Annuity Present Value Formula

Annuity Present Value Formula

Annuity present value is calculated for the investment decision. Annuity present value is the present value of future expected cash flows.

Present Value annuity = C x Annuity Factor

Where

Annuity Factor =1-(1+i)^-n

                          i

i=interest rate

n=number of periods

Example

50,000 for 5 Year

Cost of capital = 12%

Calculate annuity by short & long methods.

Solution

Annuity Factor

1-(1+i)^-n

     i

Where;

i=interest rate

n=number of periods

=1-(1+.12)^-5

       .12

=3.6047

PV of Annuity = 3.6047 x 50,000

180,238

Annuity Factor Formula

Annuity Factor Formula

Annuity Factor is used to calculate the present value of annuity. Annuity Factor can be calculated by following formula

Annuity Factor =1-(1+i)^-n

                          i

i=interest rate

n=number of periods

Example

Years= 4 Years

Interest Rate =14%

Calculate Annuity Factor

Solution

Annuity Factor =1-(1+i)^-n

                          i

Annuity Factor =1-(1+14%)^-4

                            i

=2.913

Negative NPV Formula

Negative NPV Formula

NPV negative mean when present value of cost exceeds the benefit. In simple word when cost is more than benefit at present date. It is logical that a project with negative NPV would be rejected.

Negative NPV = PV of Benefits < PV of Cost

Example

Investment required for a project = 500,000

First & Second Year income =     300,000 & 280,000

Weighted Cost of capital= 12%

Solution

 Years                  Year 0                Years 1                   Year 2

Initial investment      500,000

Income                                                           300,000

Income                                                                                                    280,000

Discount Factor        (1+.12)^-0                                      (1+.12)^-1                                   (1+.12)^-2

PV                               (500,000)                      267857                         223,214

NPV = 267,857+223,214-500,000

=(8,929)

Positive NPV Formula

Positive NPV Formula

NPV is positive, when present value of benefit is greater than present value of costs. It means that if all thing happening today, benefits are greater, and therefore project is to be selected. It is important that NPV does not take into account relevant risk associated with project.

Positive NPV = PV of Benefits > PV of Cost

Example

Initial investment for a proposed = 300,000

First Year income from project =     180,000

Second Year Income from Project= 180,000

Cost of capital= 12%

Solution

                                Year 0            Years 1         Year 2

Initial investment            300,000

Income First Year                                           180,000

Income  2^nd Year                                                                        180,000

Discount Factor                (1+.12)^-0                       (1+.12)^-1                    (1+.12)^-2

PV                                      (300,000)              160,714             143,495

NPV = 160,714+143,495-300,000

=4,209

NPV Formula

NPV Formula

Net present value shortly known is NPV is calculated by deducting present value of cost from the present value of benefit. It is important to remember that benefits are cash inflows , where cost are cash outflows. The NPV formula can be mathematically expressed as under

NPV = PV Inflows- PV of Outflow

Example

Project cost = 50,000

Project income = 30,000

Calculate NPV?

Solution

PV of Cost = 50,000 x (1+12%) ⁰

= 50,000 x 1

= 50,000

PV of Benefit

  Years                                     1                               2               Total

Cash Flows                                   30,000                      30,000

Discount                                      (1+12%)^-1                          (1+12%)^-2

PV                                                  26,786                      23,916           50,702

NPV = 50,702-50,000

= 702        

Present Value Formula

Present Value Formula

Present Value of future cash flows can be simply calculated multiplying the cash flows with the discount factor. This formula can be mathematically expressed as under;

C x (1+i)^-n

Where

C=Cash flow

n= period in which cash flow occurring

Example

Expected Cash flow at end of year 3 = 40,000

Solution

C x (1+i)^-n

40,000 x (1+12)^-3

=28,471