Question

David Palmer identified the following bonds for investment:

1. Bond A: A $1 million par, 10% annual coupon bond, which will mature on July 1, 2025.
2. Bond B: A $1 million par, 14% semi-annual coupon bond (interest will be paid on January 1 and July 1 each year), which will mature on July 1, 2031.
3. Bond C: A $1 million par, 10% quarterly coupon bond (interest will be paid on January 1, April 1, July 1, and October 1 each year), which will mature on July 1, 2026.

The three bonds were issued on July 1, 2011.

(Each Part is Independent)

1. If Bond B is issued at face value and both Bond B and Bond A are having the same yield to maturity (EAR), calculate the market price of Bond A on July 1, 2011. [Note: Full mark would only be given to correct answer of which the values of those variables not provided in the question directly are derived.]                                                                       

2. David purchased the Bond C on January 1, 2014 when Bond C was priced to have a yield to maturity (EAR) of 10.3812891%. David subsequently sold Bond C on January 1, 2016 when it was priced to have a yield to maturity (EAR) of 12.550881%. Assume all interests received were reinvested to earn a rate of return of 3% per quarter (from another investment account), calculate the current yield, capital gain yield and the 2-year total rate of return (HPY) on investment for David on January 1, 2016. [Hint: Be careful with how many rounds of coupons has David received during the holding period and thus how much interests (coupons and reinvestment of coupons) he has earned in total during the 2-year holding period.]                                                                                                      

3. David purchased Bond B on a coupon payment day. Bond B is priced to have a yield to maturity (EAR) of 12.36% and its market value is $1,101,058.953 on the date of purchase. Find the remaining life until maturity (in terms of 6-month period or year) of Bond B.       

Answer 1

Part (a)

Bond B is issued at face value. That means, its YTM is equal to coupon rate which is given as 14%. Also given that YTM of bond A is equal to that of Bond B ie., 14%.

Hence market price of bond A is $759,917.14 arrived at using the PV function of Excel as follows:

Part (b)

Purchase price of the Bond C on Jan 1, 2014 was $ 974,008.439898 ascertained using the PV function of Excel as follows:

Sale Price on Jan 1, 2016 was $855,819.733322 as follows:

(i) Current yield= (Amount of interest per year/Investment price)*100

Yearly interest= Face Value*Coupon Rate= $ 1,000,000*10%= $100,000

Therefore, Current Yield= $100,000/$974,008.44 = 10.266851%

(ii) Capital gain yield= (P₁/P₀)-1 Where P₁= Selling price and P₀= Purchase price.

Hence Capital gains yield for two years= (855,819.73/974,008.44)-1 = 0.878657-1 = -0.121343 or -12.1343% (Negative)

(iii) Period of invest ment= 2 years. Number of coupon payments= 2*4=8. Amount of each coupon= $25,000

Proceeds of these interest payments, reinvested at 3% per quarter (12% per year) is the FV of annuity as follows:

Total Holding Period Yield (HPY) = (P1-P0+D)/P0

Where P1= Sale price, P0= Investment price and D= Income received

Therefore, HPY=($855,819.73-$974,008.44+222,308.40)/$974,008.44 = $104,119.69/$974,008.44 = 0.106898139

Or, 10.6898139%

(This is for two years. Annualized yield= 10.6898139%/2= 5.344907%)

Part (c)

Number of future coupon payments is ascertained at 23.91 (Semi annual) using NPER function of Excel. as follows:

Rounding to 24 half years, the remaining life until maturity= 24/2= 12 years.