Time Value Flashcards
The Time Value of Money is the concept that
money is worth more today that it is in the future.
Being given $100 today is better than being given $100 in the future because
you don’t have to wait for your money.
The process of determining how much a future cash flow is worth today is called
discounting
Discounting
the process of determining how much money paid/received in the future is worth today. You discount future values of cash back to the present using the discount rate.
Single-period investments use
a specified way of calculating future and present value.
Multi-period investment:
an investment that takes place over more than one periods.
Simple interest increases the balance linearly, while compound interest increases it
exponentially
The Future Value can be calculated by knowing the
present value, interest rate, and number of periods, and plugging them into an equation.
The future value of a present value is calculated by
plugging the present value, interest rate, and number of periods into one of two equations.
Calculating FV is a matter of identifying
PV, i (or r), and t (or n), and then plugging them into the compound or simple interest formula.
Simple Interest Formula:
Simple interest is when interest is only paid on the amount you originally invested (the principal). You don’t earn interest on interest you previously earned.
The time value of money framework says that
money in the future is not worth as much as money in the present.
Future Value:
the value of an asset at a specific date. It measures the nominal future sum of money that a given sum of money is “worth” at a specified time in the future, assuming a certain interest rate, or more generally, rate of return, it is the present value multiplied by the accumulation function.
Present Value:
also known as present discounted value, is the value on a given date of a payment or series of payments made at other times. If the payments are in the future, they are discounted to reflect the time value of money and other factors such as investment risk. If they are in the past, their value is correspondingly enhanced to reflect that those payments have been (or could have been) earning interest in the intervening time. Present value calculations are widely used in business and economics to provide a means to compare cash flows at different times on a meaningful “like-to-like” basis.
Time period assumption:
Business profit or losses are measured on a timely basis.
The Fisher Equation
approximates the amount of interest accrued after accounting for inflation.
A company will theoretically only invest if
the expected return is higher than their cost of capital, even if the return has a high nominal value.
Fisher Equation:
The nominal interest rate is approximately the sum of the real interest rate and inflation.
Explain the importance of the five components of TVM, as applied in a calculation
(discount rate, duration, payment, present value, future value).
Amortization of a loan is
the process of identifying a payment amount for each period of repayment on a given outstanding debt.
Amortization:
This is the process of scheduling intervals of payment over time to pay back an existing debt, taking into account the time value of money.
The present value of a perpetuity is simply
the payment size divided by the interest rate and there is no future value.
Perpetuities are a special type of annuity; a perpetuity is an
annuity that has no end, or a stream of cash payments that continues forever.
To find the future value of a perpetuity requires having a
future date, which effectively converts the perpetuity to an ordinary annuity until that point.
Perpetuities with growing payments are called
Growing Perpetuities; the growth rate is subtracted from the interest rate in the present value equation.
The future value (FV) measures the
nominal future sum of money that a given sum of money is “worth” at a specified time in the future assuming a certain interest rate, or more generally, rate of return. The FV is calculated by multiplying the present value by the accumulation function.
The FV of multiple cash flows is the sum of
the FV of each cash flow.
Annuity:
a specified income payable at stated intervals for a fixed or a contingent period, often for the recipient’s life, in consideration of a stipulated premium paid either in prior installment payments or in a single payment. For example, a retirement annuity paid to a public officer following his or her retirement.
Incremental cash flows:
the additional money flowing in or out of a business due to a project.
FV of a single payment:
The FV of multiple cash flows is the sum of the future values of each cash flow.
The PV of multiple cash flows is simply the
sum of the present values of each individual cash flow.
Sum FV:
The PV of an investment is the sum of the present values of all its payments.
You have $300,000 that you want to invest in a one year Certificate of Deposit (CD) with a 4% annual interest rate. What will be the value of that CD in a year?
FV = $300,000 × 1.04 = $312,000 Using Calculator: N = 1, I/Y = 4, PV = 300,000. [CPT] FV = $312,000.
What is the future value in 30 years of $100,000 invested today in a savings account earning a 1% compound interest rate every year (rounded up to the nearest dollar)?
FV = $100,000 × 1.0130 = $134,785 Using Calculator: N = 30, I/Y = 1, PV = 100,000. [CPT] FV = $134,785
You plan to invest $100,000 in a 3 year Certificate of Deposit that has a 5% compound interest rate. What is its future value?
FV = $100,000 × 1.053 = $115,763 Using Calculator: N = 3, I/Y = 5, PV = 100,000. [CPT] FV = $115,763.
You plan to invest $100,000 in a 3 year Certificate of Deposit that has a simple interest rate of 5%. What is its future value?
FV = $100,000 + (3 × 5% × $100,000) = $115,000.
What is the future value in 30 years of $100,000 invested today in a savings account earning a 1% simple interest rate every year (rounded up to the nearest dollar)?
FV = $100,000 + (30 × 1% × $100,000) = $130,000.
