Question

1. You buy a zero coupon bond at the beginning of the year that has a face value of $1,000, a YTM of 10 percent, and 22 years to maturity. You hold the bond for the entire year. Assume semiannual compounding. How much interest income will you have to declare on your tax return? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

what is the Interest income $ ?

2. Ayden, Inc., has an issue of preferred stock outstanding that pays a dividend of $6.75 every year, in perpetuity. This issue currently sells for $93 per share.

What is the required return? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Required return ?

%

Answer 1

(1) Bond Face Value = $ 1000, YTM = 10%, Compounding Frequency: Semi-Annual, Tenure = 22 years or (22 x 2) = 44 semi-annual periods, Semi-Annual Yield = 10/2 = 5 %

Initial Bond Price = Present Value of Face Value discounted at the semi-annual yield = 1000/ (1.05)^(44) = $ 116.86

The bond is held by the investor for a year and then sold off.If the compounding is done twice in one year, then the bond earns interest twice during the bond investors holding period.

Interest Earned in First Semi-Annual Period = Price at beginning of first period x Periodic Interest Rate = 116.86 x 0.05 = $ 5.843

Interest Earned in Second Semi-Annual Period = Price at beginning of second period x Periodic Interest Rate (Price at the beginning of second period = Interest Accrued in first semi-annual period + Price at the beginning of first semi-annual period as the interest format is compound interest) = (116.86 + 5.843) x 0.05 = $ 6.135

Therefore, Total Interest Expense for the Year = $ 6.135 ~ $ 6.13

(2) Perpetual Annual Dividend = D = $ 6.75 and Preferred Stock Price = P = $ 93

Therefore, Preferred Stock Required Return = Ke = (D/P) = (6.75/93) = 0.072581 or 7.258 % ~ 7.26 %