Joven Liew Jia Wen
201506858
FM473: Finance I
Present Value, How to calculate PV, Valuing Bonds, Valuing Common Stocks, Risk and return, Portfolio
theory and CAPM, Market Efficiency, Put and Call options, Valuing Options, Forwards and Futures
Lecture 1: Present Value
There are sole proprietorships, partnerships and corporations in US. Corporations only take up 16% of
firms but they generate 84% of revenues.
A corporation is a legal entity owned by its stockholders and is legally distinct from them.
Ideally, a firm should maximize the total welfare of shareholders. In practice, firms are run by managers.
As a result, what a firm does crucially depends on the managerial incentives. Incentives depend on the
corporate governance of a firm.
In practice, main objective assigned to managers is to maximize shareholder value**
HSBC: Aim to run a sustainable business for the long term and achieve sustainable profits for our
shareholders
Goldman Sachs: Providing superior returns for our shareholders; significant employee stock ownership
aligns the interests of our employees and our shareholders
Values and Discounting
Discount rate is the interest rate used to compute present values of future cash flows
Present Value: Value today of a future cash flow
Future Value: Amount to which an investment will grow after earning interest
Discount factor: Present Value of a $1 future payment
FV of your $100 with interest on government securities as r = 100 x (1+r)t
Time value of money: A pound today is worth more than a pound tomorrow
,Joven Liew Jia Wen
201506858
Present Values convert future cash flows to their current values. Future cash flows is Ct.
Ct = PV x (1+r)t
PV = Ct / (1+r)t
Discount factor is (DF) as a present value of $1 = 1/ (1+r)t
PV = DF x Ct
Discount factor is today’s value of $1 at time t. DF reflects the minimal investment made today that
gives you $1 in the future if you pursue alternative investment.
Discount rate is the reward investors demand for accepting delayed payment
Investors demand at least what they can receive from risk equivalent alternative investments
Discount rate is also called the opportunity cost of capital because it is the return foregone by investing
in a capital project rather than investing in freely available securities
NPV = Net Present Value = present value of all future cash flows minus the required investment
NPV = -Cost + Ct/ (1+r)t
NPV is a decreasing function of r
Only accept investments with positive net present value
Return on investment = Profit/investment x 100%
Risk and Present value
Risk is a core concept in finance
Higher risk projects require higher rates of return
Safe dollar is worth more than a risky one
Risky investments can generate random returns that occur at diff probabilities
Expected value is the probability weighted average outcome
Expected cash flow (capital budgeting)
Expected return (portfolio management)
Use expected cash flows to compute present values of risky cash flows
Some people prefer to consume now and some prefer to consume later. Borrowing and lending allow us
to reconcile these opposing desires, which may exist within the firms’ shareholders
BMA Chapter 2
How to value an investment that delivers a steady stream of cash flows forever (a perpetuity) and one
that produces a steady stream of income for a limited period of time (an annuity)
Money has a time value: a dollar today is worth more than a dollar tomorrow
Wealth grows at a compound rate and interest you earn is called compound interest
, Joven Liew Jia Wen
201506858
Future value of $100 = 100 (1+r)t
Discount factor measures the present value of $1 received in year t
Rate of return r is also called discount rate, hurdle rate, opportunity cost of capital. It is an opportunity
cost because it is the return foregone by investing in the project rather than investing in financial
markets
A safe dollar is worth more than a risky dollar
For risky investments, properly discount the payoff by the rate of return offered by risk equivalent
investment in financial markets.
Value of investment therefore depends on timing of cash flows and their risk.
Return = profit/investment
If return is higher than opportunity cost, invest.
Net present value rule = Accept investments that have positive net present value
Rate of return rule = Accept investments that offer rates of return in excess of their opportunity cost of
capital
Discounted cash flow = DCF
Consols are perpetuities or bonds that the government issued and it is under no obligation to repay but
that offer a fixed income for each year to perpetuity.
Return = Cash flow/present value
Perpetuity formula tells us the value of a regular stream of payment starting one period from now. Ex. if
you want to provide $1bn a year with first payment in 4 years’ time, in year 3, this endowment will be a
normal perpetuity with payments starting in one year. PV of endowment would mean you calculate the
perpetuity in year 3 then times the discount factor for 3 years.
An annuity is an asset that pays a fixed sum each year for a specified number of years.
A level of stream of payments starting immediately is called an annuity due. An annuity due is worth
(1+r) times the value of the ordinary annuity.
Mortgage loan is an example of an amortizing loan. Amortizing means part of the regular payment is
used to pay interest on loan and part is used to reduce the amount of loan.
Table of formulas = pg 35
Annual percentage rate = APR
There is a difference between quoted annual interest rate and effective interest rate
Quoted annual interest rate is the total annual payment divided by number of payments in a year. When
interest is paid once a year, quoted and effective interest rates are the same. When interest is paid
more frequently, effective interest rate is higher than quoted rate.
