Corporate Finance Guide: PV, NPV, IRR, and ARR with Excel Examples & Calculations

Corporate Finance Guide: PV, NPV, IRR, and ARR with Excel Examples & Calculations

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1. Present Value (PV)

Present Value (PV) is the current value of a future sum of money or cash flows, discounted at a given rate of return.

Formula:

$$PV = \frac{FV}{(1 + r)^n}$$

Where:

• FV = Future Value
• r = Discount Rate (or interest rate)
• n = Number of periods

Example Calculation in Excel:

Suppose a company expects to receive $10,000 in 5 years, and the discount rate is 8%.
Excel formula:

=PV(8%, 5, 0, 10000)
  

This will return the Present Value of $6,805.83.

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2. Net Present Value (NPV)

Net Present Value (NPV) is the sum of the present values of cash inflows and outflows over time. It helps in investment decision-making—whether a project is profitable.

Formula:

$$NPV = \sum \frac{C_t}{(1+r)^t} - C_0$$

Where:

• C_t = Cash inflow at time t
• r = Discount rate
• t = Time period
• C_0 = Initial investment

Company Example: Tesla

Tesla is considering an investment in a new EV battery factory requiring an initial investment of $100 million. The expected cash flows over the next 5 years are:

Year	Cash Flow ($ million)
1	30
2	35
3	40
4	45
5	50

Assume the discount rate is 10%.

Excel Calculation:

Formula in Excel:

=NPV(10%, 30, 35, 40, 45, 50) - 100
  

If NPV is positive, Tesla should invest; if negative, it should not.

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3. Internal Rate of Return (IRR)

IRR is the discount rate that makes NPV = 0. It represents the expected rate of return for a project.

Formula:

IRR is calculated by solving for r in:

$$NPV = \sum \frac{C_t}{(1+r)^t} - C_0 = 0$$

Company Example: Apple

Apple is considering launching a new iPhone model and expects the following cash flows:

Year	Cash Flow ($ million)
0	-200
1	60
2	70
3	90
4	100

Excel Calculation:

Formula in Excel:

=IRR(-200, 60, 70, 90, 100)
  

If the IRR is higher than Apple's cost of capital, the investment is worth pursuing.

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4. Accounting Rate of Return (ARR)

ARR is the ratio of the average annual accounting profit to the initial investment. It does not consider the time value of money.

Formula:

$$ARR = \frac{\text{Average Annual Accounting Profit}}{\text{Initial Investment}} \times 100$$

Company Example: Amazon

Amazon is investing in a warehouse automation system with an initial investment of $50 million. The expected annual accounting profits for the next 4 years are:

Year	Accounting Profit ($ million)
1	10
2	12
3	14
4	16

Calculation in Excel:

Find Average Profit:

=(10+12+14+16)/4
  

Result: $13 million

ARR Calculation:

=(13/50) * 100
  

Result: 26% ARR

If ARR is higher than Amazon's required return, the investment is considered favorable.

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Summary of Excel Formulas

Metric	Excel Formula Example
PV	=PV(8%, 5, 0, 10000)
NPV	=NPV(10%, 30, 35, 40, 45, 50) - 100
IRR	=IRR(-200, 60, 70, 90, 100)
ARR	=(AVERAGE(10,12,14,16)/50)*100