Question

An investor must choose between two bonds:

Bond A pays $87 annual interest and has a market value of $780. It has 10 years to maturity.

Bond B pays $92 annual interest and has a market value of $820. It has two 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.)

	Current Yield Bond A % Bond B %

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

	Bond B
	Bond A

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 A is 12.56 percent. What is the approximate yield to maturity on Bond B? 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.)

	Approximate yield to maturity % Exact yield to maturity %

d. Has your answer changed between parts b and c of this question in terms of which bond to select?
  

	No
	Yes

Answer 1

Part a:

The formula to calculate the current yield= Coupon interest payment/Market value of the bond.

Bond A pays $87 annual interest, this is the coupon payment here.
The market value of the bond=$780
Current yield on bond A=$87/$780=0.111538462 or 11.15% (rounded upto two decimal places)

Bond B pays $92 annual interest, this is the coupon payment here.
The market value of bond B=$820
Current yield on bond B=$92/$820=0.112195122 or 11.22% (rounded upto two decimal places)

Part b:
Based on current yield, she should select bond B as it has higher current yield.

Part c:

The approximate yield to maturity on Bond B is calculated using the formula:
[Annual coupon or interest payment + (Face or par value of the bond - Market value of the bond)/Years to maturity]/ (Face value of the bond + Market value of the bond)/2

Given that:
Annual coupon interest payment for bond B=$92
Face or par value of the bond B=$1000
Market value of bond B=$820

Years to maturity for bond B=2

[$92+($1000-$820)/2]/($1000+$820)/2

[$92+($180)/2]/($1820)/2
=[$92+$90]/$910
=$182/$910
=.2 or 20%
So, the approximate yield to maturity on Bond B=20%

The exact yield to maturity value we have calculated using excel and the value is =21.15%

Note: We have taken the present value as negative because it is a cash outflow.

Part d:
No, the answer will still be bond B. This is because, even when we consider the yield to maturity or YTM, bond B gives higher YTM which makes it attractive.