201506858
FM473: Finance I
Present Value, How to calculate PV, Valuing Bonds, Valuing Common Stocks, Risk and return, Portfolio
theory and CAPM, Market Efficiency, Put and Call options, Valuing Options, Forwards and Futures
Lecture 1: Present Value
There are sole proprietorships, partnerships and corporations in US. Corporations only take up 16% of
firms but they generate 84% of revenues.
A corporation is a legal entity owned by its stockholders and is legally distinct from them.
Ideally, a firm should maximize the total welfare of shareholders. In practice, firms are run by managers.
As a result, what a firm does crucially depends on the managerial incentives. Incentives depend on the
corporate governance of a firm.
In practice, main objective assigned to managers is to maximize shareholder value**
HSBC: Aim to run a sustainable business for the long term and achieve sustainable profits for our
shareholders
Goldman Sachs: Providing superior returns for our shareholders; significant employee stock ownership
aligns the interests of our employees and our shareholders
Values and Discounting
Discount rate is the interest rate used to compute present values of future cash flows
Present Value: Value today of a future cash flow
Future Value: Amount to which an investment will grow after earning interest
Discount factor: Present Value of a $1 future payment
FV of your $100 with interest on government securities as r = 100 x (1+r)t
Time value of money: A pound today is worth more than a pound tomorrow
,Joven Liew Jia Wen
201506858
Present Values convert future cash flows to their current values. Future cash flows is Ct.
Ct = PV x (1+r)t
PV = Ct / (1+r)t
Discount factor is (DF) as a present value of $1 = 1/ (1+r)t
PV = DF x Ct
Discount factor is today’s value of $1 at time t. DF reflects the minimal investment made today that
gives you $1 in the future if you pursue alternative investment.
Discount rate is the reward investors demand for accepting delayed payment
Investors demand at least what they can receive from risk equivalent alternative investments
Discount rate is also called the opportunity cost of capital because it is the return foregone by investing
in a capital project rather than investing in freely available securities
NPV = Net Present Value = present value of all future cash flows minus the required investment
NPV = -Cost + Ct/ (1+r)t
NPV is a decreasing function of r
Only accept investments with positive net present value
Return on investment = Profit/investment x 100%
Risk and Present value
Risk is a core concept in finance
Higher risk projects require higher rates of return
Safe dollar is worth more than a risky one
Risky investments can generate random returns that occur at diff probabilities
Expected value is the probability weighted average outcome
Expected cash flow (capital budgeting)
Expected return (portfolio management)
Use expected cash flows to compute present values of risky cash flows
Some people prefer to consume now and some prefer to consume later. Borrowing and lending allow us
to reconcile these opposing desires, which may exist within the firms’ shareholders
BMA Chapter 2
How to value an investment that delivers a steady stream of cash flows forever (a perpetuity) and one
that produces a steady stream of income for a limited period of time (an annuity)
Money has a time value: a dollar today is worth more than a dollar tomorrow
Wealth grows at a compound rate and interest you earn is called compound interest
, Joven Liew Jia Wen
201506858
Future value of $100 = 100 (1+r)t
Discount factor measures the present value of $1 received in year t
Rate of return r is also called discount rate, hurdle rate, opportunity cost of capital. It is an opportunity
cost because it is the return foregone by investing in the project rather than investing in financial
markets
A safe dollar is worth more than a risky dollar
For risky investments, properly discount the payoff by the rate of return offered by risk equivalent
investment in financial markets.
Value of investment therefore depends on timing of cash flows and their risk.
Return = profit/investment
If return is higher than opportunity cost, invest.
Net present value rule = Accept investments that have positive net present value
Rate of return rule = Accept investments that offer rates of return in excess of their opportunity cost of
capital
Discounted cash flow = DCF
Consols are perpetuities or bonds that the government issued and it is under no obligation to repay but
that offer a fixed income for each year to perpetuity.
Return = Cash flow/present value
Perpetuity formula tells us the value of a regular stream of payment starting one period from now. Ex. if
you want to provide $1bn a year with first payment in 4 years’ time, in year 3, this endowment will be a
normal perpetuity with payments starting in one year. PV of endowment would mean you calculate the
perpetuity in year 3 then times the discount factor for 3 years.
An annuity is an asset that pays a fixed sum each year for a specified number of years.
A level of stream of payments starting immediately is called an annuity due. An annuity due is worth
(1+r) times the value of the ordinary annuity.
Mortgage loan is an example of an amortizing loan. Amortizing means part of the regular payment is
used to pay interest on loan and part is used to reduce the amount of loan.
Table of formulas = pg 35
Annual percentage rate = APR
There is a difference between quoted annual interest rate and effective interest rate
Quoted annual interest rate is the total annual payment divided by number of payments in a year. When
interest is paid once a year, quoted and effective interest rates are the same. When interest is paid
more frequently, effective interest rate is higher than quoted rate.
