Response: We use a present value table to look up the value of the $1000 principal to be paid 8 years or 16 semi-annual periods. Looking at the 3% row (rate per semi-annual period), we find the factor of .623. Multiplying by $1000, the investor is selling the value of the principal for $623.00. Using a present value of an annuity table, we also look up R=3% and N=16 to find the factor 12.561. Multiplying 12.561 times the $40 semi-annual coupon, we find our investor is selling the remaining stream of 16 coupon payments for $502.44. Thus the price of the bond is $623.00 + $502.44 = $1,125.44. But the bond originally cost our investor $1,000, so the capital gain is 125.44 (using financial calculator, the answer is $125.61). Section: Measuring Bond Yields.
-Now let's look from the view of the investor who buys an 8 percent semiannual bond with 8 years remaining to maturity, when market rates are 6%. If this investor pays $1,125.44 for the bond, what is his current yield?
A) 3.55 percent
B) 7.11 percent
C) 8.00 percent
D) 10.00 percent

Question

Response:  We use a present value table to look up the value of the $1000 principal to be paid 8 years or 16 semi-annual periods.  Looking at the 3% row (rate per semi-annual period), we find the factor of .623.  Multiplying by $1000, the investor is selling the value of the principal for $623.00.  Using a present value of an annuity table, we also look up R=3% and N=16 to find the factor 12.561.  Multiplying 12.561 times the $40 semi-annual coupon, we find our investor is selling the remaining stream of 16 coupon payments for $502.44.  Thus the price of the bond is $623.00 + $502.44 = $1,125.44.  But the bond originally cost our investor $1,000, so the capital gain is 125.44 (using financial calculator, the answer is $125.61). Section: Measuring Bond Yields.
-Now let's look from the view of the investor who buys an 8 percent semiannual bond with 8 years remaining to maturity, when market rates are 6%. If this investor pays $1,125.44 for the bond, what is his current yield? 
A) 3.55 percent
B) 7.11 percent
C) 8.00 percent
D) 10.00 percent

Quizplus · Accepted Answer

The current yield formula is annual interest payment divided by the market price of the bond, expressed as a percentage. To calculate the annual interest payment, we need to take half of the 8% coupon rate, which is 4%. So, the annual interest payment is $80 (4% of $1,000).

Next, we need to calculate the current yield:

Annual Interest Payment / Market Price of the Bond = Current Yield

$80 / $1,125.44 ≈ 0.0711 or 7.11%

Therefore, the current yield for this bond is 7.11%, which is closest to option B.

Response: We Use a Present Value Table to Look