Question

Norma has one share of stock and one bond. The total value of the two securities is 1,321.7 dollars. The stock pays annual dividends. The next dividend is expected to be 4.55 dollars and paid in one year. In two years, the dividend is expected to be 8.18 dollars and the stock is expected to be priced at 102.07 dollars. The stock has an expected return of 14 percent per year. The bond has a coupon rate of 10.9 percent and a face value of 1,000 dollars; pays semi-annual coupons with the next coupon expected in 6 months; and matures in 11 years. What is the YTM of the bond? Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.

#2 Caruso is planning to save 2,818.16 dollars every quarter for 5 years. He plans to make his first savings contribution in 3 months from today. If he currently has 6,415 dollars and expects to have 96,729.71 dollars in 5 years from today, then what is the EAR that he expects to earn? Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098

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Answer 1

Solution:

1.Calculation of YTM of bond

First we have to calculate the current price of bond.For this we have to calculate the price of share.

Price of shares=Dividend in 1st year/(1+rate of return)+Dividend in 2nd year+Share price at the end of 2nd year/(1+rate of return)^2

=$4.55/(1+0.16)+($8.18+102.07)/(1+0.16)^2

=$85.86

Thus,current price of bond is;

=total value of the two securities-Price of shares

=$1,321.7-$85.86=$1235.84

YTM of bond=[Annual coupon+(Face Value-Price of bond)/Years to maturity]/(Face Value+Price of bond)/2

=[$109+($1000-$1235.84)/11]/($1000+$1235.84)/2

=$87.56/$1,117.92=0.0783 or 7.83%

Thus  YTM of the bond is 0.0783