Present Value of Single Cash Flow for Multiple Period Investment with Compound Interest

Present Value of Single Cash Flow for Multiple Period Investment with Compound Interest

Present Value with a Single Cash Flow:

Present value (PV) is the current value of a single future cash flow discounted at the appropriate discount rate.

Time value of money for a single cash flow is a cash inflow or outflow that investors or lenders received from or paid to once respectively for specific periods

There are often four parts to equation (time value of money for a single cash flow): the present value (PV), the future value (FV), the discount rate (r), and the number of periods of the investment (t). If three of these (FV, r and t) are given, so we can find the present value (PV).

Multiple-Period Investment:

Multiple-period investment may be investment for more than one year. Term multiple-period can refer to more than one day or one month investment, so it isn’t always more than one year investment.

If period investments are based on one day, one month or one year etc., so discount rates are based on one day, one month or one year respectively.

Definition of Compound Interest:

Compound Interest means Interest earned on both the principal and the interest reinvested from previous periods.

Formula of compound interest future value for Multiple-Period Investment:

 FV=PVx(1+r)^t

So

Which

PV: Present Value or principal is worth today

FV: Future value is worth in the future

r : Interest rate, rate of return, or discount rate per period , but not always one year.

t : time is referred to number of periods of investment

Question

Mr. David will receive $10,000 three years from now. Mr. David can earn 8 percent on his investments. What is the present value of his future cash flow?

Solution

PV=FV/(1+r)^t=10,000 * 1/(1+0.08)^3=10,000*0.7938=$7,938

Today David invests $7,938, and after three years, David will get $10,000.