Question

Court has one share of stock and one bond. The total value of the two securities is 1,190 dollars. The bond has a YTM of 9.24 percent, a coupon rate of 7.95 percent, and a face value of 1,000 dollars. The bond matures in 11 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 10.9 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 10.13 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

K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =11

Bond Price =∑ [(7.95*1000/100)/(1 + 9.24/100)^k]     +   1000/(1 + 9.24/100)^11

k=1

Bond Price = 913.2

price of stock = total value - bond price

=1190-913.2=276.8

As per DDM

Price = Dividend in 1 year* (1 + growth rate )/(cost of equity - growth rate)

276.8 = 10.9/ (0.1013 - Growth rate)

Growth rate% = 6.19