Question

Myra Breck must choose between two bonds:

Bond A pays $100 annual interest with semiannual payment and has a market value of $800. It has 10 years to maturity.

Bond B pays $100 annual interest with semiannual payment and has a market value of $900. It has 2 years to maturity.

Assume the par value of the bonds is $1,000.

a. Compute the current yield on both bonds. (Round the final answers to 2 decimal places.)

	Current yield
Bond A	%
Bond B	%

b. Which bond should she select based on the answer to part a?

• Bond A

• Bond B

c. A drawback of the current yield is that it does not consider the total life of the bond. What is the yield to maturity on these bonds? (Round the final answers to 2 decimal places.)

	Yield to maturity
Bond A	%
Bond B	%

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

• Yes

• No

Answer 1

a) Current yield of Bond A = Annual interest / Price of bond = $100/$800 =12.5%

Current yield of Bond B = Annual interest / Price of bond = $100/$900 =11.11%

b) Bond A should be selected as the Current yield of Bond A is higher

c) let the six monthly yield be y

The approximate value of y is given by

y = [C +(M-P)/n] / (0.4*M+0.6*P)

Where:

C    = the periodic interest payments

M = the maturity (face) value of the bond

P   = the current market price of the bond

N = the number of periods to maturity

For Bond A,

y = (50+(1000-800)/20) / (0.4*1000+0.6*800)

= 0.068182 or 6.82%

Putting this value in 50/(1+y) + 50/ (1+y)^2+ ... + 50/(1+y)^20 + 1000/(1+y)^20

gives value as 804.63

Putting y =6.86% gives value as 800.79

Putting y =6.87% gives value as 799.87

So, y lies between 6.86% and 6.87%

Approximate y = 6.86% + (800.79 -800)/(800.79-799.87) * (6.87%-6.86%) =6.8686% which is the correct 6 monthly yield

So, annual YTM of bond A = (1+6.8686%)^2-1 = 14.21% (round to two decimal places)

  

For Bond B,

y = (50+(1000-900)/4) / (0.4*1000+0.6*900)

= 0.079787 or 7.98%

Putting this value in 50/(1+y) + 50/ (1+y)^2+ ... + 50/(1+y)^4 + 1000/(1+y)^4

gives value as 901.2547

Putting y =7.99% gives value as 900.9454

Putting y =8% gives value as 900.6362

Putting y =8.02% gives value as 900.0183

Putting y =8.03% gives value as 899.7095

So, y lies between 8.02% and 8.03%

Approximate y = 8.02% + (900.0183-900)/(900.0183-899.7095) * (8.03%-8.02%) =8.0206% which is the correct 6 monthly yield

So, annual YTM of bond A = (1+8.0206%)^2-1 = 16.68% (round to two decimal places)

d) As Bond B has a higher YTM than Bond A, one should purchase Bond B. So, the answer has changed (YES)