Compounding, Discounting & Bond Maths Flashcards
Why are investment decisions crucial to businesses or investors?
- Significant resources are required.
- Investments can comprise a significant proportion of an investor’s total resources.
- Any mistakes could have significant, if not catastrophic, effects.
- It is often difficult and/or expensive to escape from an existing investment.
What does a rational investor need to be compensated for - in order to be willing to make an investment?
Loss of interest
Loss of Purchasing Power
Risk of returns not received
An investment should yield a return which is greater than:
The available risk free rate + inflation + risk premium
What is an opportunity cost?
It is necessary to evaluate the opportunity cost for each possible decision. If choosing option A means surrendering option B, then the benefits and returns of option B are the opportunity cost for option A.
What is the formula for simple interest?
FV = PV×(1+(i×n))
What is the formula for compound interest?
FV = PV×(1+ i)^n
What is the difference between compound and simple interest?
within the compound interest basis, the interest earned in earlier periods are reinvested and attract interest in subsequent periods. This is not the case with the simple interest basis.
How can you find a PV given a FV?
Discounting back to a PV using the formula:
FV/(1+r)^n
What is net future value? (net terminal value)
The differences between two opportunities future values (FV)
It is worth observing that if either of the investment scenarios registered a zero or negative NFV, then they would not have exceeded the opportunity cost of leaving the money in the bank and should be eliminated from consideration.
What is compounding?
When money is invested at compound interest, each interest payment is reinvested in addition to the principal amount, so that interest on an increasing sum is accrued in subsequent periods.
What is an annuity?
An annuity is an investment product which pays out regular cash flows each year, similar to Option A that was considered in section 1. In many countries, annuities are a type of product whereby an individual pays a lump sum to an annuity provider in exchange for a series of future income payments, either for life or for a set period.
What type of companies usually provide annuities?
Insurance Companies
Are annuities always available in all markets?
In some countries the annuities market is either small, still in an early stage of development, or may not even exist at all.
What is the present value of an annuity?
How much money an individual would need today to fund
a series of future annuity payments, given a set discount rate.
What is meant by the “discount rate” of an annuity?
The discount rate is the rate of return that could be earned instead of pursuing the project or investment – in other words, this rate of return is subtracted (ie, discounted) from the expected returns of the project/investment to arrive at the true gain, so that investors can determine whether it is worth the risk.
The same logic can be applied to other investments or projects that provide a recurring payment over a set period of time, such as government and corporate bonds, to help an investor determine whether or not they should proceed.
What are some advantages of the NPV method?
1) NPV is reinvested at a more realistic rate than compared to the IRR.
2) Inflation and risk can be added to the minimum discount rate (Cost of capital) 3) Can work with negative and positive cash flows.
4) Helpful when trying to decide which investment out of many to choose.
What is the formula to calculate APR?
((r+f)/principal)/ y *365
r = rate f = fees principal = loan amount y = days
What is the annuity discount factor formula?
1/r x (1- 1/(1+r)^n)
What is the Annuity discount factor formula for a growing annuity?
A/(r-g)*(1-(1+g/1+r)^n)
