Bond P is a premium bond with a coupon rate of 9.7 percent. Bond D is a discount
ID: 2759458 • Letter: B
Question
Bond P is a premium bond with a coupon rate of 9.7 percent. Bond D is a discount bond with a coupon rate of 5.7 percent. Both bonds make annual payments, have a YTM of 7.7 percent, and have twelve years to maturity. Requirement 1: What is the current yield for bond P?Requirement 2: What is the current yield for bond D? Requirement 3: If interest rates remain unchanged, what is the expected capital gains yield over the next year for bond P?Requirement 4: If interest rates remain unchanged, what is the expected capital gains yield over the next year for bond D?
Explanation / Answer
Formula for Current Yield= Annual coupons/ Bond Price
Now we do not know Bond price so let us calculate bond price as follows
Assume Face Value of Bond= $1000, Periods(N)= Years till Maturity=12
YTM=7.7%, Coupon Payments = 9.7%*1000=$97(Annual coupon Payemnt),
Using financial calulator we get Price of bond= $1153.09
Or we can use below bond price calcultor by putting above values and solving for price
http://www.zenwealth.com/businessfinanceonline/BV/BondCalculator.html
Thus
Current Yield for Bond P= 97/1153.09
=0.084
Current Yield for Bond P= 8.4%
2. What is the current yield for bond D
Here FV= $1000, N=12, YTM=7.7%, Coupon = $57(5.7%*1000)
Price of bond D= $846.91
Current Yield= 57/846.91
Current Yield of bond D= 0.0673 or 6.73%
3. If interest rates remain unchanged, what is the expected capital gains yield over the next year for bond P
Capital Gains forumla = Next year price- Purchase price/ Purchase Price
Now next years price can be calculated just by changing N= 11 as 1 year has passed and keeping all other values same as before
Next years price for bond P=$1144.88
Capital Gains Yield= (1144.88-1153.09)/1153.09= -0.0071
Capital Gains yield for bond P= -0.71%
Next years price for bond D= $855.12
Capital Gains Yield= (855.12-846.91)/846.91= 0.0097
Capital Gains Yield for Bond D= 0.97%
Note: Capital Gains for premium bond is negative because as bond nears maturity its price start decreasing to reac face value at maturity while reverse happens for discount bonds. (Its price stat increasing)