What is the difference between IRR and NPV?
What is the difference between Internal rate of return and Net present value ?
Answer:
IRR:-
Often used in capital budgeting, it's the interest rate that makes net present value of all cash flow equal zero.
The true annual rate of earnings on an investment. Equates the value of cash returns with cash invested. Considers the application of Compound Interest factors. Requires a trial-and-error method for solution. The formula is
n periodic cash flow
∑ _______________ = investment amount
t - 1 (1 + i)t
where i = internal rate of return
t = each time interval
n = total time intervals
∑ = summation
Example: Abel sells for $200,000 land that he bought 4 years earlier for $100,000. There were no Carrying Charges or Transaction Costs. The internal rate of return was about 19%. That is the annual rate at which compound interest must be paid for $100,000 to become $200,000 in 4 years.
Example: Baker received $3,000 per year for 5 years on a $10,000 investment. The internal rate of return was about 15%.
Method used to determine the Policyholder's return on premiums paid into a life insurance policy. This method is illustrated in two ways:
1. Surrender of Policy Approach-calculation of the interest rate required for the accumulated value of the total premiums paid (minus any Dividends) into the policy at a given time to equal the Cash Surrender Value of the policy at that time;
2. Death Benefit Paid Approach-calculation of the interest rate required for the accumulated value of the total premiums paid (minus any dividends) into the policy at a given time to equal the death benefit of the policy at that time.
NPV:-
Net present value or NPV is a standard method in finance of capital budgeting – the planning of long-term investments. Using the NPV method a potential investment project should be undertaken if the present value of all cash inflows minus the present value of all cash outflows (which equals the net present value) is greater than zero.
A key input into this process is the interest rate or “discount rate” which is used to discount future cash flows to their present values. If the discount rate is equal to the shareholder’s required rate of return, any NPV > 0 means that the required return has been exceeded, and the shareholders will expect an additional profit that has a present value equal to the NPV. Thus if the goal of the corporation is to maximize shareholder wealth, managers should undertake all projects that have an NPV > 0, or if two projects are mutually exclusive, they should choose the one with the highest positive NPV.
Alternative capital budgeting methods include the internal rate of return method and Modified Internal Rate of Return - which in most, but not all, cases results in the same decision as NPV - and real options methods, which attempt to value the managerial flexibilty that is assumed away in the NPV calculations.
Example:
X corporation must decide whether to introduce a new product line. The new product will have startup costs, operational costs, and incoming cash flows over six years. This project will have an immediate (t=0) cash outflow of $100,000 (which might include machinery, and employee training costs). Other cash outflows for years 1-6 are expected to be $5,000 per year. Cash inflows are expected to be $30,000 per year for years 1-6. All cash flows are after-tax, and there are no cash flows expected after year 6. The required rate of return is 10%. The present value (PV) can be calculated for each year:
T=0 -$100,000 / 1.10^0 = -$100,000 PV.
T=1 ($30,000 - $5,000)/ 1.10^1 = $22,727 PV.
T=2 ($30,000 - $5,000)/ 1.10^2 = $20,661 PV.
T=3 ($30,000 - $5,000)/ 1.10^3 = $18,783 PV.
T=4 ($30,000 - $5,000)/ 1.10^4 = $17,075 PV.
T=5 ($30,000 - $5,000)/ 1.10^5 = $15,523 PV.
T=6 ($30,000 - $5,000)/ 1.10^6 = $14,112 PV.
The sum of all these present values is the net present value, which equals $8,882. Since the NPV is greater than zero, the corporation should invest in the project.
More realistic problems would need to consider other factors, generally including the calculation of taxes, uneven cash flows, and salvage values.
Formula:
Net Present Value can thus be calculated by the following formula, where t is the amount of time (usually in years) that cash has been invested in the project, N the total length of the project (in this case, six years), i the cost of capital and C the cash flow at that point in time.
if the only cash outflow is the initial investment, then the formula may be written:
The above example is based on a constant rate being used for future interest rate predictions and works very well for small amounts of money or short time horizons. Any calculations which involve large amounts or protracted time spans will use a yield curve to give different rates for the various time points on the calculation. So, the rate for 1 year may be the 10% - the (money market) rate while the rate for 2 years may be 11% and that for 3 years 11.5%, and so on..
IRR assumes that cash re-invested in the course of the life of the project is earns at the same rate as the rest of the project. The NPV method assumes that the re-investment rate is the same as the discount rate used namely the cost of capital .
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NPV is the difference between the present value of cash inflows and the present value of cash outflows. NPV is used in capital budgeting to analyze the profitability of an investment or project.
IRR is essentially, this is the return that a company would earn if it expanded or invested in itself, rather than investing that money elsewhere.
You'll find a really good tutorial that compares the two methods below:
Here is a great online tutorial on IRR:
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