Question

This question consists of sub-questions, (a) and (b), answer both.
(a) You hold a bond with a coupon interest rate of 8.00% and a face (par) value of $10,000. If the maturity date is 4 years and the market’s required yield to maturity for similar rated debt is 6.00%, what is the value of this bond?













(b) An ordinary share pays a $2.00 dividend at the end of last year and is expected to pay a cash dividend every year from now to infinity. Each year, the dividends are expected to grow at a rate of 5.00%. Based on an assessment of the riskiness of the ordinary shares, the investor’s required rate of return is 12.00%. What is the value of this ordinary share?

Answer 1

a) Value of the Bond today is the Present value of the all coupon payments and maturity value discounted at YTM.

Calculate the price of bond with annual coupon payments:

Coupon = 8% Annual Coupon = 10000 x 0.08 = 800, No of periods = 4 years, YTM = 6%

Price of the bond = Coupon payment x Cumulative discounting factor @6% for 4 periods + Marutiry value x discounting factor 4th period.

[ For cumulative annuty discouting factor refer to the tables or you can calculate as it is sum of (100/106) + (100/106)² + ...................(100/106)⁴ and for 4th year it is (100/106)⁴ ]

= ( 800 x 3.465105606) + (10000 x 0.79209366)     

= 2772.084484 + 7920.9366

= 10693.02112

Price of the bond = 10693.02 approx  

b)

Price of any security today is the present value of all the incomes that security is going to generate in future discounted at required rate of return.

There is widely used formula to calculate the price of share whose dividend is contant, called gordan growth formula

GGn formula =  

P0 = Price today , D1= Expected dividend , Ke = cost of capital , g is growth

D0 = 2, D1 = 2 x 1.05 = 2.10 , G = 5%, Ke = 12%

Putting values in Formulas:

= 2.10 / (0.12 - 0.05)

= 2.10 / 0.07

Price of the share = 30