FINANCE STUDY NOTES
Introduction
Finance is the economics of allocating resources over time with the intention of earning returns from
the investment that finance is allotted to.
Financial Markets
- Participation is financial markets is driven in part by the desire to shift future resources to he
present so as to increase personal consumption, and thus satisfaction.
- Or one may shift resources to the future by lending them, buying common stock, etc. In
exchange, they get an expectation of increased future resources, in the form of interest,
dividends, and/or capital gains.
- Where financial investments serve the purpose of reallocating the same resources over time, real
asset investment can actually create new future resources.
- The provision of funds for real asset investment is important, as is the allocative information that
financial markets provide to those interested in making real asset investment.
- Financial markets can help tell the investor whether a proposed investment is worthwhile by
comparing the returns from the investment with those available on competing uses.
- Financial market participants are risk-averse, they would choose the less risky of two otherwise
identical investments.
Market Interest Rate & Prices
- The market interest rate is the rate of exchange between present and future resources.
- Determined by the supply and demand of resources to be borrowed and lent.
- At any given time there are numerous market interest rats covering different lengths of time and
investment riskiness.
A Simple Financial Market
Shifting Resources in Time
- A financial exchange line is comprised of any transaction that a participant with an initial
amount of money may take by borrowing or lending at the market rate of interest.
- The line appears on a graph with CF1, the cash flow later on the vertical axis, and CF0, the now
cash flow on the horizontal.
CF1
$2640
$1540
0 CF0
$1000 $2400
PREPARED BY MR. ANTONY AMBIA Page 1
, - If a participant had $1000 at t0 and wished to borrow whatever he could with a promise to repay
$1540 at t1, how much could he borrow? Assume a 10% interest rate.
CF1 = CF0 (1+ i)
CF1 $1540
CF0 = --------- or ---------- = $1400
(1+ i) 1.10
The participant could borrow $1400 with a promise to repay $1540 at t1. The maximum amount the
participant could consume at t0 is thus $2400 (present wealth). $1400 is the present value of $1540.
- Present value is defined as the amount of money you must invest or lend at the present time so as to
end up with a particular amount of money in the future.
- Finding the present value of a future cash flow is often called discounting the cash flow.
- Present value is also an accurate representation of what the financial market does when it sets a price
on a financial asset.
Investing
- Investing in real assets allows for an increase in wealth because it does not require finding
someone to decrease their own.
- For wealth to increase the present value of the amount given up for real asset investment must be
less than the present value of what is gained from the investment.
Net Present Value
- The present value of the difference between an investments cash inflows and outflows
discounted at the opportunity costs (i) of those flows.
CF1
NPV = -------- – CF0
(1+ i)
- It is generally true that NPV = Change in present wealth.
- It is also the present value of the future amount by which the returns from the investment exceed
the opportunity costs of the investor.
Internal Rate of Return
- Calculates the average per period rate of return on the money invested.
- Once calculated, it is compared to the rate of return that could be earned on a comparable
financial market opportunity of equal timing and risk.
- IRR is the discount rate that equates the present value of an investments cash inflows and
outflows. This implies that it is the discount rate that causes an investments NPV to be equal to
zero.
CF0
NPV = 0 = – CF1 + -----------
(1+ IRR)
CF0
(1+IRR) = --------
CF1
PREPARED BY MR. ANTONY AMBIA Page 2
,- An IRR greater than the financial market rate implies an acceptable investment (and a + NPV),
an IRR lower than it does not (and a –NPV).
- IRR and NPV usually give the same answer as to whether an investment is acceptable, but often
give different answers as to which of two investments is better.
Corporate Example
- The sole task of a company is to maximise the present wealth of its shareholders.
- A company would accept investments up to the point where the next investment would have a –
NPV or an IRR less than its opportunity cost.
More Realistic Financial Markets
Multiple Period Finance
- Multiple period exchange rates (interest) are written as (1 + In)n, where n is the
number of periods.
Compound Interest
- Compounding means that the exchange rate between two time points is such that interest is
earned not only on the initial investment, but also on previously earned interest. The amount of
money you end up with by investing CF0 at compounding interest is written CF0 = [1 + (i/m)]m t,
where m is the number of times per period that compounding takes place, and t is the number of
periods the investment covers.
- The most frequent type of compounding is called continuous. Interest is calculated and added to
begin calculating interest on itself without any passage of time between compoundings. This
reduces the above formula to CF0(eit), where e is = 2.718…., the base of a natural logarithm.
Multiple Period Cash Flows
- To find the present value of a cash flow occurring at any one future time point the following
formula is used;
CFt
PV = ---------
(1+ it)t
- The present value of a set (stream) of cash flows is the sum of the present values of each of the
future cash flows associated with the asset, calculated;
CF1 CF2 CF3
PV = --------- + --------- + --------
(1+ i1)1 (1+ i2)2 (1+ i3)3
Multiple Period Investment Decisions
- Calculating NPV when the investment decision will affect several future cash flows must include
all present and future cash flows associated with the investment.
