An increase in interest rates will generally lower the...

An increase in interest rates will generally lower the prices of assets. To see this, calculate the present value of the following two assets at interest rates of 5 percent, 10 percent, and 20 percent per year: a. A perpetuity yielding $\$ 100$ per year b. A Christmas tree that will sell for $\$ 50$ one year from now Explain why the price of the long-lived asset is more sensitive to interest-rate changes than the price of the short-lived asset.

An increase in interest rates will generally lower the prices of assets. To see this, calculate the present value of the following two assets at interest rates of 5 percent,
10 percent, and 20 percent per year:
a. A perpetuity yielding $\$ 100$ per year
b. A Christmas tree that will sell for $\$ 50$ one year from now Explain why the price of the long-lived asset is more sensitive to interest-rate changes than the price of the short-lived asset.

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Key Concepts

Present Value

Present value is the current worth of a future stream of cash flows discounted at a chosen interest rate. It is a fundamental concept in finance because it allows investors to determine how much a future payment or series of payments is worth today, reflecting the time value of money.

Interest Rate Sensitivity

Interest rate sensitivity refers to the degree to which the present value of an asset changes in response to changes in the discount rate. Assets with cash flows that extend further into the future exhibit greater sensitivity because a small change in the rate has a more pronounced effect when discounting distant cash flows.

Time Value of Money

The time value of money is the principle that a sum of money today is worth more than the same sum in the future due to its earning potential. This concept is key to understanding why future cash flows are discounted to determine their present value, and why assets with longer time horizons are more affected by changes in interest rates.

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