Question

Sure Tea Co. has issued 6.3% annual coupon bonds that are now selling at a yield to maturity of 9.20% and current yield of 8.777%. What is the remaining maturity of these bonds? (Do not round intermediate calculations. Round your answer to the nearest whole number.)

Answer 1

Answer:

Ans. 26 years is the remaining maturity of this bond.

Explanation:

Hi, we have to find the price of the bond, so we use the following formula.

$CurrentYield=\frac{Coupon}{Price}$

This means that:

$Price=\frac{Coupon}{CurrentYield} =\frac{63}{0.08777} =717.79$

Let´s not forget that the Coupon is calculated by the following formula.

$Coupon=FaceValue*CouponRate=1,000*0.063$

Now that we found that the price of the bond is $717.79, we have to bring to present value the remaining coupons and the principal that is paid at the end, so we have to solve for "n" the following equation, discounted at the yield to maturity.

$Price=\frac{Coupon((1+YTM)^{n}-1) }{YTM(1+YTM)^{n} } +\frac{FaceValue}{(1+YTM)^{n} }$

Let´s fill up what we can

$717,79 =\frac{63((1+0.092)^{n}-1) }{0.092(1+0.092)^{n} } +\frac{1,000}{(1+0.092)^{n} }$

But to solve for "n" is pretty painful, so we can use a financial calcultator o MS Excel. Please find the MS Excel sheet that I used with the "Seek Goal" formula instruccions as follow.

Set Cell: $C$19

To Value: 717,79

By Changing cell: $C$14

So the answer is 26

Best of luck.

Download xlsx