Week 2 Flashcards
Time Value of Money
Time value of money is a very important concept in financial planning. It is used as the basis of valuing all investments
Concept that a dollar received today is worth more than a dollar received in the future. Applying this concept allows financial planners to determine the financial needs and requirements of clients
People prefer cash now rather than later because:
Risk or uncertainty of future collection.
Opportunity cost.
Postponement of present consumption.
The number of time periods between the present value and the future value is represented by
n
The rate of interest for discounting or compounding is called
i
Present value is shortened to
PV
Future value is shortened to
FV
All time value questions involve four values
PV, FV, i and n. Given three of them, it is always possible to calculate the fourth.
Future value (FV)
Future value (FV) measures cash flows at the END of the project’s life
Present value (PV)
Present value (PV) measures cash flows at the BEGINNING of the project’s life
Simple interest
- applies when interest is calculated only on the original principal or amount borrowed for the entire period of the loan
Compound interest:
Used to calculate the amount of interest on the outstanding balance where the interest is reinvested onto the principal
For each succeeding period that the interest rate is calculated, the principal figure has grown by the amount of interest earned in the previous period.
Principle of compounding is a strong recommendation for establishing savings and investment programs early and sticking to them
Nominal interest rate
is the annual interest rate when the compounding period, may be more frequent than yearly, is not considered.
Calculating interest on a fixed deposit
Cash is traded in the short term money market
The interest is calculated on a simple interest basis, and paid to the nearest cent.
I = PV x i x n
where:
I = Interest amount
PV = Present value of cash deposit
i = Interest rate per annum expressed as a decimal (e.g. 12% = 12/100 = 0.12)
n = Number of days cash is on deposit/365
$10,000 deposited in the short term account with NAB at 4.50% for 90 days. What is the interest amount?
I = PV x i x n
= $10,000 x .045 x (90/365)
= $110.96
Future values
Future value of a single sum is the amount that a sum will grow to on maturity
Need to discount money that we will be receiving in the future when comparing with money we have now.
FV =
FV = PV (1 + in)
i.e. Future value = principal + interest
PV = Present Value or price
FV = Future Value or Maturity Value
i = the interest rate
n = number of days in period/365 or number of full years
$100,000 is deposited in a term deposit account for 30 days. If the rate offered is 12.60% p.a., how much will be in the deposit account on maturity?
FV = PV (1 + in) FV = 100,000 (1 + (.126 x 30/365)) FV = 101035.62
Present value of a future amount
Aim is to determine what an amount, that will be received in the future, is worth today.
The factor that determines this is the applicable interest rate
PV = FV/(1+in)
You want to receive $4,560 in 4 years time. How much must you invest now at 13% simple interest in order to receive the $4,560?
PV = FV/(1 + in) PV = 4560/(1+ (.13 x 4)) PV= 4560/ 1.52 = $3000
Application in the money market
Typical money market securities such as Short term notes and bonds, Bank bills, Treasury notes use simple interest calculations.
The price of these are calculated as a discount to the face value.
A bank bill which has 90 days to maturity has a
face value of $100,000. What is the purchase
price to achieve a yield of 2.25% simple
interest?
PV = FV/(1 + in)
PV= $100,000/(1 + 0.0225 x 90/365)
PV= $100,000/1.00554794521
PV = $99448.26
Future Value Formula
FV = PV(1 + i)^n
FV = future value of an amount invested today.
PV = amount of present sum of money
i = interest rate per period
n = number of periods
Using the formula for the example, we get
How much interest a $10,000 deposit earn over four years at an annually compound rate of 9.45% pa? Also how much interest has been earned over this period?
Using the formulate:
FV = PV(1 + i)^n
Interest earned = FV - PV
FV= 10,000 (1+ .0945)^4 = $14,350.36
Interest earned = 14350.36 – 10000= $4,350.36
Present value compound interest of a single amount
In interest rate markets, we use this formula to calculate the present value of a bond.
