Question

Rogoff Co.'s 15-year bonds have an annual coupon rate of 9.5%. Each bond has face value of $1,000 and makes semiannual interest payments. If you require an 11.0% nominal yield to maturity on this investment, what is the maximum price you should be willing to pay for the bond?

Answer 1

Answer:

maximum sum of $891.00

Explanation:

given data    

Face Value = $1,000

Annual Coupon Rate = 9.50%

Time to Maturity = 15 years

yield to maturity = 11%

to find out

maximum price you should be willing to pay for the bond

solution

we know that Semiannual Coupon Rate will be  = 4.75%  

so semiannual Coupon will be = Semiannual Coupon Rate ×  Face Value

semiannual Coupon = 4.75% × $1,000

Semiannual Coupon = $47.50

and Semiannual Period will be for 15 year  = 30

and Semiannual yield to maturity will be here YTM = 5.50%

so

Current Price  will be here

Current Price = Semiannual Coupon × $\frac{1-(\frac{1}{1+r})^t}{r}$ + $\frac{faevalue}{(1+r)^t}$     ...................1

put here value

Current Price = $47.50 × $\frac{1-(\frac{1}{1.055})^{30}}{0.055}$ + $\frac{}{1.055^{30}}$

Current Price = $891.00

so pay a maximum sum of $891.00