Solve the equation by completing the square. Round to the nearest hundredth if necessary.
1 answer:
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Answer:
The current yield of the bond is 2.5%.
Step-by-step explanation:
To calculate the current yield of a bond we need two things. The current trading price of the bond and the annual interest i.e. the coupon yield.
In the given question, the current trading price of the bond is $400 and the annual coupon yield is 2% i.e. $10.
Therefore, the current yield is : = 2.5%.
It would be very important also to learn why a bond that is of nominal value of $500, is selling at $400.
The annal coupon interest rate of the bond is 2% , therefore, it pays $10 annually as interest. If the interest rate prevailing in the market is higher than 2%, in that case the bond's price would come lower. The reason for this decrease in price is that the investors, the one who purchase the bond, are expecting to earn the market rate of interest when they invest in a bond but in this case they are only getting a lower interest rate of 2%.
This is the reason why the bond is priced lower so as to be able to give the invetors a higher yield which is equal to the market interest rate.
Using this information, we can also calculate the market interset rate. But we don't know the number of years the bond is issued for which is needed to calculate the market interest rate. So, let's assume the bond is issued for a period of 5 years after which it is redeemed and the nominal amount of $500 is paid back to the investor.
The investor therefore, is expecting to get $10 every year as interest for a period of 5 years and at the end of the 5th year the investor is also expecting to get $500 redeemed.
The investor will discount all these amounts at the market interest rate to calculate the present value of the bond and that present value is what the investor would be willing to pay.
We already know that we need the present value to come out to be $400 because that is the current trading price in the market, so we can take the market interest rate that is only a little bit higher than the coupon rate so that we get an amount that is higher than the present value of $400. Secondly, we will do the calculation again with a discount factor that is much higher than the coupon to get a value lower than the present value of $400.
After getting the lower and higher value, we can use the interpolation technique to get the exact market interest rate.
The present value calcuation at 3% interest rate and 7% interest rate are shown in the attached picture number 1. We get a present value of 477.1 and 397.5 respectively. Now, we can use this information to interpolate and get the exact market intereset rate.
The calculation of market interest rate is as follows :
= Lower interest rate +
= 3% +
= 3% +
= 3% + 3.9%
= 6.9%
The market interest rate therefore, for a bond of nominal value $500, with coupon rate of 2%, trading at $400 would be 6.9%
