PRESENT VALUE (PV) 

In finance, present value (PV), also known as present discounted value, is the value of an expected income stream determined as of the date of valuation. The present value is always less than or equal to the future value because money has interest-earning potential, a characteristic referred to as the time value of money.

Future cash flows are discounted at the discount rate. The higher the discount rate, the lower the present value of the future cash flows. Determining the appropriate discount rate is the key to properly valuing future cash flows, whether they are earnings or obligations. If you received Rs.10,000 today, the present value would be Rs.10,000 because present value is what your investment gives you if you were to spend it today. If you received Rs.10,000 in a year, the present value of the amount would not be Rs.10,000 because you do not have it in your hand now, in the present. To find the present value of the Rs.10,000 you will receive in the future, you need to pretend that the Rs.10,000 is the total future value of an amount that you invested today. In other words, to find the present value of the future Rs.10,000, we need to find out how much we would have to invest today in order to receive that Rs.10,000 in the future.

The Present Value formula has a broad range of uses and may be applied to various areas of finance including corporate finance, banking finance, and investment finance. Apart from the various areas of finance that present value analysis is used, the formula is also used as a component of other financial formulas.

PV =    FV x {1/(1+r)ⁿ }         or        PV = FV (1+r)^-n

FV = PV (1+r)ⁿ

1. Example of Present Value Formula:

An individual wish to determine how much money she would need to put into her money market account to have Rs.1000 for two years from today if she is earning 5% simple interest on her account.

The Rs.1000 she would like two years from present day denotes the FV portion of the formula, 5% would be r, and the number of periods would simply be 2.

Putting this into the formula, we would have

PV = 1000 (1+.05)^-2

PV = 907.03

When we solve for PV, she would need Rs. 907.03 today in order to reach Rs.1000 two years from now at a rate of 5% interest.

2. Example:

Let’s add a little spice to our investment knowledge. Suppose that you have to receive Rs. 15000 from a person. You have two options, either get Rs. 15000 today or get Rs. 18000 in four years. Which would you choose? The decision is now more difficult. You should find the future value of Rs.15,000, but since we are always living in the present, let’s find the present value of Rs.18,000 if interest rates are currently 4%. Remember that the equation for present value is the following: 

           PV = FV (1+r)^-n

In the equation above, all we are doing is discounting the future value of an investment. Using the numbers above, the present value of an Rs.18,000 payment @4% in four years would be calculated as the following:

           Present Value = 18000 (1+.04)^-4

                Present Value = Rs.

From the above calculation we now know our choice is between receiving Rs.15, 000 or Rs.15, 386.48 today. Of course we should choose to postpone payment for four years! 

Financial management is concerned with the values of assets today; i.e. present values. Since capital projects provide benefits in to the future and since we want to determine the present value of the project, we will discount the future cash flows of a project to the present.

Present values are calculated by referring to tables or we can use calculators and spreadsheets for discounting. The discount rate we will use is the opportunity costs of the

Investment; i.e. the rate of return we require on any other project with similar risks. 

Present Value Annuity of Rs. 1.00, year = n, rate = k
Year (n)	K = 8%	K = 9%	k = 10%	k = 11%	k = 12%
1	0.926	0.917	0.909	0.901	0.893
2	1.783	1.759	1.736	1.713	1.690
3	2.577	2.531	2.487	2.444	2.402
4	3.312	3.240	3.170	3.102	3.037
5	3.993	3.890	3.791	3.696	3.605

3. Example:

 Calculate the Present Value of Cash Flows.

You will receive Rs. 500 at the end of next year. If you could invest Rs. 500 today, you estimate that you could earn 12%. What is the Present Value of this future cash inflow?

Rs. 500 x .893 (Present value table) = Rs. 446.50

If we were to receive the same cash flows year after year into the future, then we could use the present value tables for an annuity. 

4. Example:

Calculate the Present Value of Annuity Type Cash Flows

You will receive Rs. 500 each year for the next five years. Your opportunity cost for this investment is 10%. What is the present value of this investment?

Rs. 500 x 3.791 (Present Value Annuity) = Rs. 1,895.50

NET PRESENT VALUE (NPV)

The Net Present Value (NPV) is the total net present value of the project. It represents the total value added or subtracted from the organization if we invest in this project. The net present value is one of the discounted cash flow or time-adjusted techniques. It recognizes that cash flow streams at different time period differs in value and can be computed only when they are expressed in terms of common denominator i.e. present value.

The NPV is the difference between the present value of future cash inflows and the present value of the initial outlay, discounted at the firm’s cost of capital. The procedure for determining the present values consists of two stages. The first stage involves determination of an appropriate discount rate. With the discount rate so selected, the cash flow streams are converted into present values in the second stage.

 Method to compute NPV

The important steps for calculating NPV are given below.

1. Cash flows of the investment project should be forecasted based on realistic assumptions. These cash flows are the incremental cash inflow after taxes and are inclusive of depreciation (CFAT) which is assumed to be received at the end of each year. CFAT should take into account salvage value and working capital released at the end.
2. Appropriate discount rate should be identified to discount the forecasted cash flows. The appropriate discount rate is the firm’s opportunity cost of capital which is equal to the required rate of return expected by investors on investments of equivalent risk.
3. Present value (PV) of cash flows should be calculated using opportunity cost of capital as the discount rate.
4. NPV should be found out by subtracting present value of cash outflows from present value of cash inflows. The project should be accepted if NPV is positive (i.e. NPV >0)
5. The NPV can be calculated with the help of equation.

