. – If they take the £25 earned out of the capital market and reinvest the £500 capital at 5% they will again earn £25 in a year’s time. – This process could continue for many years with the annual earnings never contributing further to the investor’s wealth. Compound interest With compounding, interest is also paid on the interest already earned. For example, from the previous case: – Interest in year 1: £500 x 5% = £25 – Interest in year 2: £525 x 5% = £26.25 – Total interest = £25 + £26.25 = £51.25 Notice that the total interest in this case is higher than the total simple interest: £51.25 ˃ £50.00. This is due to compounding. FV – many periods (compounding)

n = ´ + ( 1 ) F V r C F 0 The Future Value formula for many periods can be written as: where: FV = future value. CFo = Initial or Present value (cash flow at date 0). r = the appropriate interest rate per period. n = number of periods (typically years) over which cash is invested. •

The term

(1 + r ) n

is the future value factor.

Example: Example 1 Jack has put £300 in a savings account, which earns 5%, compounded annually. How much will Jack have at the end of five years? Solution:

F V =C F

0

´ (1 + r ) n = £ 3 0 0 ´ (1 .0 5 ) 5 » £ 3 8 2 .8 8

Example 2 You invest £5,000 at the start of year 1, in an account paying 5% interest per annum, compounded annually. How long will it take for the investment to reach £6,000? Solution: £6000 = £5,000 x (1.05)n 1.2 = (1.05)n Log 1.2 = Log (1.05)n Log 1.2 = n x Log 1.05 Log 1.2 / Log 1.05 = n n = 3.74 years (or 4 years as interest is paid at the end of each year) more frequent compounding Compounding an investment m times a year for n years:

F V = C F 0 ´ (1 +

r mn ) m

Example 3 What is the value in one year’s time if Tom receives a stated annual interest rate of 18% compounded monthly on a £1 investment?

1 8 % 1 2 ´1 » £ 1 .1 9 5 6 ) 12

F V = £ 1 ´ (1 +

Solution: The annual rate of return is 19.56%; this annual rate of return is the so-called Effective Annual Rate (EAR). Continuous compounding Formula for continuous compounding (every infinitesimal instant):

F V = C F 0 ´e rt Example 4 You invest £1000 at 3% pa for 4 years. What is the FV under Solution: FV = 1000 x e(0.03x4) = £1,127.50 Notice how this is higher than annual compounding: FV = 1000 (1.03)4 = £1,125.51

continuous compounding?

The more frequent the compounding, the more you earn! Stated annual interest rates vs effective annual rate • Stated Annual Interest Rate is the rate expressed as a per-year percentage, and that does not account for compounding that occurs throughout the year. • The Effective Annual Rate (EAR) on the other hand, does account for intra-year compounding that can occur on a daily, monthly or quarterly basis. • The EAR allows you to compare interest rates across different investments/borrowings. • EAR formula:

E A R = (1 +

r mn ) -1 m

Example 5 A bank charges 8% interest compounded quarterly. What is the EAR?

E A R = (1 +

0 . 0 8 4 ´1 ) - 1 = 8 .2 4 % 4

Solution: Example 6 Suppose that you have an investment that pays 5% per annum, stated rate. However, your bank compounds your investment on a daily basis. What is EAR?

E A R = (1 +

0 . 0 5 ( 3 6 5 )(1 ) ) - 1 = 5 .1 3 % 365

Solution: The EAR is the actual return you will receive at the end of the year, so if you invest £1,000 at the beginning of the year, at the end you will receive £1,051.3

Future value (annuity) FV - Ordinary anuity: é 1 + n -1ù ( r) ú F V =C F * ê ê ú r êë úû Formula -

Example 7 You save £1,000 at the end of each year, in an account which pays an annual rate of 5%. Interest is compounded annually. How much will you have at the end of 6 years?

é (1 + 0 . 0 5 ) 6 - 1 ù ú = $ 6 ,8 0 2 F V =1 ,0 0 0 * ê 0 .0 5 êë úû Solution: FV - Annuity duen ù é + ( 1 r ) - 1ú F V =C F * (1 + r ) ê ê ú r êë úû Formula

Example 8 You have decided to save £300 at the beginning of each month. Your bank account is paying 12% per annum, but compounded monthly. How much will you have at the end of 3 years? (to the nearest £). Solution: é ù 0 . 1 2 ö1 2 * 3 ê æç 1 + - 1ú ÷ 0 .1 2 ö ê è 12 ø æ ú =1 3 ,0 5 2 .2 9 F V = 3 0 0 * ç1 + ÷ê ú 0 . 1 2 1 2 ø è ê ú 1 2 êë úû FV – growing annuity Formula:

(

FV =CF1∗

n

n

(1+r ) −( 1+ g ) r−g

)

Example 9 Lina is 30 years old, and she considers saving £10,000 per year for her retirement. Although £10,000 is the most she can save in the first year, she expects her salary to increase each year so that she will be able to increase her savings by 5% per year. If she earns 10% per year on her savings, how much will Lina have saved at age 60? Solution:

(

(1+ 0.1 ) − (1 +0.05 ) FV =10,000∗ 0.1−0.05 30

30

)

=£ 2.625 million

See also example 15 for an alternative method. Present Value (PV) (Single Cash Flow) Present value – discounting • PV is the current worth of a future sum of money or stream of cash flows given a specified interest rate, known as the discount rate

•

Future cash flows are discounted at the discount rate, and the higher the discount rate, the lower the present value of the future cash flows Discounting: • Discounting is the process of converting a future value to its present value. • The discount factor is the quantity that converts a particular future sum of money to its present value: PV = FV * DISCOUNT FACTOR • We should never compare cash flows occurring at different times without first discounting them to a common date. • Compounding and discounting form the basis for the valuation process used in finance.

