Question

			Present Value
6a. What is the present value of $1,000,000, due 25 years from now?
b. What is the present value of a $40,000 ordinary annuity for 25 years?
c. What is the present value of a $40,000 perpetuity, if the first payment is 1 year from now?
d. What is the present value of a $40,000 perpetuity, if the first payment is now?

Using formula or Excel function

Answer 1

Note :

Rate of Interest is not given in the question

We will take rate of interest as 10% per annum compounded annually to solve this question

Summary of Answers

Question	Answer
6a	92,295.99
6b	363,081.60
6c	400,000.00
6d	440,000.00

Rate of Interest is not given in the question

We will take rate of interest as 10% per annum compounded annually to solve this question

Question 6a

To calculate present vaue of a single amount we use the following formulae

Presemt Value = Amount due in 25 Years / (1+Interest rate)^Number of years

Present value = 1,000,000 / 1.1^25

Present Value = 1,000,000 / 10.83 = 92295.99

Question 6b

Alternative 1

present value of a $40,000 ordinary annuity for 25 years

Present Value = Annuity Amount * Present Value Annuity Factor 10%, 25 Years

Present Vlaue = 40,000 * 9.077 = 363081.60

Alternative 2

Same can be calculated using following excel formulae

=PV(0.1,25,-40000)

this formulae will result in the answer 363081.60

Question 6c

present value of a $40,000 perpetuity, if the first payment is 1 year from now is

=Periodic cash flow / Interest Rate

Present Vlaue of Prepetuity = 40000 / 0.10 = 400000

Question 6d

present value of a $40,000 perpetuity, if the first payment is now is

= Periodic cash flow + (Periodic cash flow / Interest Rate)

Present Value of perpetuity = 40000 + (40000/0.10) = 440000