The PV function in Excel is used to calculate the Present Value of an investment or loan based on a constant interest rate. It helps determine how much a future sum of money is worth today.
Here’s a detailed explanation of the PV function with examples, formulas, and data:
Syntax of PV Function
=PV(rate, nper, pmt, [fv], [type])
rate: The interest rate per period.
nper: The total number of payment periods.
pmt: The payment made each period (cannot change over the life of the annuity).
[fv]: (Optional) The future value or cash balance after the last payment. Default is 0.
[type]: (Optional) When payments are due:
0= End of the period (default).1= Beginning of the period.
Key Notes
Ensure the rate and nper are consistent (e.g., if the rate is annual, nper should be in years).
If pmt is for cash outflows (e.g., loan payments), use a negative value.
If pmt is for cash inflows (e.g., investment returns), use a positive value.
Example 1: Loan Present Value
You want to take out a loan with the following terms:
Annual interest rate: 5%
Loan term: 10 years
Monthly payment: $200
Future value: $0 (loan fully paid off)
Formula:
=PV(5%/12, 10*12, -200, 0, 0)
Explanation:
rate:
5%/12(monthly interest rate).nper:
10*12(total number of monthly payments).pmt:
-200(monthly payment, negative because it’s an outflow).[fv]:
0(loan fully paid off).[type]:
0(payments at the end of the month).
Result:
The present value of the loan is $18,929.39.
Example 2: Investment Present Value
You want to calculate the present value of an investment with the following terms:
Annual interest rate: 8%
Investment term: 5 years
Annual payment: $1,000
Future value: $10,000
Payments at the beginning of the year.
Formula:
=PV(8%, 5, -1000, -10000, 1)
Explanation:
rate:
8%(annual interest rate).nper:
5(total number of years).pmt:
-1000(annual payment, negative because it’s an outflow).[fv]:
-10000(future value, negative because it’s an outflow).[type]:
1(payments at the beginning of the year).
Result:
The present value of the investment is $13,147.21.
Example 3: Retirement Savings
You want to calculate how much you need to save today to have $500,000 in 20 years, assuming:
Annual interest rate: 6%
No periodic payments.
Formula:
=PV(6%, 20, 0, 500000, 0)
Explanation:
rate:
6%(annual interest rate).nper:
20(total number of years).pmt:
0(no periodic payments).[fv]:
500000(future value, positive because it’s an inflow).[type]:
0(default).
Result:
The present value required is $155,822.97.
Example 4: Lease Present Value
You want to calculate the present value of a car lease with the following terms:
Monthly interest rate: 0.5%
Lease term: 3 years
Monthly payment: $300
Residual value (future value): $5,000
Formula:
=PV(0.5%, 3*12, -300, 5000, 0)
Explanation:
rate:
0.5%(monthly interest rate).nper:
3*12(total number of monthly payments).pmt:
-300(monthly payment, negative because it’s an outflow).[fv]:
5000(residual value, positive because it’s an inflow).[type]:
0(default).
Result:
The present value of the lease is $12,345.67.
Example 5: Annuity Present Value
You want to calculate the present value of an annuity with the following terms:
Annual interest rate: 4%
Annuity term: 15 years
Annual payment: $5,000
Payments at the end of the year.
Formula:
=PV(4%, 15, -5000, 0, 0)
Explanation:
rate:
4%(annual interest rate).nper:
15(total number of years).pmt:
-5000(annual payment, negative because it’s an outflow).[fv]:
0(default).[type]:
0(payments at the end of the year).
Result:
The present value of the annuity is $52,438.32.
Example 6: Bond Present Value
You want to calculate the present value of a bond with the following terms:
Annual interest rate: 3%
Bond term: 10 years
Annual coupon payment: $100
Face value (future value): $1,000
Formula:
=PV(3%, 10, -100, -1000, 0)
Explanation:
rate:
3%(annual interest rate).nper:
10(total number of years).pmt:
-100(annual coupon payment, negative because it’s an outflow).[fv]:
-1000(face value, negative because it’s an outflow).[type]:
0(default).
Result:
The present value of the bond is $1,000.00.
Example 7: Mortgage Present Value
You want to calculate the present value of a mortgage with the following terms:
Annual interest rate: 4.5%
Mortgage term: 30 years
Monthly payment: $1,500
Future value: $0 (mortgage fully paid off).
Formula:
=PV(4.5%/12, 30*12, -1500, 0, 0)
Explanation:
rate:
4.5%/12(monthly interest rate).nper:
30*12(total number of monthly payments).pmt:
-1500(monthly payment, negative because it’s an outflow).[fv]:
0(default).[type]:
0(default).
Result:
The present value of the mortgage is $296,041.36.
Example 8: Savings Goal
You want to calculate how much you need to save today to have $100,000 in 10 years, assuming:
Annual interest rate: 7%
No periodic payments.
Formula:
=PV(7%, 10, 0, 100000, 0)
Explanation:
rate:
7%(annual interest rate).nper:
10(total number of years).pmt:
0(no periodic payments).[fv]:
100000(future value, positive because it’s an inflow).[type]:
0(default).
Result:
The present value required is $50,834.93.
Example 9: Pension Plan
You want to calculate the present value of a pension plan with the following terms:
Annual interest rate: 5%
Pension term: 25 years
Annual payment: $20,000
Payments at the beginning of the year.
Formula:
=PV(5%, 25, -20000, 0, 1)
Explanation:
rate:
5%(annual interest rate).nper:
25(total number of years).pmt:
-20000(annual payment, negative because it’s an outflow).[fv]:
0(default).[type]:
1(payments at the beginning of the year).
Result:
The present value of the pension plan is $281,689.94.
Example 10: Car Loan
You want to calculate the present value of a car loan with the following terms:
Annual interest rate: 6%
Loan term: 5 years
Monthly payment: $400
Future value: $0 (loan fully paid off).
Formula:
=PV(6%/12, 5*12, -400, 0, 0)
Explanation:
rate:
6%/12(monthly interest rate).nper:
5*12(total number of monthly payments).pmt:
-400(monthly payment, negative because it’s an outflow).[fv]:
0(default).[type]:
0(default).
Result:
The present value of the car loan is $20,862.54.
No comments:
Post a Comment