Present value (annuity) Discount factor – annuity

1 r

é 1 ù ê1 - + n ú ë (1 r ) û

Discount (Present Value) factor appropriate to an n period annuity assuming a constant discount rate of r per period PV – Ordinary annuity Formula:

PV =

CF 1

+

CF2

+…

CF n

n (1+r ) (1+r ) (1+r) CF CF ∗1 1 1 1− = 1 1− PV = 1 n r r (1+ r ) (1+r ) n 1

[

2

] [

]

Example 12 Jack will receive £50,000 at the end of each year for 20 years. What is the PV of all these cash flows if the interest rate is 9%? Solution:

PV =

£ 5 0 ,0 0 0 é 1 ù ´ ê1 ú = £ 4 5 6 ,4 2 7 0 .0 9 ë 1 .0 9 2 0 û

PV – Annuity due Example 13 30 cashflows of £1 million per year (starting today). If the interest rate is 8%, what is the present value? Solution: Because the first payment is today, the last payment will occur in 29 years. PV = the PV of £1 million today + the PV of the final 29 payments (which is an ordinary annuity).

[

(

])

1 1 1− =£ 12.6 m 0.08 (1.08)29

PV =£ 1 m+ £ 1 m x

PV – Delayed annuity Example 14 Calculate the present value of a five-year annuity, £10,000 each year, with the first payment in three years from now. Assume the interest rate is 4% per annum. Solution: Step 1 – calculate the value of this annuity in year 2. In this year this is an ordinary annuity.

Value ( year 2) =

[

]

[

]

CF 1 1 10,000 1 =£ 44,518 1− 1− 5 n = r 0.04 (1+r ) ( 1+0.04 )

Step 2 – find the present value in year 0.

PV =

44,518 =£ 41,159 2 (1+0.04)

PV – Growing annuity Formula:

[ (

PV =CF∗

( ) )]

1+g 1 1− 1+ r r−g

n

The present value of an: • n - period growing annuity • with initial cash flow CF • growth rate g • interest rate r Example 15 • Lina is 30 years old, and she considers saving £10,000 per year for her retirement. Although £10,000 is the most she can save in the first year, she expects her salary to increase each year so that she will be able to increase her savings by 5% per year. If she earns 10% per year on her savings, how much will Lina have saved at age 60? • Solution: • Step 1 – calculate the PV of her savings today (a 30-year growing annuity):

PV =10,000∗

• • • •

[

( (

1+ 0.05 1 1− 0.1 −0.05 1+ 0.1

) ) ]=£ 150,463 30

Step 2 – find the FV (of the amount Lina will have at age 60): FV ¿ 150,463 x 1.130 = £2.625 million

Present value (perpetuity) Discount factor – perpetuity

1 r Discount (Present Value) factor appropriate to a periodic perpetuity assuming a constant discount rate of r per period PV – Ordinary perpetuity Formula:

PV =

CF 1

+

CF 2

(1+r ) (1+r ) CF 1∗1 CF1 PV = = r r 1

2

+

CF3 (1+r)3

+…

Example 16 If the rate of interest is 10% and the aim is to provide £100,000 a year forever, the amount which must be set aside today is:

PV = Solution:

1 0 0 ,0 0 0 = £ 1 ,0 0 0 ,0 0 0 0 .1 0

PV – delayed perpetuity Example 17 Calculate the present value of £10,000 every year, forever, with the first payment five years from now. The estimated interest rate is 5%. Solution:

10,000 =£ 200,000 0.05 200,000 =£ 164,540 PV time0 ( now) = 4 (1+0.05) Value(Year 4) =

PV – Growing perpetuity We use the following formula for calculating the PV of a perpetuity with cash flows growing each year at a constant rate g:

PV =

CF 1 r−g

g = constant growth rate. First payment starting at T1: Example 18

What is the present value of £10,000 paid at the end of every year in perpetuity, assuming a rate of return of 10% and a constant growth rate of 6%? Solution:

PV =

10,000 =£ 250,000 0.1−0.06

First payment starting at T0: Example 19 Jack is just about to receive a payment of £1,000 (i.e., first payment to be received now); it is expected that this annual payment will rise by 3% a year forever; the applicable discount rate is 10% per annum. Calculate the present value of this growing annuity. Solution:

PV =CF0 +

CF1 r−g

(because we do not need to discount the first payment, which is received now)

CF1=CF 0∗(1+g) CF0∗(1+ g ) PV =CF0 + r −g 1,000∗ (1+0.03 ) PV =1,000+ =£ 15,714 0.1−0.03 Calculating cash payments (when we know PV or FV) - A loan is the best example when you know the present value (how much to borrow) and the interest rate, but you do not know how much you need to repay each year. - Savings is the best example when you know the future value (how ...