Question

URGENT!!

A bond is issued with a coupon of 6% paid annually, a maturity of 38 years, and a yield to maturity of 9%. What rate of return will be earned by an investor who purchases the bond for $679.28 and holds it for 1 year if the bond's yield to maturity at the end of the year is 12%? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Negative amount should be indicated by a minus sign.) Rate of return

Answer 1

Solution :

It is given that the current maturity = 38 year

YTM = 9%

Face value = 1000

Coupon = 6% = 1000* 6% = 60

f Bond Price = C+1-(1+r) -^ r *(1+r)n

Where r = YTM and n = period

It is given that the investor purchases the bond at 679.28.

Let check the price by using the formula

$Price =C* \frac{(1-(1+r)^{-n})}{r} + \frac{F}{(1+r)^{^{n}}}$

$Price =60* \frac{(1-(1+0.09)^{-38})}{0.09} + \frac{1000}{(1+0.09)^{^{38}}}$

$Price =60* \frac{0.962174}{0.09} + \frac{1000}{26.43668}$

$Price =641.45 + 26.44 = 679.28$

Since investor is selling the bond after one year and YTM is now 12%. The time to maturity is now 37 years.

Let's calculate the price again

$Price =60* \frac{(1- 1+0.12)^{-37}}{0.12} + \frac{1000}{(1+0.12)^{37}}$

$Price =60* \frac{0.984902}{0.12} + \frac{1000}{66.23184}$

$Price =492.4508+ 15.09 = 507.55$

Price of the bond after one year would be 507.55.

When the investor purchases the bond at 679.28 and holds it for one year then he will receive one coupon payment of $60 as the coupon payment is annually. He will now sell the bond at $507.55

So total loss = selling price - purchase price + coupon received = 507.55 - 679.28 + 60 = -111.73

Rate of return = -111.73 / 679.28 =-16.45%

Answer is -16.45%