Question

Norma has one share of stock and one bond. The total value of the two securities is 1,298.97 dollars. The stock pays annual dividends. The next dividend is expected to be 3.59 dollars and paid in one year. In two years, the dividend is expected to be 6.58 dollars and the stock is expected to be priced at 124.1 dollars. The stock has an expected return of 16.6 percent per year. The bond has a coupon rate of 10.58 percent and a face value of 1,000 dollars; pays semi-annual coupons with the next coupon expected in 6 months; and matures in 14 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.

Answer 1

It is given that the,

price of one bond + price of stock =1298.97

Now to calculate the ytm of bond we need to calculate the price of bond, and for the same we need to first find the value of stock

Value of stock is the discounted value of all the future cash flows

Value of stock = 3.59 / 1.166 + 6.58 /1.166^2 + 124.1 / 1.166^2

= 3.08 + 4.84 + 91.28

= $99.20

Price of bond = 1298.97 - 99.20

= 1199.77

ytm can be calculated by the approximate formula as given below.

ytm = [C + ( F - P) / N ] / ( F + P) / 2

Where C is the coupon = 105.8 for year and 52.9 semiannually

F= Face value = 1000

P = Price of bond = 1199.77

N = Periods to maturity

ytm = [ 52.90 + ( 1000 - 1199.77 )/28 ] / ( 1000 + 1199.77) / 2

= [52.90 - 199.77/28 ] / 2199.77 / 2

= (52.90 - 7.13 ) /1099.885

= 4.16%

yearly ytm = 8.32%