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.

(a) If Bond B is issued at face value and both Bond B and Bond A are having the same yield to maturity (EAR) at issuance, 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.]  

(b) David Palmer purchased 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 (in another investment account).

Calculate:

i) the current yield,

ii) the 2-year capital gains yield and

iii) the 2-year total rate of return on investment for David.

[Note that this question is NOT asking for average yearly (total) return. Hint: think of total accumulation as FV (Annuity) of coupons and selling price.]

Answer 1

(a) The market price of a bond calculation, first we have to identify the present value of a 14 year with 10%

So the current market value at issuance = 1000000/3.687=271250

(b) (i) Current Yield = interest rate/ price*100

   =5682/227284*100=2.50%

(ii) Capital gain means an increase in the value of the bond. Calculating the future value of the annuity is the best for ascertaining

Fv of annuity =2.1000 the future price of a bond =227284*2.1000=477296

The capital gain = 477296-227284= 250012.4

(iii) The return on investment is capital gain + interest rate = 261376.4