Time Value of Money Flashcards
Present value
Present value is the amount of money deposited (generally) or received when an investment or loan begins.
Future value
FV - almost always a positive input except it can be zero
Payment
PMT - can be negative or positive—depends on the cash flow in or out
Time
N
Interest
I/YR
Ordinary annuity and annuity due (payments)
Annuity payments are repeated amounts that are paid out or received. When one of the inputs or the solution is a (repeated) payment, the calculator must be in the proper mode (begin or end). In addition, payments are either positive (+) or negative (-).
Positive input - annuity due
Money is deposited into the client’s checking account*. Examples include the following:
* CD or bond interest received by the client
* Dividends received by the client
* Pension or IRA distributions received by the client, but not pension deposits
* Withdrawals from mutual funds received by the client
* Rent received from an investment property owned by the client
Negative input - annuity due
Money moves out of the client’s checking account*.
Examples include the following:
* Investments into mutual funds, stocks, bonds, IRAs
* A repair is made to the investment property owned by the client
* Pension or 401(k) deposits made by client’s employer. The employer has to write the check (negative), but the money isn’t deposited into the client’s personal account until he takes
distributions (positive). If you enter the pension deposit or 401(k) deposit as a positive, you
will get a wrong answer or no answer.
Use of Payment Begin or End mode
Begin mode
* College tuition paid
* Retirement benefits received
* Family needs
End mode
* 401(k) deferrals
* Profit-sharing contributions
* Bond interest paid
* Mortgage payments
The real rate of return
The inflation adjusted interest rate is the “real” rate of return. The real rate is the nominal rate of return adjusted for inflation. Whenever a question asks for today’s dollars, use the real rate return formula:
Real Rate of Return =
[ (1 + after−tax return)/
(1 + inflation rate) − 1 ] × 100
Unequal cash flows/IRR/Net present value
You must also write the keystrokes down. With all calculators, the following rules apply:
1. If there are both positive and negative cash flow in the same period, they must be netted. Example:
Rents received (positive) and expenses paid (negative)
2. If there is no cash flow (in or out) for a period, a zero must be entered.
3. The first cash outflow, usually the purchase of an investment, is “cash flow 0” (CFj
on the 10B). Some amount must always be entered. If the amount is not known, it is entered as 0.
Unequal cash flows - 1st variation—calculate PV
Always enter zero as first input and the required rate of return as stated in the problem.
- solve for NPV
Unequal cash flows - 2nd variation—Calculate Internal Rate of Return (IRR)/dollar weighted return
Always enter the initial investment as a negative input.
- solve for IRR/YR
Unequal cash flows - 3rd variation—calculate net present value (NPV)
Always enter the initial investment as a negative input and the required rate of return.
Net Present Value (NPV)
The amount of NPV often facilitates investment decisions. If the NPV is positive, the investment will earn more than the client’s required rate of return.
When the NPV is negative, the client should usually not buy the investment. Why? The actual rate of return is less than his or her required rate of
return for making investments.
If NPV is positive, the IRR › Required rate of return
If NPV is negative, the IRR ‹ Required rate of return
If NPV is 0, the IRR = Required rate of return
