Question

Ten years ago you purchased for $1,200 a bond issued by the ASD Corporation. The bond had twenty years to maturity, a par value of $1,000, a 12% coupon, and paid interest semiannually. Since you had no immediate use for the interest payments, you deposited them in your savings account. For the first 5 years, your bank paid 2% compounded semiannually, but for the last 5 years you have earned 4% compounded semiannually. Tomorrow you will receive your 20th interest payment, and you plan to sell the bond immediately afterwards at its fair market price. The market rate of return for bonds of this type is currently 16%. What will be your annualized holding period return on this investment?

Answer 1

Annual Coupon is $120 so Semi-annual coupon is $60

Deposited in the bank for 5 years at a semi-annual interest rate of 2%

The future value of these $60 after 5 years is $627.73

You can use the FV function in Excel

=FV(rate,nper,pmt,pv)

nper= periods, PMT = repeated payments, pv=present value (keep zero if not required)

$627.73=FV(2%/2,10,-60,0,)

Deposited in the bank for 5 years at a semi-annual interest rate of 4%

The future value of these $60 after 5 years (6-10th) is $585.28

$585.28=FV(4%/2,9,-60,0,)

The period is 9 because you still have not received the 10th year last payment.

The future value of $627.73 (which you received after 5th year) after 5 years at 4% is $765.20

$765.20=FV(4%/2,10,0,-627.73,)

Total Return from bank = $585.28+$765.20 = $1350.48 + 60 (Last Copoun payment) = $1410.48

You sold the Bond at 16% return = 1200*(1+16%)= $1392

Total Return = $1410.48+$1392 = $2802.48

Net Return = Return - Investment = $2802.48 -$1200 = $1602.48

Annualized HPR = ((Net Return + (End amount - Beg Amount))/Beg Amount)^(1/n)-1

=((1602.48+(2802.48-1200))/1200)^(1/10)-1 = 10.32%