Question

Terry has one share of stock and one bond. The total value of the two securities is $1,200. The bond has a YTM of 10.20 percent, a coupon rate of 9.20 percent, and a face value of $1,000; pays semi-annual coupons with the next one expected in 6 months; and matures in 8 years. The stock pays annual dividends that are expected to grow by 1.90 percent per year forever. The next dividend is expected to be paid in one year. The stock has an expected return of 14.10 percent per year. What is the dividend in 1 year expected to be for the stock?

Answer 1

Total Terry's investment = $1200

Given about bond,

Face value = $1000

YTM = 10.20%

Coupon rate = 9.2% semiannually

So, coupon = 9.2% of 1000/2 = $46

Years to maturity = 8 years,

So price of bond can be calculated usinf financial calculator with values

FV = 1000

PMT = 46

N = 8*2 = 16

I/Y = 10.2/2 = 5.1

compute PV, we get PV = -946.19

So price of the bond = $946.19

So investment in bond = $946.19

So investment in stock = 1200-946.19 = $253.81

Given for stock,

Investment = price of stock P0 = $253.81

growth rate g = 1.90%

expected return Ke = 14.10%

So stock price can be calculated using constant dividend growth model,

P0 = D1/(Ke-g)

So, D1 = 253.81*(0.141-0.019) = $30.96

So, dividend in 1 year expected for the stock will be $30.96