CF1 CF2 CF3
NPV = --------- + --------- + --------
(1+ i1)1 (1+ i2)2 (1+ i3)3
- Calculating the IRR of a set of cash flows involves finding the discount rate that causes NPV to
equal zero;
PREPARED BY MR. ANTONY AMBIA Page 3
, CF1 CF2 CF3
NPV = ----------- + ----------- + ------------
(1+ IRR) (1+ IRR)2 (1+ IRR)3
- The only way to solve for the IRR of a multiple period cash flow stream is with the trial and error
technique.
Calculating Techniques and Short Cuts in Multiple Period Analysis
- The instruction to calculate the PV of a stream of future cash flows is;
T CFt
PV = Σ ---------
t=1 (1+ it)t
- When discount rates are consistent across the future this changes to;
T CFt
PV = Σ --------
t=1 (1+ i)t
Calculation Methods
- Start with the CF furthest from the present, discount it one period closer and add the CF from the
closer time point, discount that sum one period nearer, etc. Continue process until all cash flows
are included and discounted back to t0. PREFERRED METHOD
- Use present value tables. Adding up the cash flows after discounting each one for its respective
time period.
- Tables are valuable when finding the present value of annuities. A constant annuity is a set of
cash flows that are the same amount across future time points.
- A perpetuity is a cash flow stream assumed to continue forever. Formula is simply a division of
the constant per-period CF by the constant per-period discount rate, or PV = CF/i.
- A slight modification of the above allows for the assumption that the cash flows will continue
forever, but will grow or decline at a constant percentage rate during each period (AKA growth
perpetuity), PV = CF/(i – g) where g is the constant per-period growth rate of the cash flow.
- This equation will not work when i<g.
Interest Rates, Interest Rate Futures and Yields
- Interest rates that begin at the present and run to some future time point are called spot interest
rates.
- The set of spot rates in a financial market is called the term structure of interest rates.
- A coupon bond has a face value that is used, along with its coupon rate, to figure a pattern of cash
flows promised by the bond.
- These cash flows comprise interest payments each period which continue until the maturity
period when the face value itself, as a principal payment plus the final interest payment, is
promised.
The Yield to Maturity (YTM)
- The YTM is the IRR of the bonds promised cash flows, or the average per period interest rate on
the money invested in the bond.
PREPARED BY MR. ANTONY AMBIA Page 4
Introduction
Finance is the economics of allocating resources over time with the intention of earning returns from
the investment that finance is allotted to.
Financial Markets
- Participation is financial markets is driven in part by the desire to shift future resources to he
present so as to increase personal consumption, and thus satisfaction.
- Or one may shift resources to the future by lending them, buying common stock, etc. In
exchange, they get an expectation of increased future resources, in the form of interest,
dividends, and/or capital gains.
- Where financial investments serve the purpose of reallocating the same resources over time, real
asset investment can actually create new future resources.
- The provision of funds for real asset investment is important, as is the allocative information that
financial markets provide to those interested in making real asset investment.
- Financial markets can help tell the investor whether a proposed investment is worthwhile by
comparing the returns from the investment with those available on competing uses.
- Financial market participants are risk-averse, they would choose the less risky of two otherwise
identical investments.
Market Interest Rate & Prices
- The market interest rate is the rate of exchange between present and future resources.
- Determined by the supply and demand of resources to be borrowed and lent.
- At any given time there are numerous market interest rats covering different lengths of time and
investment riskiness.
A Simple Financial Market
Shifting Resources in Time
- A financial exchange line is comprised of any transaction that a participant with an initial
amount of money may take by borrowing or lending at the market rate of interest.
- The line appears on a graph with CF1, the cash flow later on the vertical axis, and CF0, the now
cash flow on the horizontal.
CF1
$2640
$1540
0 CF0
$1000 $2400
PREPARED BY MR. ANTONY AMBIA Page 1
, - If a participant had $1000 at t0 and wished to borrow whatever he could with a promise to repay
$1540 at t1, how much could he borrow? Assume a 10% interest rate.
CF1 = CF0 (1+ i)
CF1 $1540
CF0 = --------- or ---------- = $1400
(1+ i) 1.10
The participant could borrow $1400 with a promise to repay $1540 at t1. The maximum amount the
participant could consume at t0 is thus $2400 (present wealth). $1400 is the present value of $1540.
- Present value is defined as the amount of money you must invest or lend at the present time so as to
end up with a particular amount of money in the future.
- Finding the present value of a future cash flow is often called discounting the cash flow.
- Present value is also an accurate representation of what the financial market does when it sets a price
on a financial asset.
Investing
- Investing in real assets allows for an increase in wealth because it does not require finding
someone to decrease their own.
- For wealth to increase the present value of the amount given up for real asset investment must be
less than the present value of what is gained from the investment.
