In finance 251 you are required to determine the value of cash or a stream of cash flows at a certain period of time. Below are a list of fomula’s that you can use in present value and future value calculations.

1. Future value of single cash flow:

FV = PV x (1+r)^t

(FV = future value, PV=present value, r = rate of interest, t =time)

Example: What is the future value of $400 in 3 years if interest is 8% per annum?

FV = 400 * (1+8)^3 = $503.88

2. Present Value of a single cash flow:

PV = FV/(1+r)^t

Example: What is the present value of a cash inflow of $400 in 5 years time, given r =6% p.a?

PV = 400/(1.06)^5 = $298.9

3. PV of Multiple Cash flows:

PV = C1/(1+r) + C2/(1+r)^2 + C3/(1+r)^3 +….

(C1 = Cash flow in period one C2 =is flow in period two etc) 

Example: What is the present value of the following cash flows? Given r = 8%

Year 1                           -$300
Year 2                          +$200
Year 3                          +$500
Year 4                           -$600

PV = -300/(1.08) + 200/(1.08)^2 + 500/(1.08)^3 -600/(1.08)^4                                        

      = -150.41

4. Present value of an annuity*:

*An annuity is an equally spaced steam of cash flows with a finite maturity.

PV = C * [1/r - 1/(r(1+r)^t]

Example: You are looking at purchasing a car. The car dealer offers you the car for five annual payments of $2,000. Given that the first payment is in exactly one year’s time and the rate of interest is 8% per annum, what is the PV of this offer?

PV=2000 [1/0.08-1/〖0.08(1+0.08)〗^5 ]
      = 7985.42

5. Present Value of perpetuities*:

* A stream of equal cash flows that are paid forever (never end)

PV= C/r

Example: You have won the lottery. The lottery commission has offered you wither of the following options:
Option One: Receive $10,000 right now Option Two: Receive payments of $1,000 each year forever.

Given that interest rates are 12%, which option is the most valuable?
PV (option one) = $10000
PV(option two) = 1000/.12 = $8333.33

The first option is the most valuable.

Future Value of an annuity:

FV=C [((1+r)^t-1)/r]

Example: You decide to invest $5000 a year into a savings found yielding 6% per annum. What will the account balance be in 4 years time?

FV=5000[((1+0.06)^4-1)/0.06]
= 21 873

This entry was posted on Sunday, May 10th, 2009 at 10:37 pm and is filed under Finance. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.