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Business Mathematics and Statistics > Time Value of Money > Present and Net Present Value
Time Value of Money

Present and Net Present Value

Present and net present value, both of them aim to calculate the present value of the future cash. Present value is the current value of tomorrow’s cash, available at a  discount rate of interest. Furthermore, the net present value is primarily the current value of cash inflows subtracted by the cash outflows. Well, let’s understand the whole concept in a better manner.

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Present Value

Net Present Value

As mentioned earlier, present value is nothing but the current cost of the total amount of cash. The simple formula to calculate present value is as follows: Suppose, the present value (P) of some quantity (An), at the end of the value period (n),  and at an interest rate (i) is:

A= P(1 + i)

⇒ P = An/(1 + i)n

For i is positive (greater than 1), the value 1/(1 + i)is negative (less than 1 ) (for different values of i and n). A simple example to help and better understand the concept.

Example 1: What is the present value of Rs. 10 and at an interest rate of 10% at the end of two years compounded annually?

Solution: Given:  ARs. 10
= 10% = 0.1
= 2

Present Value = An/(1 + i)n

                        = 10(1+0.1)2

                                 = 10/1.21 = 8.264

                       = Rs. 8.264

Therefore, the growth after 2 years at an interest rate of 10% will be Rs. 8.264 compounded annually.

Present Value for Multiple Time Period

Calculating the present value for multiple periods is a useful way to calculate the earnings overall. Here is the formula to calculate present value for “n” number of time periods.

Present Value = Payment 1/(1+i) + Payment 2/(1+i)+ Payment 3/(1+i)+ Payment N/(i+i)n

Present Value of Annuity – Due or Immediate

The present value in both cases i.e. annuity due and annuity immediate is same. It is more or less similar to the value of annuity regular i.e. for ( n – 1 ) years + initial receipt. The initial receipt can also be a payment process done during the start of the time span.

Net Present Value

The following formula makes the meaning of net present value.

Net Present Value = Cash Inflow of present value – Total net investment 

Furthermore, there is a chance that there is an additional addition to the investment process. For the same, the formula comes off as:

Net Present Value = Cash inflow of present value – Cash outflow of present value

Here are simple steps to calculate the net present value:

  • In every year of investment, calculate the net cash inflow.
  • Furthermore, select the rate of return.
  • For the rate of return, calculate the discounted factor for each and every year.
  • Now, calculate the present worth of net cash flows. This is to be done by multiplying the discount factors with the cash flows.  This is called the present value of the cash flows.
  • Finally, add all the present value of cash flow.

Formula for NPV

The formula to calculate net present value is:

Net Present Value = Z1/(1+r)+Z2/(1+r)– X0

Where,

ZCash flow for time period 1
Z2 = Cash flow for time period 2
r = Rate of discount
X= Cash outflow

A simple example to make the concept of net present value clear.

Example 2: A company “A” wants to buy another company “B.” Before buying, company “A” looks for the projection of company “B” for the coming 10 years.

Solution: The cost to buy company “B” at the present time – Rs. 1,000,000

The present value of cash flows for 10 years are as follows.

Year 1: Rs. 200,000
Year 2: Rs. 150,000
Year 3: Rs. 100,000
Year 4: Rs. 75,000
Year 5: Rs. 70,000
Year 6: Rs. 55,000
Year 7: Rs. 50,000
Year 8: Rs. 45,000
Year 9: Rs. 30,000
Year 10: Rs. 10,000

Total: Rs. 785,000

The total cash flow for the coming 10 years is now in the bucket. Therefore, we can simply use the formula to calculate the net present value.

Net Present Value: Rs. 785,000 – Rs. 1,000,000 = Rs. -215,000

The negative value indicates that it might not be a wise idea for company “A” to but company “B.”

Decision Rule

  • If Net Present Value is greater than 0, accept the proposal.
  • If Net Present Value is less than 0, then reject the proposal.

Importance of Net Present Value

Net present value is generally used to find out the decision behind any investment. As a result, the clear picture comes forward. It gives a clear sign to the company and probably tells about the value it will add to the company in the coming time. Hence, a +ve net present value is likely to add to the worth of the company.

Possibilities

The difference in the values of cash inflow and cash outflow is termed as net present value. Furthermore, this is primarily the result of the different projects taken up on investments. Therefore, there are three possibilities of a net present value.

Positive Net Present Value

First of all, in this case, the investment project is acceptable. However, for the same to happen, the present value of the cash inflow should be greater than cash outflow. Consequently, the net present value turns out to be positive.

Negative Net Present Value

In this case, the investment project is rejected, However, for it to happen, the present value of the cash inflow should be less than the cash outflow’s present value. Therefore, the net present value becomes negative.

Zero Net Present Value

In this case, the present value of cash inflow is equal to the present value of cash outflow. Therefore, in this case, the proposal is acceptable. However, due to the cancellation, the present value becomes zero.

Drawbacks of Net Present Value

Some of the key drawbacks that NPV comes forward with are:

  • Need of assumptions.
  • Takes into account a constant rate of discount.
  • Risk Adjustment
  • Sensitivity for even the insignificant and limited changes.

More Solved Examples for You

Example 3: Calculate the net present value for an investment project worth Rs. 1,00,000. The net cash flow for the other respective year is Year one: Rs. 55,000, Year two: Rs. 80,0000 and Year three: Rs. 15,000. The capital cost is 10%.

Solution: So, first of all, you need to calculate the present value of each year at 10% rate which comes out to be 0.909 for year one, 0.826 for year two, and 0.751 for year 3.

Year Net Cash Flow Present Value (10%) Cash Flow (Discount)
0 1,00,000 1.000 1,00,000
1 55,000 0.909 49,995
2 80,000 0.826 66,080
3 15,000 0.751 11,265
Net Present Value  27,340

Since, the value is positive, the company should look forward to accept the proposal.

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