How do you find the present value of an annuity?
There are generally 5 elements that you will need to know in order to calculate either of them:
1. present value (PV)
2. future value (FV)
2. future value (FV)
3. years to maturity (n)
4. discount rate (r)
5. annuity payment (PMT)
There are 3 ways to calculate the PV of an annuity. You can use the timeline, formula or financial calculator.
A) Formula:
PV = PMT ((1-(1+r)^-n)/r)
B) Financial Calculator:
Question 1 – ordinary annuity:
You will receive $500 at the end of each of the next 5 years. The current interest rate is 9% per annum. What is the present value of this series of cash flows?
PV = ?
FV = 0
PMT = 500
n = 5
r = 9%
input the values into the financial calculator and compute for PV
Question 2: annuity due
An investor wants to buy a 3 period annuity that pays $100 per year for the next three years, each instalment being paid at the beginning of the year. If a bank is prepared to pay interest at 12%, how much must be invested today?
Change your financial calculator to beginning mode:
PV = ?
FV = 0
PMT = 100
n = 3
r = 12%
PRACTICE QUESTIONS
Question 3 onwards: Try it out on your own
Question 3 onwards: Try it out on your own
You take out a $5000 loan with ten equal payments at the beginning of each 6 months. The interest rate is 10% p.a. compounded half yearly. How much are your repayments?
Question 4:
An investor pays 3 instalment of $100 at the beginning of each year into a savings account yielding 12% per year interest compounded annually. What is the future value of the investment at the end of three years?
Question 5:
An investor wishes to invest a sum of money today which will yield three equal instalments of $100, the first payable three years from today. If interest accrues at 12%, what amount must be invested?
Question 6:
An investor wants to buy 1,000 non-redeemable 9% preference shares of $1 each. If the return which he requires is 12%, what is the present value of the investment?
Question 7:
If a company has just made a payment of $10,000 and this is expected to grow at the expected inflation rate of 3% per year and the discount rate is 8%, then the present value of this perpetual payment stream is?