Question

Norma has one share of stock and one bond. The total value of the two securities is 1,246.06 dollars. The stock pays annual dividends. The next dividend is expected to be 3.27 dollars and paid in one year. In two years, the dividend is expected to be 7.58 dollars and the stock is expected to be priced at 121.24 dollars. The stock has an expected return of 17.34 percent per year. The bond has a coupon rate of 11.22 percent and a face value of 1,000 dollars; pays semi-annual coupons with the next coupon expected in 6 months; and matures in 13 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.

please help ASAP!

Answer 1

Given for the stock,

The stock pays annual dividends.

The next dividend D1 is expected to be $3.27

In two years, the dividend D2 is expected to be $7.58

the stock is expected to be priced P2 at $121.24

The stock has an expected return Ke of 17.34%

So stock price today is sum of PV of dividend and PV of price at year 2

So, P0 = D1/(1+Ke) + D2/(1+Ke)^2 + P2/(1+Ke)^2

P0 = 3.21/1.1734 + 7.58/1.1734^2 + 121.24/1.1734^2 = $96.30

Given for the bond,

coupon rate = 11.22% semiannually

Face value = $1000

so, coupon = 11.22% of 1000/2 = $56.1

years to maturity = 13 years

Total invest ment = $1246.06

So price of bond = total investment - stock price = 1246.06 - 96.30 = $1149.76

So using financial calculator to solve it,

FV = 1000

PMT = 56.1

PV = -1149.76

N = 13*2 = 26

compute for I/Y, we get, I/Y = 4.61%

So yield to maturity = 2*4.61% = 9.22%