Net Present Value
- The present value of the difference between an investments cash inflows and outflows
discounted at the opportunity costs (i) of those flows.
CF1
NPV = -------- – CF0
(1+ i)
- It is generally true that NPV = Change in present wealth.
- It is also the present value of the future amount by which the returns from the investment exceed
the opportunity costs of the investor.
Internal Rate of Return
- Calculates the average per period rate of return on the money invested.
- Once calculated, it is compared to the rate of return that could be earned on a comparable
financial market opportunity of equal timing and risk.
- IRR is the discount rate that equates the present value of an investments cash inflows and
outflows. This implies that it is the discount rate that causes an investments NPV to be equal to
zero.
CF0
NPV = 0 = – CF1 + -----------
(1+ IRR)
CF0
(1+IRR) = --------
CF1
PREPARED BY MR. ANTONY AMBIA Page 2
,- An IRR greater than the financial market rate implies an acceptable investment (and a + NPV),
an IRR lower than it does not (and a –NPV).
- IRR and NPV usually give the same answer as to whether an investment is acceptable, but often
give different answers as to which of two investments is better.
Corporate Example
- The sole task of a company is to maximise the present wealth of its shareholders.
- A company would accept investments up to the point where the next investment would have a –
NPV or an IRR less than its opportunity cost.
More Realistic Financial Markets
Multiple Period Finance
- Multiple period exchange rates (interest) are written as (1 + In)n, where n is the
number of periods.
Compound Interest
- Compounding means that the exchange rate between two time points is such that interest is
earned not only on the initial investment, but also on previously earned interest. The amount of
money you end up with by investing CF0 at compounding interest is written CF0 = [1 + (i/m)]m t,
where m is the number of times per period that compounding takes place, and t is the number of
periods the investment covers.
- The most frequent type of compounding is called continuous. Interest is calculated and added to
begin calculating interest on itself without any passage of time between compoundings. This
reduces the above formula to CF0(eit), where e is = 2.718…., the base of a natural logarithm.
Multiple Period Cash Flows
- To find the present value of a cash flow occurring at any one future time point the following
formula is used;
CFt
PV = ---------
(1+ it)t
- The present value of a set (stream) of cash flows is the sum of the present values of each of the
future cash flows associated with the asset, calculated;
CF1 CF2 CF3
PV = --------- + --------- + --------
(1+ i1)1 (1+ i2)2 (1+ i3)3
Multiple Period Investment Decisions
- Calculating NPV when the investment decision will affect several future cash flows must include
all present and future cash flows associated with the investment.
CF1 CF2 CF3
NPV = --------- + --------- + --------
(1+ i1)1 (1+ i2)2 (1+ i3)3
- Calculating the IRR of a set of cash flows involves finding the discount rate that causes NPV to
equal zero;
PREPARED BY MR. ANTONY AMBIA Page 3
, CF1 CF2 CF3
NPV = ----------- + ----------- + ------------
(1+ IRR) (1+ IRR)2 (1+ IRR)3
- The only way to solve for the IRR of a multiple period cash flow stream is with the trial and error
technique.
Calculating Techniques and Short Cuts in Multiple Period Analysis
- The instruction to calculate the PV of a stream of future cash flows is;
T CFt
PV = Σ ---------
t=1 (1+ it)t
- When discount rates are consistent across the future this changes to;
T CFt
PV = Σ --------
t=1 (1+ i)t
Calculation Methods
- Start with the CF furthest from the present, discount it one period closer and add the CF from the
closer time point, discount that sum one period nearer, etc. Continue process until all cash flows
are included and discounted back to t0. PREFERRED METHOD
- Use present value tables. Adding up the cash flows after discounting each one for its respective
time period.
- Tables are valuable when finding the present value of annuities. A constant annuity is a set of
cash flows that are the same amount across future time points.
- A perpetuity is a cash flow stream assumed to continue forever. Formula is simply a division of
the constant per-period CF by the constant per-period discount rate, or PV = CF/i.
- A slight modification of the above allows for the assumption that the cash flows will continue
forever, but will grow or decline at a constant percentage rate during each period (AKA growth
perpetuity), PV = CF/(i – g) where g is the constant per-period growth rate of the cash flow.
- This equation will not work when i<g.
Interest Rates, Interest Rate Futures and Yields
- Interest rates that begin at the present and run to some future time point are called spot interest
rates.
- The set of spot rates in a financial market is called the term structure of interest rates.
- A coupon bond has a face value that is used, along with its coupon rate, to figure a pattern of cash
flows promised by the bond.
- These cash flows comprise interest payments each period which continue until the maturity
period when the face value itself, as a principal payment plus the final interest payment, is
promised.
The Yield to Maturity (YTM)
- The YTM is the IRR of the bonds promised cash flows, or the average per period interest rate on
the money invested in the bond.
PREPARED BY MR. ANTONY AMBIA Page 4