PV = FV/(1 + i)^n
What would you pay for a cash flow of $50,000 to be received in three years if the three-year interest rate is now 7.82% p.a.(compounding)?
PV = FV/(1 + i)^n
PV = 50000/(1+.0782)^3
= 50000/(1.25342393177)
= $39890.73
Nominal and Effective Interest Rates
A nominal interest rate is the stated interest rate that a bank might quote.
However, the value of the investment is affected by the frequency at which the interest rate is determined.
The effective interest rate is the real rate after adjusting for frequency of compounding.
Periodic interest rate formula is
i = j/m
j = annual interest rate
m = number if compounding periods
Jason invests $1000 compounded quarterly at 9% p.a. over 4 years. Determine the FV.
FV = PV (1 + i)^n
FV = $1000 (1 + 0.0225)^16
= $1427.62
Effective Interest Rate :
ie = (1 + i/m)^m -1
where m = no. of compounding periods for annum
For example a nominal interest rate is stated by the bank at say 6 %. What is the effective interest rate if paid semi annually?
ie = (1 + i/m)m -1
= ( 1 + 0.06/2)2 – 1
= (1+ 0.03) 2 – 1
= 0.0609
= 6.09%
ANNUITIES
An annuity is a stream equal periodic cash flows over a specified period
Characteristics of annuities
has a fixed term to maturity
is a regular stream of equal payments
can be paid in arrears (general) or in advance
Types of annuity
Ordinary annuity : paid end of each period
Annuity due : paid beginning of each period
Deferred annuity : paid sometime in the future
Perpetuity : payments continue forever
Annuties FV and PV formulas
Slide 29
Definitions of risk
the chance of loss of capital
the chance of loss of purchasing power
the variability of returns
Expected return E(R) =
= mean of annual returns
Expected return E(R):
Weighted expected return
Example Share A
Return
10% chance of 20%
40% chance of 12%
50% chance of 10%
= 0.20 (10%) + 0.12(40%) + 0.10(50%)
= .02 + .048 + .05
= 11.8%
Sd
Standard deviation of returns is a measure of the riskiness of an investment.
Variance of returns s^2
See slide 37
How can diversification reduce risk?
Risk refers to the variability of returns.
Risk can be measured by using the standard deviation.
For a portfolio, we must consider the risk and returns of the whole portfolio rather than just the individual components.
The expected return for a portfolio is the weighted average returns of the individual shares.
Portfolio risk is not simply a weighted average of the standard deviations of individual shares in portfolio.
It is necessary to understand the concept of correlation between the shares.
Principle of correlation
to select the combination of assets within a portfolio that reduces the overall risk whilst maximising return
Need to select those particular assets whose riskiness moves in different directions so that they cancel out each others’ risk.
The shape of the efficient frontier will depend on the correlation between the asset returns of the two assets.
correlation coefficient
The correlation coefficient shows the extent of correlation among shares.
It has a numerical value of –1 to +1 which indicates the risk reduction between shares:
Negative correlation (–1) Large risk reduction
Positive correlation (+1) No risk reduction
On average, the correlation coefficient for returns on two randomly selected shares would be in the range of +0.5 to +0.7.
Adding Stocks to a Portfolio
What would happen to the risk of an average 1-stock portfolio as more randomly selected stocks were added?
sp would decrease because the added stocks would not be perfectly correlated, but the expected portfolio return would remain relatively constant.
Modern portfolio theory assumes there are only two asset types
risky assets
risk-free assets
Financial planners need to help clients make decisions about investments in
growth assets
fixed-interest assets
This will depend on a client’s risk tolerance which can be assessed by risk profiling.
Modern portfolio theory states the risk-return relationship by the formula:
Slide 56
Stand-alone risk =\
Market risk + Diversifiable risk
Market risk is that part of a security’s stand-alone risk that cannot be eliminated by diversification.
Firm-specific, or diversifiable, risk is that part of a security’s stand-alone risk that can be eliminated by diversification.
