Question 1

Why is the discount rate different from the interest rate?

Accepted Answer

While both are expressed as percentages, they move in opposite directions in time. An interest rate is used to compound money forward into the future, determining how much a present sum will grow. A discount rate is used to bring future money backward into the present, determining how much a future sum is worth today. Furthermore, a discount rate is often a theoretical construct that includes opportunity cost and risk premiums, whereas an interest rate is usually a stated, contractual figure provided by a bank or lender.

Question 2

How does compounding frequency affect present value?

Accepted Answer

Compounding frequency dictates how often the discount is applied within a given year. The more frequently cash flows are compounded (or discounted), the greater the impact of the rate. If you are discounting a future sum, a higher compounding frequency (like daily or monthly instead of annually) will result in a slightly lower present value. This is because the math accounts for the interest-on-interest effect occurring more frequently throughout the year, meaning you need even less money today to reach the target future value.

Question 3

Can present value ever be negative?

Accepted Answer

The present value of a positive future cash flow cannot be negative as long as the discount rate is positive. However, if the future cash flow itself is a liability or an outflow (such as a future debt payment or a required maintenance expense), its present value will be negative. In Net Present Value (NPV) calculations, the final result can easily be negative if the present value of the future cash inflows is smaller than the initial upfront cost of the investment.

Question 4

What is the difference between nominal and real discount rates?

Accepted Answer

A nominal discount rate is the stated rate that does not account for the effects of inflation. A real discount rate has been explicitly adjusted to remove the impact of inflation. The critical rule in present value calculations is consistency: if your future cash flow estimates are nominal (they include expected inflation in their pricing), you must use a nominal discount rate. If your future cash flows are in "real" dollars (stripped of inflation), you must use a real discount rate. Mixing the two will severely distort your valuation.

Question 5

Why do bond prices fall when interest rates rise?

Accepted Answer

This is the purest real-world demonstration of present value. A bond promises a fixed stream of future cash flows (coupon payments and principal). When prevailing market interest rates rise, the discount rate used by investors to value those fixed future cash flows also rises. Because the discount rate is in the denominator of the present value formula, a larger denominator mathematically results in a smaller present value. Therefore, the current price (present value) of the existing bond must fall to offer new buyers a competitive yield.

Question 6

How do I choose the right discount rate for a personal financial decision?

Accepted Answer

For personal decisions, your discount rate should represent your personal opportunity cost of capital. Look at your next best, realistically available investment alternative. If you are deciding whether to pay off a 4% mortgage early or invest the money, and you are confident you can earn a 7% long-term return in a diversified index fund, your personal discount rate is 7%. You would use 7% to discount the future saved mortgage payments to see if paying the loan off early makes mathematical sense compared to investing.

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