Question

What is the difference between discounted present value and net present value?  

What is the NPV of the following cash flows, assuming a 6% discount rate?

Initial investment – year 0: $(1,000,000)

Year 1 cash flows: $100,000

Year 2 cash flows: $100,000
Year 3 cash flows: $100,000

Year 4 -sale: $1,200,000

Answer 1

Part 1)

In case of discounted present value, the cash flows are discounted to the current/present date and no adjustment is made with respect to the initial capital outlay/investment. In other words, discounted present value is merely a sum total of cash flows (discounted to today's value) occuring in the future. Net present value, on the other hand, is arrived at by deducting the initial investment/capital outlay from the present value of discounted cash flows. The following example indicates the difference between the two terms:

Let us assume that a company undertakes a project which is expected to generate a cash flow of $2,000 for next 5 years. The company uses a discount rate of 10% to determine the present value of cash flows. The initial investment associated with the project is $7,000.

The formulas for calculating discounted present value and net present value are given as below:

Discounted Present Value = Cash Flow Year 1/(1+Discount Rate)^1 + Cash Flow Year 2/(1+Discount Rate)^2 + Cash Flow Year 3/(1+Discount Rate)^3 + Cash Flow Year 4/(1+Discount Rate)^4 +Cash Flow Year 5/(1+Discount Rate)^5 = 2,000/(1+10%)^1 + 2,000/(1+10%)^2 + 2,000/(1+10%)^3 + 2,000/(1+10%)^4 + 2,000/(1+10%)^5 = $7,581.57

Net Present Value = Discounted Present Value - Initial Investment = 7,581.57 - 7,000 = $581.57

_____

Part 2)

NPV is calculated with the use of following formula:

NPV = -Cash Flow Year 0 + Cash Flow Year 1/(1+Discount Rate) + Cash Flow Year 2/(1+Discount Rate)^2 + Cash Flow Year 3/(1+Discount Rate)^3 + Cash Flow Year 4/(1+Discount Rate)4

Using the values provided in the question in the above formula, we get,

NPV = -1,000,000 + 100,000/(1+6%)^1 + 100,000/(1+6%)^2 + 100,000/(1+6%)^3 + 1,200,000/(1+6%)^4 = $217,813.59