Question

Problem 1 (15 marks) Four and a half years ago, you purchased at par, a 10-year 6% coupon bond that pays semi- annual interest. Today the market rate of interest is 4% and you are considering selling the bond. a. What was the market rate of interest at the time you purchased the bond? b. Suppose you wish to sell the bond today i. How much should you sell the bond for? ii. What is the current yield on the bond? iii. What will be your effective annual holding period return on the bond? C. Suppose your friend offers you a price of $1125 for the bond today. Would you be willing to sell the bond to her? Explain your answer. Problem 2 (15 marks) The Weatherfield Way Construction Company has common and preferred stock outstanding. The preferred stock pays an annual dividend of $7.50 per share, and the required rate of return for similar preferred stocks is 11%. The common stock paid a dividend of $3.00 per share last year, but the company expected that earnings and dividends will grow by 25% for the next two years before dropping to a constant 9% growth rate afterward. The required rate of return on similar common stocks is 13% a) What is the per-share value of the company's preferred shares? b) What is the per-share value of the company's common stock? (7 marks) c) Calculate the expected market price of the share in one year. (3 Marks) d) Calculate the expected dividend yield and capital gains yield expected at the end of the first year? (3 marks)

problem one

Answer 1

It looks like the Par Value of the Bond is 1000 $.

a) A bond is priced at Par only when the coupon rate and its yield/discount rate is same. At the coupon rate is 6% paying semi annual interest, the Market Interest Rate at the time of purchase should also be equal to 6% Per Annum (Compounded semi annually) i.e. 3% for every 6 months. The calculation is shown below:

Time Period	Cash Flow	PV Factor @ 3.00%	PV
1	30	0.9709	29.126
2	30	0.9426	28.278
3	30	0.9151	27.454
4	30	0.8885	26.655
5	30	0.8626	25.878
6	30	0.8375	25.125
7	30	0.8131	24.393
8	30	0.7894	23.682
9	30	0.7664	22.993
10	30	0.7441	22.323
11	30	0.7224	21.673
12	30	0.7014	21.041
13	30	0.6810	20.429
14	30	0.6611	19.834
15	30	0.6419	19.256
16	30	0.6232	18.695
17	30	0.6050	18.150
18	30	0.5874	17.622
19	30	0.5703	17.109
20	1030	0.5537	570.286
		Total Price	1000.000

b) i) As 4.5 years have passed, only 5.5 years are left to maturity i.e. 11 coupon payments of 3% each. As the market interest rate today is 4%, the value of the bond today is 1097.868 $ considering a discount rate of 2% (4%/2) for every six months. The calculation are shown below:

Time Period	Cash Flow	PV Factor @ 2.00%	PV
1	30	0.9804	29.412
2	30	0.9612	28.835
3	30	0.9423	28.270
4	30	0.9238	27.715
5	30	0.9057	27.172
6	30	0.8880	26.639
7	30	0.8706	26.117
8	30	0.8535	25.605
9	30	0.8368	25.103
10	30	0.8203	24.610
11	1030	0.8043	828.391
		Total Price	1097.868

b) ii) The Current Yield of the bond is 4% Per Annum (Compounded Semi Annually) which is the current Market Interest Rate.

Another meaning of Current Yield = Interest or Coupon Payment/Current Value of Bond = 30/1097.868 = 2.73% Per 6 Months or 5.47% (2.73% * 2) Per Annum (Compounded Semi Annually)

b) iii) As we have received 9 coupons of 30 $ and current value is 1097.868, the holding period return is 3.9275% per 6 months i.e. 7.855% (3.9275% * 2) Per Annum (Compounded Semi Annually)

Time Period	Cash Flow	PV Factor @ 3.9275%	PV
0	-1000	1.0000	-1000.00
1	30	0.9622	28.87
2	30	0.9258	27.78
3	30	0.8909	26.73
4	30	0.8572	25.72
5	30	0.8248	24.74
6	30	0.7936	23.81
7	30	0.7636	22.91
8	30	0.7348	22.04
9	30	0.7070	21.21
9	1097.87	0.7070	776.20
		Total	0.00

c) As the friend is offering a Price of 1125 $ which is more than the current value of the Bond i.e. 1097.87 $, The Bond should be sold to the friend for 1125 $.