NPV = Present value of cash inflows – Initial investment

                     A₁                   A₂                               A_n                            A

W =           ———- + ————– + …… + ————-  –  C =  ∑ ——–  – C

                   (1+K)¹        (1+K)²                            (1+K)ⁿ                    (1+K)ⁿ

Where,

A₁, A₂ represent the stream of benefits expected to occur if a course of action is adopted,

C is the cost of that action &

K is the appropriate discount rate to measure the quality of A’s.

W is the NPV or, wealth which is the difference between the present worth of the stream of benefits and the initial cost.

Decision Rule: The present value method can be used as an accept-reject criterion. The present value of the future cash streams or inflows would be compared with present value of outlays. The present value outlays are the same as the initial investment.

• If the NPV is greater than 0, accept the project.
• If the NPV is less than 0, reject the project.

11. Example:

Assuming that the cost of capital is 8% for a project involving a lumpsum cash outflow of Rs.7,500 and cash inflow of Rs.2,000 per annum for 5 years, the Net Present Value calculations are as follows:

1. a) Present value of cash outflows Rs.7500
2. b) Present value of cash inflows

Present value of an annuity of Rs. 1 at 8% for 5 years = 3.993

Present value of Rs.2000 annuity for 5 years = 3.993 X 2000 = Rs. 7986

1. c) Net present value = present value of cash inflows – present value of cash flows

   NPV = 7986 – 7500 = Rs. 486

Since the net present value of the project is positive (Rs.486), the Project is accepted. .

12. Example:

Calculate NPV for a Project X initially costing Rs. 250000. It has 10% cost of capital. It generates five years cash flows Rs. 90000, 80000, 70000, 60000, 50000 respectively:

Year	Year Cash flows	PVF @ 10%	PV
1	90000	.909	81810
2	80000	.826	66080
3	70000	.751	52570
4	60000	.683	40980
5	50000	.621	31050
		ΣPV	272490
		Initial Costing Rs.	250000
		NPV Rs.	22490

Here the NPV is positive with expected cost of capital, it means project can be accepted.

13. Example:

A company is considering an investment proposal to install new machine. The project will cost Rs. 50000. The machine has a life expectancy of 5 years and no salvage value. The company tax rate is 35%. The firm uses straight line depreciation. The estimated profit before tax from the proposed investment proposal are Rs. 10000, Rs. 11000, Rs. 14000, Rs. 15000 and Rs. 25000 from the end of first year to end of fifth year. Calculate the NPV @10% discount rate.

Solution

          Initial Outflow = Rs. 50000, Discount Rate = 10%   

          Life of machine 5 years, then annual depreciation will be Rs. 10000

S. No.	Profit	Dep.	PBT	Tax @35%	PAT	Dep.	Cash Flow (CF)	PVF @10%	PV
1	10000	10000	—	—	—	10000	10000	.909	9090
2	11000	10000	1000	350	650	10000	10650	.826	8797
3	14000	10000	4000	1400	2600	10000	12600	.751	9463
4	15000	10000	5000	1750	3250	10000	13250	.683	9050
5	25000	10000	15000	5250	9750	10000	19750	.621	12265
							ΣPV		48665
							Initial Costing Rs.		50000
							NPV Rs.		-1335

Here, the NPV is negative with expected cost of capital, it means project can be rejected.

Expected Net Present Value

Once the probability assignments have been made to the future cash flows, the next step is to find out the expected net present value. It can be found out by multiplying the monetary values of the possible events by their probabilities. The following equation describes the expected net present value.

ENPV= ∑ ENCF_t / (1+k)^t

Where ENPV is the expected net present value, ENCF_t expected net cash flows in period t and k are the discount rate. The expected net cash flow can be calculated as follows:

 ENCFT = NCF_jt X P_jt

Where NCF_jt is net cash flow for j^th event in period t and P_jt probability of net cash flow for j^th event in period t.

14. Example:

A company is considering an investment proposal costing Rs. 7,000 and has an estimated life of three years. The possible cash flows are given below:

 Expected Net Present Value

Cash Flow	Prob.	Expected Value	Cash Flow	Prob.	Expected Value	Cash Flow	Prob.	Expected Value
2000	0.2	400	3000	0.4	1200	4000	0.3	1200
3000	0.5	1500	4000	0.3	1200	5000	0.5	2500
4000	0.3	1200	5000	0.3	1500	6000	0.2	1200
		3100			3900			4900

 If we assume a risk-free discount rate of 10%, the expected NPV for the project will be as follows.

Year	ENCF	PV@10%	PV
1	3100	.909	2817.9
2	3900	.826	3221.4
3	4900	.751	3679.9
		ΣPV	9719.2
		Initial Costing Rs.	7000
		NPV Rs.	2719.2

Decision Tree Approach: Sometimes cash flow is estimated under different managerial options with the help of decision tree approach. A decision tree is a graphic presentation of the present decision with future events and decisions. The sequence of events is shown in a format that resembles the branches of a tree.