Calculating Bond Values
In the earlier article we discussed how to basic bond valuations and in the article before that I presented various ways of calculating WACC or Weighted Average Cost of Capital. In this article, I will a discuss few more examples in calculating values of bonds and related variables like Yield to Maturity and Effective Annual Interest Rate.
Problem 1
You are looking at 2 bonds being issued by Indews Financial Inc. The first bond is a 5 Year $1000 bond being sold at its par value, with $60 semi annual interest payments. The second bond is a 6 year bond, with $30 semiannual interest payments and face value of $1000, and is also being sold at par.
Answer the following Questions
What the yield on the 5 Year bond (Effective Annual Yield)?
What is the yield on the 6 Year bond (Effective Annual Yield)?
Listed Variables: Bond 1
Time to Maturity: 5 Years
Face Value (Future Value): $1000
Current Value: $1000 (The bond is being sold at par)
Semi-Annual Payment: $60
Total Number of Payments: 10
Annual Coupon Rate: 12%
Annual Interest Rate: 12% (The bond is being sold at par value, as such assumption can be made that the prevailing interest rate and the coupon rate are the same)
Semi-Annual Interest Rate: 6% (Half of Annual Interest Rate)
Effective Annual Yield:?
Effective Annual Yield
The formula for effective annual yield or effective rate is
r = (1+ i/n)^n - 1
r = Effective Annual Yield
i = the annual nominal rate
n = Number of Compounding Periods Per Year (Since the bond is a semi-annual bond, n would equal 2)
If we list the known variables according to the Effective Annual Yield Formula, we have:
i (nominal rate) = 12%
n = 2
r = (1 + .12/2)^2 - 1
r = (1.06)^2 - 1
r = 1.1236 - 1
r = .1236
r = 12.36%
With the above formula, we know that the Effective Annual Yield on the Bond 1 is 12.36%.
Listed Variables: Bond 2
Time To Maturity: 6 Years
Semi-Annual Interest Payments: $30
Face Value (Future Value): $1000
Current Value: $1000 (Since its being Sold at par)
Semi-Annual Coupon Rate: 3% (Semi-Annual Interest Rate / Face Value) ($30/$1000)
Annual Coupon Rate: 6%
Since the bond is being sold at Par, assumption can be made here that the annual interest rate of the bond and the prevailing market interest rates are the same. So, the stated interest rates are:
Annual Interest Rate or Nominal Rate: 6%
Stated Annual Interest Rate: 3%
Effective Annual Yield
Effective Annual Yield is r = (1+ i/n)^n - 1
So, r = (1 + .06/2)^2 - 1
r = (1.03)^2 - 1
r = 1.0609 - 1
r = .0609
From the above EAR formula, we get Effective Annual Yield as 6.09%
Problem 2
Consider a bond issued by Ryzone Financial has an annual coupon of $80, a face value of $1000. Calculate the Yield To Maturity of the bond, given the following variables:
a. The bond has a 20 year life, and is currently being sold at $1200.
b. The bond has a 10 year life, and is currently being sold at $950.
a
We have the following variables for a:
Face Value: $1000
Current Price: $1200
Annual Payments: $80
Time to Maturity: 20 Years
Number of Payments: 20
We can find out the YTM by plugging in the following variables in the the BA II Plus Calculator.
N = 20 | PV = -1200 | PMT = 80 | FV = 1000 | CPT = I/Y
We get I/Y as 6.224%. So, the Yield to Maturity is 6.22%
b
Face Value: $1000
Current Value: $950
Annual Payment: $60
Time to Maturity: 10
Number of Payments: 10
N = 10 | PV = -950 | PMT = 80 | FV = 1000 | CPT = I/Y
I/Y = 8.771%
So, the Yield to Maturity for the second bond is 8.77%
*Note: It is important to note that in Problem 2, the bonds are ANNUAL bonds, and not semi-annual bonds.
Calculate Bond Values - 2
Bond Valuation
WACC - Weighted Average Cost of Capital
WACC Calculation - Intermediate Problems
Leave a comment