The Difference Between Net Present Value and Internal Rate of Return

NPV, or Net Present Value, takes into account the net amount of cash inflows and outflows and discounts them to the present moment using a certain discount rate, thereby reflecting the true economic value of a project. On the other hand, IRR, or Internal Rate of Return, represents the actual expected rate of return on a project investment. It is the specific discount rate that makes the project's NPV equal to zero.

How to Define Net Present Value

When using NPV for investment decisions, we first need to clarify what cash flow is. In the context of investment decisions, cash flow refers to the changes in a company's cash inflows and outflows caused by a project. It specifically encompasses three core concepts: cash outflows, cash inflows, and net cash flows. Within the framework of capital budgeting, we usually focus on net cash flows.

From a theoretical perspective, the cash flow used for capital budgeting is defined as the after-tax incremental cash flow from debt and equity financing. This definition emphasizes three key points: First, the independence between investment decisions and financing decisions, meaning that the determination of cash flows is not affected by the company's financing methods. Second, the after-tax nature of cash flows ensures their true economic value. Third, the incremental cash flows of the enterprise after the project is put into operation, rather than the cash flows of a single project. This approach eliminates the potential competitive impact of a new project's launch on existing projects. According to this definition, the formula for calculating cash flow is: increased sales revenue minus increased cash operating costs, and then minus increased taxes.

NPV Analysis of Financing Lease vs. Purchase Decision: Taking A Company's Equipment Purchase as an Example

Although financing leases offer many advantages, when enterprises face equipment needs, they still need to conduct in-depth research and analysis to decide whether to lease or purchase. It cannot be simply assumed that financing leases are always superior to purchases. When evaluating the decision between financing leases and purchases, various methods can be employed, such as the NPV method, the optimal debt level method, and the APV method. Among them, the NPV method is highly favored for its simplicity and ease of operation.

The NPV method, or Net Present Value method, focuses on comparing the net present value of expected cash flows when purchasing machinery and equipment with that when leasing machinery and equipment.

Take A Company as an example. Suppose it needs a machine worth $1 million, with a useful life of 5 years and no residual value. If it chooses a financing lease, it needs to pay an annual rent of $250,000. The income tax rate is 25%, and the internal rate of return is 8%. So, how should A Company make the decision between leasing and purchasing?

Purchase:

Lease:

Annual depreciation amount = 100 / 5 = $200,000 Financing cost allocation rate = 1 / 5 = 0.2 NPV of lease minus purchase = 100 - 23.75 × P/A(8%, 5) = 100 - 23.75 × 3.992 = $51,900. Clearly, in this case, it is better for the enterprise to choose leasing over self-purchase.

Calculation of the Internal Rate of Return for Financing Leases

The internal rate of return of a lease, as the internal rate of return of a financing plan, plays a central role in financing decisions. Through practical calculation and comparative analysis, we find that using the IRR function in Excel to calculate this indicator is not only simple but also accurate, significantly reducing the workload of financial personnel and improving work efficiency.

When the rent payment intervals in a financing plan are uneven but follow a pattern, for example, when the interval of the longer period is a multiple of the interval of the shorter period, when using the IRR function method, we should list the cash flow statement with the shortest interval as one interest period. For instance, a certain university adopts the sale-and-leaseback method for financing, with a financing period of 2 years and rent paid in 5 installments. The rent payment intervals are not completely the same but follow a pattern. In this case, we take the shortest interval of 3 months as one interest period, with a total of 8 periods. After listing the cash flow situation during the lease term, we use the IRR function to calculate the actual interest rate during the interest period and then obtain the annual rate of return.

If the rent payment intervals in a financing plan are uneven and follow no discernible pattern, when using the IRR function method, we should list the cash flow statement with the greatest common divisor of all intervals as one interest period.

Example: A certain university adopts the sale-and-leaseback method for financing. Suppose it finances $10 million and receives the full amount on July 1, 2015. The financing period is 2 years, and rent is paid in 5 installments. It pays $2.5 million at the end of September 2015 and December 2015 respectively, and $2.1 million at the end of June 2016, December 2016, and June 2017 respectively. Calculate the internal rate of return (IRR) of this financing lease.

First, since the rent payment intervals are not completely the same, when using the IRR function method, we take the shortest interval of 3 months as one interest period, with a total of 8 periods. Second, list the cash flow situation during the lease term in an Excel table, as shown in Table 1. Then, use the IRR function to calculate the actual interest rate during the interest period. The actual interest rate r for the 3-month interest period is 3.18%. Finally, the annual rate of return I = (1 + 3.18%)^4 - 1 = 13.33%.

If the rent payment intervals in a financing plan are uneven and follow no discernible pattern, when using the IRR function method, we should list the cash flow statement with the greatest common divisor of all intervals as one interest period.

Example: A certain university adopts the sale-and-leaseback method for financing. Suppose it finances $10 million and receives the full amount on May 20, 2015. The financing period is 2 years, and rent is paid in 5 installments. It pays $2.5 million on September 20, 2015, and March 20, 2016 respectively, and $2.1 million on September 20, 2016, January 20, 2017, and May 20, 2017 respectively. Calculate the internal rate of return (IRR) of this financing lease.

First, since the rent payment intervals are not completely the same and follow no pattern, with intervals of 4 months and 6 months, when using the IRR function method, we take 2 months as one interest period, with a total of 12 periods. Second, as in the previous example, list the cash flow situation during the lease term in an Excel table, as shown in Table 2. Then, use the IRR function to calculate the actual interest rate during the interest period. The actual interest rate r for the 2-month interest period is 1.76%. Finally, the annual rate of return R = (1 + 1.76%)^6 - 1 = 11.03%.