Question

what is the approximate market value of a bond that pays $190 interest each year if comparable interest rates have dropped to 5 percent?

Answer 1

If comparable interest rates have dropped to 5 percent, one would expect to pay more than the $10,000 face value for a bond that pays $190 interest each year, because its yield is higher than the market rate. The exact value would require discounting the bond's future cash flows at the current market rate to calculate its present value. Conversely, if market rates rise above the bond's coupon rate, the bond's price would decrease to attract investors.

Step-by-step explanation:

The approximate market value of a bond that pays $190 interest each year when comparable interest rates have dropped to 5 percent would be more than its face value since the coupon rate of the bond (interest payment) is higher than the current market interest rate. Investors would be willing to pay a premium for a bond that offers a higher return than what is currently available in the market. To calculate the exact value, you would need to discount the bond's future cash flows (interest payments and the principal repayment at maturity) using the current market interest rate of 5 percent.

Given that comparable interest rates have dropped to 5 percent, the price of the bond would generally rise, because its fixed interest payments are more attractive compared to new bonds that would be issued at the current lower rate. Therefore, you would expect to pay more than $10,000 for the bond.

In another scenario, consider a bond with one year left to maturity that was originally issued with an 8% coupon rate. If current market interest rates rise to 12%, the bond becomes less attractive, leading to its price dropping below the face value, to compensate the investor for the lower interest rate compared to the current 12%. For example, if one could invest $964 at a 12% return to receive $1,080 after a year, then one would not pay more than $964 for a bond with future payments totaling $1,080, as the bond's interest rate is less than the market interest rate.

Answer 2

The approximate value of a bond paying higher interest than the current market rate would be greater than its face value, meaning an investor would pay more than $1,000 for such a bond. This is based on comparing the bond's payment schedule to current market interest rates and the principle of present value, accounting for the time value of money.

Step-by-step explanation:

When the market interest rates drop, the value of existing bonds that have higher interest rates rises because they become more attractive to investors who cannot get that higher interest rate in the current market. In this case, since a bond is paying $190 interest each year, and now comparable interest rates have dropped to 5%, the bond is paying a higher return than what is currently available in the market. Therefore, investors will be willing to pay more for this bond. The reciprocal of this is that when market interest rates rise, the approximate value of existing bonds with lower interest rates declines, as less interest is earned compared to the new market rates.

To calculate the bond's future payments and to compare it to the market interest rates, you would use present value calculations and compare the resulting price to $1,000, which is typically the face value of a bond. If the bond's interest payments represent a higher percentage compared to the current 5% market interest rates, the bond's value will be higher than its face value, indicating you would expect to pay more than $1,000 for the bond.

Using the information provided where a bond's last payment is expected to be $1,080 considering the final interest payment and the repayment of the original $1,000, if the market interest rate is now 12%, you would not pay more than $964 for the bond since you could invest $964 at the 12% rate to receive $1,080 in one year. This is based on the calculation that $964(1 + 0.12) equals $1,080.