Question

2. Determine the Price of the Bond at each time period. If you purchase the bond today (at time =0) and hold it until maturity, what is the interest yield, capital gain yield, and total return the you will earn? Time Periods Remaining Price Face Value Coupon Rate Discount Rate Time $1,000 8.00% 6.00% 3 years w 3. Beans Corp just paid a dividend of S4.00. The dividend will grow at a rate of 15% for 2 years and then settle down to a more normal 6% growth rate, that will last indefinitely. If investors expect a 9% return on the stock what should the selling price be today?

Answer 1

Part A)

Coupon payment = 8% per year so 4% per semi-annual hence $40 received after every 6 months.

Discount Rate = 6% so 3% per semi-annual.

Discounted payment = (Coupon Payment + Principal Repayment) / (1+Discount Rate)^Time

Capital Gain : Total Price - Face Value

Interest Yield% = Capital Gain / Face Value

Face Value	$1,000	Time	Coupon Payment	Discounted Payment	Capital Gain	Interest Yield
Coupon	8%	1	40	38.83	54.17	5.42%
Discount	6%	2	40	37.70
Time	3 Years	3	40	36.61
		4	40	35.54
		5	40	34.50
		6	40	870.98
			TOTAL PRICE	1054.17
Face Value	$1,000	Time	Coupon Payment	Discounted Payment	Capital Gain	Interest Yield
Coupon	8%	1	40	38.83	45.80	4.58%
Discount	6%	2	40	37.70
Time	2.5	3	40	36.61
		4	40	35.54
		5	40	897.11
			TOTAL PRICE	1045.80
Face Value	$1,000	Time	Coupon Payment	Discounted Payment	Capital Gain	Interest Yield
Coupon	8%	1	40	38.83	37.17	3.72%
Discount	6%	2	40	37.70
Time	2	3	40	36.61
		4	40	924.03
			TOTAL PRICE	1037.17
Face Value	$1,000	Time	Coupon Payment	Discounted Payment	Capital Gain	Interest Yield
Coupon	8%	1	40	38.83	28.29	2.83%
Discount	6%	2	40	37.70
Time	1.5	3	40	951.75
			TOTAL PRICE	1028.29
Face Value	$1,000	Time	Coupon Payment	Discounted Payment	Capital Gain	Interest Yield
Coupon	8%	1	40	38.83	19.13	1.91%
Discount	6%	2	40	980.30
Time	1
			TOTAL PRICE	1019.13
Face Value	$1,000	Time	Coupon Payment	Discounted Payment	Capital Gain	Interest Yield
Coupon	8%	1	40	1009.71	9.71	0.97%
Discount	6%
Time	0.5
			TOTAL PRICE	1009.71

For Part B:

Now, the dividend for next year will be = 4 x 1.15 = $4.6

Dividend for the year after will be = $4.6 x 1.15 = $5.29

Present value for next year's dividend of $4.6 will be = (4.6 / 1.09^1 = $4.22 ) (Formula=Dividend / (1+Growth Rate)^Period)

Present value for the year after's dividend will be = (4.45 / 1.09^2 = $4.45) (Using same formula as above)

Now, the present value for dividend received thereafter is:

Dividend in the next year / (Required Rate - Growth Rate)

= 5.29 x 1.06 / ( 0.09 - 0.06 )

= 186.91

But note that this is the present value of dividend received after 3 years, so we again need to discount this figure to present value:

= 186.91 / 1.09^3

=$144.33

So, the total price would be = $4.22 (present value of dividend received after 1 year) + $4.45 (present value of dividend received after 2 year) + $144.33 (present value of dividend after 3 years)  = $153