1. Bond Valuation
Lesson 3

2. Agenda Understand that a bond is part annuity, part lump sum
Calculate the value of a bond manually
Calculate the value of a bond using Excel
Calculate the Yield to Maturity (YTM)
Lesson 1
Lesson 2

3. A $25 annuity with 19 time periods
Let us rewrite our original problem as:
Six months ago, a corporation had issued a 10-year, 5% coupon bond that makes semi-annual payments and has a $1,000 par value. You can now buy the bond in the secondary market for $1,047. What is the Yield to Maturity?
YTM: If you buy the bond for $1,047 now and hold it until maturity, what is the rate of return you will receive?
Time period 1 2 3 4 5 6 7 8 9 10 … 15 19
Pmt ($)
1047 25
1000
A $25 annuity with 19 time periods
A $1000 lump sum

4. Solution strategy
There is a particular discount rate that can make the sum of the present value of the annuity (coupon payments) plus the present value of the lump sum (principal repayment) equal to the price of the bond today, ie. $1,047. That discount rate is the Yield to Maturity (YTM).
Present Value of annuity
Present Value of lump sum
PMT = $25
Discount rate (r) = YTM/2 = ?
Time periods = 19
Present value =
= ## (1) +
Future value = $1,000
= ## (2)
## (1) + ## (2) = 1047

5. If you attempt the calculation by hand
Since the price you are paying for the bond ($1,047) is greater than the par value ($1,000) YTM is less than 5% (coupon rate)
You can start with using, let’s say, 4%, and calculate the bond price. You would get $1, as your answer
Since the value ($1,078.39) is higher than the price ($1,047), you infer that 4% is too low. You raise it a little, let’s say to 4.25%. That gets you to a price of $1,058.12
You try a slightly higher rate, let’s say 4.5%. You get a price of $1, Now you start lowering the rate a little at a time, narrowing your window as you go along
This is the trial & error method. Eventually you will get to the YTM of 4.39%. If you are doing the calculation using a calculator however, it can quickly get tedious.

6. Calculating YTM using Microsoft Excel®