Question

2. Suppose there are two bonds for sale; Bond ART with 7-years to maturity, paying a semi-annual interest payment of $57.75, and available for purchase at $1,017.63; and then a second bond, Bond BMW, for sale at $989.54, maturing in 8-years, and paying $63.65 on a semi-annual basis. What is the YTM of the two bonds? And which one will you add to your portfolio based on the highest yield to maturity?

• YTM of ART = .1118 or 11.18%
• YTM of BMW = .1294 or 12.94%
• Select BMW

PLEASE show work. This is on my finance study guide and we are not allowed to use excel, I have to know how to do it by hand. Right above are the answers, just need to know how to get them

Answer 1

YTM of ART calculation:

We have following formula for calculation of bond’s yield

Bond price P0 = C* [1- 1/ (1+i) ^n] /i + M / (1+i) ^n

Where

Price of the bond P0 = $1,017.63    

M = value at maturity, or par value = $1000

C = coupon payment = $57.75 semiannual coupon

n = number of payments = 7 years *2 = 14

i = interest rate, or yield to maturity =?

Now we have,

$1,017.63 = $57.75 * [1 – 1 / (1+i) ^14] /i + $1000 / (1+i) ^14

Now you can use trial and error method by putting different values of i to calculate its value

Or you can also use calculator

For financial calculator to calculate interest rate (I/Y)–

Inputs are:

• PV = - $1,017.63
• N= 14
• PMT = $57.75
• FV = 1000

Then press I/Y to get the final answer

We got the value of i = 5.59%

Therefore YTM of bond = 2 *5.59%= 11.18%

YTM of BMW:

Price of the bond P0 = $989.54

M = value at maturity, or par value = $1000

C = coupon payment = $63.65 semiannual coupon

n = number of payments = 8 years *2 = 16

i = interest rate, or yield to maturity =?

Now we have,

$989.54= $63.65 * [1 – 1 / (1+i) ^16] /i + $1000 / (1+i) ^16

Now you can use trial and error method by putting different values of i to calculate its value

We got the value of i = 6.47%

Therefore YTM of bond = 2 *6.47%= 12.94%

You will add BMW to your portfolio based on the highest yield to maturity.