Question

Harold Reese must choose between two bonds:
  
Bond X pays $78 annual interest and has a market value of $850. It has 13 years to maturity.
Bond Z pays $88 annual interest and has a market value of $810. It has five years to maturity.
Assume the par value of the bonds is $1,000.
  
a. Compute the current yield on both bonds. (Do not round intermediate calculations. Input your answers as a percent rounded to 2 decimal places.)
  

  
b. Which bond should he select based on your answers to part a?

	Bond Z
	Bond X

c. A drawback of current yield is that it does not consider the total life of the bond. For example, the approximate yield to maturity on Bond X is 9.84 percent. What is the approximate yield to maturity on Bond Z? The exact yield to maturity? (Use the approximation formula to compute the approximate yield to maturity and use the calculator method to compute the exact yield to maturity. Do not round intermediate calculations. Input your answers as a percent rounded to 2 decimal places.)

   
    
d. Has your answer changed between parts b and c of this question?

	No
	Yes

Answer 1

Answer a.

Bond X:

Current Yield = Annual Interest / Current Price
Current Yield = $78 / $850
Current Yield = 9.18%

Bond Z:

Current Yield = Annual Interest / Current Price
Current Yield = $88 / $810
Current Yield = 10.86%

Answer b.

Bond Z should be selected as its current yield is highest.

Answer c.

Approximate YTM, Bond Z:

Approximate YTM = [Annual Coupon + (Face Value-Current Price)/Time to Maturity] / [(Face Value+Current Price)/2]
Approximate YTM = [$88 + ($1,000 - $810) / 5] / [($1,000 + $810) / 2]
Approximate YTM = $126 / $905
Approximate YTM = 13.92%

Exact YTM, Bond Z:

Par Value = $1,000
Current Price = $810
Annual Coupon = $88
Time to Maturity = 5 years

Let Annual YTM be i%

$810 = $88 * PVIFA(i%, 5) + $1,000 * PVIF(i%, 5)

Using financial calculator:
N = 5
PV = -810
PMT = 88
FV = 1000

I/Y = 14.39%

So, exact YTM is 14.39%

Answer d.

No, our answer remains unchanged. We should purchase Bond Z.