Finance: Present Value of a Single Cash Flow
You are celebrating the birth of your daughter. Assume you will need $250,000 in 18 years to pay for her college education. How much would you need to deposit today to have $250,000 in 18 years, if you invest the money at 8% per year?
Correct answer: $62,562.26 Calculator: n = 18 [18] [n] i = 8 [8] [i] PMT = 0 [0] [PMT] FV = 250,000 [250,000] [FV] PV = ? [PV] Answer: -62,562.2573, so PV = $62,562.26 Excel: Use PV function Rate 8% Nper 18 Pmt 0 Fv 250,000 Type 0 i.e. insert function as =PV (8%,18,0,250000) Formula result = -62,562.26
Again recall from the video that if the annual interest rate is 5%, the present value of $127.63 to be received in five years is $100.00. If the investment horizon increases, your money is working longer for you. So, you won't need to deposit as much. To confirm intuition, compute the present value of $127.63 to be received in ten years if the annual interest rate is 5%?
Correct answer: $78.35 Formula: PV=127.63/(1.05)^10 PV=78.35 Calculator: n = 10 [10] [n] i = 5 [5] [i] PMT = 0 [0] [PMT] FV = 127.63 [127.63] [FV] PV = ? [PV] Answer: -78.35, so PV = $78.35 Excel: Use PV function Rate 5% Nper 10 Pmt 0 Fv 127.63 Type 0 i.e. insert function as =PV(5%,10,0,127.63) Formula result = -86.86
Recall from the video that if the annual interest rate is 5%, the present value of $127.63 to be received in five years is $100.00. If the interest rate increases, your money is working harder for you. So, you won't need to deposit as much to have $127.63 in five years. To confirm intuition, compute the present value of $127.63 to be received in five years if instead the annual interest rate is 8%?
Correct answer: $86.86 Formula: PV=127.63/(1.08)^5 PV=86.86 Calculator: n = 5 [5] [n] i = 8 [8] [i] PMT = 0 [0] [PMT] FV = 127.63 [127.63] [FV] PV = ? [PV] Answer: -86.86, so PV = $86.86 Excel: Use PV function Rate 8% Nper 5 Pmt 0 Fv 127.63 Type 0 i.e. insert function as =PV(8%,5,0,127.63) Formula result = -86.86
In qualitative terms, holding all else equal, what happens to the present value of a future cash flow if the interest rate increases?
The present value decreases.
In qualitative terms, holding all else equal, what happens to the present value of a future cash flow that is to be received further out into the future?
The present value decreases.