# Understanding Discount Rate, Present Value and Net Present Value

February 26, 2023
CoStar Real Estate Manager Blog

# Understanding Discount Rate, Present Value and Net Present Value

#### The internet’s most simple explanations of discount rate, present value and net present value as they apply to ASC 842 lease accounting.

###### First things first, What is a discount rate?
• A discount rate is an interest rate.
• The term “interest rate” is used when referring to a present value of money and its future growth.
• The term “discount rate” is used when looking at an amount of money to be received in the future and calculating its present value.
• The word “discount” means “to deduct an amount.”
• A discount rate is deducted from a future value of money to provide its present value.

The below scenario clearly explains the terms “discount rate,” “present value,” and “net present value.”

###### The Situation

Bob wants to become an entrepreneur. His father, an accountant named Stan, wants Bob to first know the value of money today ― otherwise known as the present value ― and be able to calculate its future value. “Future value” refers to an amount of money that is expected to arrive at a predetermined time in the future. Stan also wants his son to be able to calculate the present value of money that is scheduled to arrive in the future. For that reason, Bob will need these skills to manage his company’s finances.

###### The Choice

Bob purchased some goods for Stan that cost exactly \$100. In the family room at home, Stan tells his son, “I’ve got an offer for you. I can either pay you back \$100 today or I can pay you \$110 one year from today. Which would you prefer?”

Bob pulls out his mobile phone, looks online and sees that a bank is offering a guaranteed 5% annual interest rate on money invested today.

Bob gets up and says, “Let me figure this out and return with an answer.”

Presently, it may seem as if the difference between the two offers is negligible. But Stan wants Bob to be able to make decisions like this involving leases and payment terms for products and services that may cost thousands of times more than \$110.

###### Present Value

Bob now knows the present value of the first offer. Clearly the present value of \$100 is \$100. He also knows that he can get 5% annual interest from the bank. But Bob doesn’t know the future value, the amount \$100 will be valued at a year from today.

Bob knows the future value of the second offer is \$110. That’s the amount he could receive a year from today. But he doesn’t know the present value of \$110. He needs to know the present value of \$110 calculated at a 5% discount rate to see if it is valued more or less than \$100.

Bob must know the present values and future values, and use the same interest rate, or discount rate, to calculate the worth of both offers to make an apples-to-apple comparison.

###### Offer One

First, let’s look at the formula for investing \$100 today with a guaranteed interest rate of 5% to be returned one year from today.

Here’s the one-year formula: (Present Value, which is the money Bob could receive today) x (1+the interest rate)

\$100 x (1 + .05)

\$100 x 1.05 = \$105 (the future value)

The above formula shows that if Bob invests \$100 today at a 5% annual interest rate, one year from today he’ll have a future value of \$105. He now knows all three variables for the first equation: the present value, the future value and the interest rate.

Present Value = \$100
Interest or Discount Rate = 5%
Future Value = \$105

##### Offer Two

In offer one, Bob was solving for the future value, the amount he’ll have in a year, which he now knows is \$105. For offer two, Bob must correspondingly solve for the present value of \$110. He’s looking at a future value, \$110, and going back in time to today, which means instead of adding an interest rate, he must deduct a discount rate. Bob must use the same rate he used in the first scenario to make an apples-to-apples comparison of the two offers.

In the first equation, to solve for the future value Bob multiplied to add that interest rate. Multiplication is a form of repeated addition. In this next equation to solve for the present value, he’ll divide to subtract the discount rate. Division similarly is a form of repeated subtraction.

Here’s the one-year formula: (Future Value) divided by (1+the discount rate)

\$110 / (1 + .05)

\$110 / 1.05 = \$104.76 (the present value)

Present Value = \$104.76
Interest or Discount Rate = 5%
Future Value = \$110

The above calculations show that receiving \$110 one year from today, using a 5% discount rate, is presently valued at \$104.76. If Bob wanted to reverse the calculation he just did to solve for the one-year future value of \$104.76, he’d need to do the same formula that he did for the first offer.

Again, here’s the formula: (Present Value, which is the value of money in-hand today) x (1+the interest rate)

\$104.76 x (1 + .05)

\$104.76 x 1.05 = \$109.99 (in other words, \$110)

##### The Comparison

With the below side-by-side comparison, Bob can easily see which deal is the best.

Offer 1 - Present Value = \$100
Interest or Discount Rate = 5%
Future Value = \$105

Offer 2 - Present Value = \$104.76, Future Value = \$110

##### The Meeting

Then, Bob rushes back to the family room.

“Dad,” he says, “I’ll take the \$110 a year from now.”

His father replies, “Good move. There’s just one more thing I want you to know.”

##### Net Present Value

“In business you will have numerous contracts for loans, leases, products and services,” says Stan. “Each contract will have a stream of upcoming payments due, usually scheduled monthly payments. In short, you’ll need to be able to figure out the present value for each of them. Then, for each contract, you’ll need to add all its upcoming scheduled present value payments. The sum of those present values is called the net present value. Markedly, each outstanding contract will have its own net present value.”

Lastly, find the present value or future value of an amount for any timeframe other than one year.

##### CoStar Real Estate Manager

CoStar Real Estate Manager is here to make every element of your lease accounting process easier. Especially when it comes to the detailed definitions, complex nuances and equally complex compliance regulations. Reach out today to work with an industry leader who will be there for any explanations you may need.

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