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)

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.]                                                                                                                           

Please provide steps thanks

Answer 1

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:

(a) 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%

(b) 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)

(c) Period of investment= 2 years.

Hence interest received= Face Value* Coupon Rate*2= $1 Million*10%*2 = $200,000

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

=($855,819.73-$974,008.44+200,000)/$974,008.44 = $81,811.29/$974,008.44 = 0.0839944 Or, 8.39944%

(This is for two years. Annualized yield= 8.39944%/2= 4.19972%)