How to Calculate The Nominl and Real Dp

Discount points (DP) are a common pricing mechanism in finance, particularly in mortgage lending. They represent the difference between the interest rate on a loan and the rate charged to the lender. Understanding how to calculate both nominal and real discount points is essential for financial analysis and decision-making.

What Are Discount Points?

Discount points are an additional fee charged to borrowers to reduce the interest rate on a loan. They are typically expressed as a percentage of the loan amount and are paid upfront at the time of loan origination.

For example, if a mortgage loan has a base interest rate of 5% and the borrower pays 1 discount point, the effective interest rate becomes 4%. The discount point is usually 0.25% to 1% of the loan amount.

Discount points should not be confused with origination fees, which are flat fees charged for processing the loan application.

Nominal vs. Real DP

There are two main types of discount points: nominal and real.

Nominal Discount Points

Nominal discount points are calculated based on the original loan amount. They represent the absolute reduction in the interest rate.

Real Discount Points

Real discount points, also known as effective discount points, are calculated based on the present value of the loan payments. They account for the time value of money and provide a more accurate measure of the true cost of the discount points.

Nominal DP = (DP Rate × Loan Amount) / Loan Amount Real DP = (DP Rate × Loan Amount) / PV of Loan Payments

Calculating Nominal DP

To calculate nominal discount points, follow these steps:

Determine the discount point rate (e.g., 1 point = 1% of the loan amount).
Multiply the discount point rate by the loan amount to find the total discount points.
Divide the total discount points by the loan amount to get the nominal discount point rate.

Nominal DP = (DP Rate × Loan Amount) / Loan Amount

For example, if a $200,000 loan has a 1-point discount, the nominal DP is 1% of $200,000, which is $2,000.

Calculating Real DP

Calculating real discount points requires more complex calculations, as it involves the present value of the loan payments. Here's how to do it:

Calculate the monthly payment using the loan amount, interest rate, and loan term.
Calculate the present value of the loan payments using the monthly payment and the discount rate.
Divide the total discount points by the present value of the loan payments to get the real discount point rate.

Real DP = (DP Rate × Loan Amount) / PV of Loan Payments

The real discount point rate will typically be higher than the nominal rate because it accounts for the time value of money.

Example Calculation

Let's calculate both nominal and real discount points for a $200,000 loan with a 1-point discount, a 5% interest rate, and a 30-year term.

Nominal DP Calculation

Nominal DP = (1 point × $200,000) / $200,000 = 1%

Real DP Calculation

First, calculate the monthly payment:

Monthly Payment = P × [r(1+r)^n] / [(1+r)^n - 1] Where: P = $200,000 r = 5%/12 = 0.004167 n = 30 years × 12 = 360

Monthly Payment ≈ $1,073.64

Next, calculate the present value of the loan payments:

PV = PMT × [(1 - (1 + r)^-n) / r] Where: PMT = $1,073.64 r = 5%/12 = 0.004167 n = 360

PV ≈ $199,999.99 (approximately equal to the loan amount)

Finally, calculate the real DP:

Real DP = (1 point × $200,000) / $200,000 = 1%

In this example, the nominal and real discount points are the same because the present value of the loan payments is approximately equal to the loan amount. However, in most cases, the real discount point rate will be higher.

FAQ

What is the difference between nominal and real discount points?: Nominal discount points are calculated based on the original loan amount, while real discount points account for the time value of money by using the present value of the loan payments.
Why are discount points charged to borrowers?: Discount points are charged to borrowers to reduce the interest rate on the loan, making the loan more affordable. They are typically used to offset the cost of the loan to the lender.
How do discount points affect the loan payment?: Discount points reduce the interest rate on the loan, which in turn reduces the total interest paid over the life of the loan and lowers the monthly payment.
Are discount points tax deductible?: In many countries, including the US, discount points are not tax deductible as they are considered a prepayment penalty.
Can discount points be negotiated?: Yes, discount points can often be negotiated with the lender, especially if the borrower has a strong credit profile or is willing to pay a higher interest rate.