Question

Suppose the following bond quote for IOU Corporation appears in the financial page today's newspaper. Assume the bond has a face value of $2,000, and the current date i April 15, 2019 Company (Ticker) IOU (OU) Last Yield Coupon 7.80 Last Maturity Price Apr 15, 204193.064 EST Vol (000s) 111 22 a. What is the yield to maturity of the bond? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b. What is the current yield? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g.. 32.16.) Yield to maturity b. Current yield

Answer 1

bnFace value in % =   $100  
years to Maturity (n)= April 15, 2019 to April 15, 2041=   22   years
Actual market price=   93.0640  

Coupon = 100%*7.8% = 7.8

Yield to Maturity is that rate (I) at which bond price is equal to Actual Market price

Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n

Assume i=8.4%

bond price =7.8*(1-(1/(1+8.4%)^22))/8.4% + 100/(1+8.4%)^22
$94.0683760

Assume i=8.6%

bond price =7.8*(1-(1/(1+8.6%)^22))/8.6% + 100/(1+8.6%)^22
$92.2124050

interpolation formula = lower rate +((uper rate - lower rate)*(Uper price - bond actual price)/(uper price - lower price))
8.4% +((8.6%-8.4%)*(94.0683760-93.064)/(94.0683760-92.2124050))
0.0850840428 or 8.51%
So yield to maturity of bond is 8.51%

B.

Current Yield = Coupon/bond price

=7.8/93.064

=0.08381328978 or 8.38%

So Current Yield is 8.38%