Question

Problem 3 of 6. (a) A bond has 6.5 years to go to maturity. The coupon rate on the bond is 9.45%, and the yield to maturity is 8.24%. What is the price of the bond?

(b) A company has a beta of 0.75. The risk-free rate is 4.65% and the market risk premium is 7.80%. The company is expected to pay annual dividends. The first dividend is expected to be paid in 4 years and is expected to be $1.30. The dividend in year 5 is expected to be $2.30, and then the dividend is expected to grow 1.5% annually thereafter. What should the price of the stock be?

I want part B to be answered please.

Answer 1

The stock price is computed as shown below:

= Dividend in year 4 / (1 + required rate of return)⁴ + Dividend in year 5 / (1 + required rate of return)⁵ + 1 / (1 + required rate of return)⁵ x [ (Dividend in year 5 x (1 + growth rate) / ( required rate of return - growth rate) ]

Required rate of return is computed as follows:

= risk free rate + beta x market risk premium

= 4.65% + 0.75 x 0.078

= 10.5% or 0.105

So, the price will be as follows:

= $ 1.30 / 1.105⁴ + $ 2.30 / 1.105⁵ + 1 / 1.105⁵ x [ ($ 2.30 x 1.015) / (0.105 - 0.015) ]

= $ 1.30 / 1.105⁴ + $ 2.30 / 1.105⁵

= $ 1.30 / 1.105⁴ + $ 28.23888889 / 1.105⁵

= $ 18.01 Approximately

Feel free to ask in case of any query relating to this question      

answered by: anonymous