Question

1. Calculate the price of a bond with Face value of bond is $1,000 and:

a. Bond yield of 8.4%, coupon rate of 7% and time to maturity is 5 years. Coupon is paid semi-annually (Bond 1)

b. Bond yield of 7%, coupon rate of 8% and time to maturity is 4 years. Coupon is paid semi-annually

c. Calculate the price of Bond 1 right after the 5th coupon payment.

2. Arcarde Ltd issues both ordinary shares and preference shares to raise capital, in which 500,000 ordinary shares have been issued at the price of $10 and 100,000 preference shares with a par value of $100.

a. Company promises to pay an annual dividend rate of 6.5% per share for its preference shares. If similar investment has a rate of return of 10% p.a, what is the fair price of Arcarde’s preference share?

b. Company also plans to pay dividend for its ordinary shares as follow: Y1 (next year): $0.8; Y2: $1; Y3: $1, after year 3, the dividend will growth at the rate of 3% and company’s rate of return is currently 9%, what should be the fair price of each ordinary shares?

Show all working out and equations

Answer 1

(1)

(a) Bond Yield = 8.4 % per annum or (8.4/2) = 4.2 % per half year, Coupon Rate = 7 % per annum payable semi-annually, Maturity = 5 years or (5 x 2) = 10 half-years, Face Value = $ 1000

Semi-Annual Coupon = 1000 x 0.07 x 0.5 = $ 35

Bond Price = 35 x (1/0.042) x [1-{1/(1.042)^(10)}] + 1000 / (1.042)^(10) = $ 943.78

(b) Bond Yield = 7 % per annum or (7/2) = 3.5 % per half year, Coupon Rate = 8 % per annum payable semi-annually, Maturity = 4 years or (4 x 2) = 8 half-years, Face Value = $ 1000

Semi-Annual Coupon = 1000 x 0.08 x 0.5 = $ 40

Bond Price = 40 x (1/0.035) x [1-{1/(1.035)^(8)}] + 1000 / (1.035)^(8) = $ 1034.37

(c) The 5th Coupon Payment is made 2.5 years from now. This implies that post this there is another 2.5 year or 5 half-years of bond tenure remaining.

Bond Price after 5th Coupon Payment = Sum of Present Values of Remaining Coupon Payments + Present Value of Face Value all calculated at year 2.5

Bond Price = 35 x (1/0.042) x [1-{1/(1.042)^(5)}] + 1000 / (1.042)^(8) = $ 969.012

NOTE: Please raise separate queries for solutions to the remaining unrelated questions, as one query is restricted to the solution of only one complete question with a maximum of four sub-parts.