Question

Court has one share of stock and one bond. The total value of the two securities is 1,376 dollars. The bond has a YTM of 8.9 percent, a coupon rate of 11.64 percent, and a face value of 1,000 dollars. The bond matures in 13 years and pays annual coupons with the next one expected in 1 year. The stock is expected to pay an annual dividend every year forever, the next dividend is expected to be 10.91 dollars in 1 year, all subsequent dividends are expected to grow at the same annual growth rate, and the expected return for the stock is 10.66 percent. What is the annual growth rate of the stock’s dividend expected to be? Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.

Answer 1

First we need to find the price of the bond. Use PV function in EXCEL to find the price of the bond.

=PV(rate,nper,pmt,fv,type)

rate=YTM=8.9%

nper=maturity time=13

pmt=(coupon rate*face value)=(11.64%*1000)=116.40

fv=1000

=PV(8.9%,13,116.40,1000,0)=1206.24

Bond price=$1206.24

Price of the Share=Total value-price of the bond=$1376-$1206.24=$169.76

growth rate formula=Expected return on stock-(dividend next year/Share price)

=10.66%-(10.91/169.76)

=10.66%-6.43%

=4.23%

growth rate=4.23%