Question

Kebt Corporation's Class Semi bonds have a 12-year maturity and an 12.00% coupon paid semiannually (6% each 6 months), and those bonds sell at their $1,000 par value. The firm's Class Ann bonds have the same risk, maturity, nominal interest rate, and par value, but these bonds pay interest annually. Neither bond is callable. At what price should the annual payment bond sell?

	a.	$850.92
	b.	$909.60
	c.	$987.85
	d.	$978.07
	e.	$1,154.12

Answer 1

If any bond (issued at par and redeemable or callable at par) is selling at par, its yield will be its nominal coupon(Interest) rate. The reason for this is we are multiplying same interests and discounting at same rate.

We can cross check it, the price of the bond is the present value of future cash flow.

Present value = Annual cash flow X discount factor for the corresponding year.

discount factor for the corresponding year.= 1/(1+i)ⁿ here i = 6% or 0.06, n = curresponding semi-annual period,

for first semi annual period = 1/(1.06¹), 2^nd semi annual period =1/(1.06²), 2^rd semi annual period = 1/(1.06³), like that....

year	Coupon	Discount Factor			Discounted Cash flow
1	60	0.943396226415094			56.60377358490570
2	60	0.889996440014240			53.39978640085440
3	60	0.839619283032302			50.37715698193810
4	60	0.792093663238020			47.52561979428120
5	60	0.747258172866057			44.83549037196340
6	60	0.704960540439676			42.29763242638060
7	60	0.665057113622336			39.90342681734020
8	60	0.627412371341827			37.64474228050960
9	60	0.591898463530025			35.51390781180150
10	60	0.558394776915118			33.50368661490710
11	60	0.526787525391621			31.60725152349720
12	60	0.496969363577001			29.81816181462000
13	60	0.468839022242453			28.13034133454720
14	60	0.442300964379673			26.53805786278040
15	60	0.417265060735541			25.03590364413240
16	60	0.393646283712774			23.61877702276640
17	60	0.371364418596957			22.28186511581740
18	60	0.350343791129204			21.02062746775230
19	60	0.330513010499249			19.83078062995500
20	60	0.311804726886084			18.70828361316510
21	60	0.294155402722721			17.64932416336330
22	60	0.277505096908227			16.65030581449360
23	60	0.261797261234177			15.70783567405060
24	1060	0.246978548334129			261.79726123417700
		Price of the bond			999.99999999999900

The price = $1000

The first specified bond's Semi-annualized return = 6%, effective annualized return =1.06² =1.1236, i.e, 12.36%,

Present value = Annual cash flow X discount factor for the corresponding year.

discount factor for the corresponding year.= 1/(1+i)ⁿ here i = 12.36% or 0.1236, n = curresponding semi-annual period. For first semi annual period = 1/(1.1236¹), 2^nd semi annual period =1/(1.1236²), 2^rd semi annual period = 1/(1.1236³), like that....

Computation table is given below

Year	Coupon/ cash flow		Discount Rate @12%		Discounted cash flow
1	0.88999644		120		106.7995728
2	0.792093663		120		95.05123959
3	0.70496054		120		84.59526485
4	0.627412371		120		75.28948456
5	0.558394777		120		67.00737323
6	0.496969364		120		59.63632363
7	0.442300964		120		53.07611573
8	0.393646284		120		47.23755405
9	0.350343791		120		42.04125494
10	0.311804727		120		37.41656723
11	0.277505097		120		33.30061163
12	0.246978548		1120		276.6159741
			Price of the bond		978.0673364

Price of the bond ronded to 2 decimal = 978.07, The price of the bond is option d - $978.07