Question

Jallouk Corporation has two different bonds currently outstanding. Bond M has a face value of $20,000 and matures in 20 years. The bond makes no payments for the first six years, then pays $900 every six months over the subsequent eight years, and finally pays $1,300 every six months over the last six years. Bond N also has a face value of $20,000 and a maturity of 20 years; it makes no coupon payments over the life of the bond. The required return on both these bonds is 5.4 percent compounded semiannually.

What is the current price of Bond M and Bond N?

Answer 1

The price of the bond is the sum of the present value of cash flows generated by the bond. The cash flows are discounted at yield to maturity for present value calculation.

For Bond M; we know that there is no cash flow for first 6 years, there after its pays coupon of $900 every six month for next 8 years and finally pays $1,300 every six months over the last six years

t = time to maturity = 20 years or 20*2 = 40 six-months

i = yield to maturity =5.4% per year; and six monthly yield to maturity = 5.4%/2 = 2.7%

F = value at maturity or face value = $20,000

Price calculation Bond M:

Time period (t) (Six Monthly)	Cash Flow from coupon payments	Cash Flow from maturity amount	Total Cash Flow from coupon payments and maturity amount (CF)	Present value (PV) discounted at 5.4%/2 (=CF/(1+2.7%)^t)
1	$0.0		$0.0	$0.00
2	$0.0		$0.0	$0.00
3	$0.0		$0.0	$0.00
4	$0.0		$0.0	$0.00
5	$0.0		$0.0	$0.00
6	$0.0		$0.0	$0.00
7	$0.0		$0.0	$0.00
8	$0.0		$0.0	$0.00
9	$0.0		$0.0	$0.00
10	$0.0		$0.0	$0.00
11	$0.0		$0.0	$0.00
12	$0.0		$0.0	$0.00
13	$900.0		$900.0	$636.54
14	$900.0		$900.0	$619.81
15	$900.0		$900.0	$603.51
16	$900.0		$900.0	$587.65
17	$900.0		$900.0	$572.20
18	$900.0		$900.0	$557.15
19	$900.0		$900.0	$542.51
20	$900.0		$900.0	$528.24
21	$900.0		$900.0	$514.36
22	$900.0		$900.0	$500.83
23	$900.0		$900.0	$487.67
24	$900.0		$900.0	$474.84
25	$900.0		$900.0	$462.36
26	$900.0		$900.0	$450.21
27	$900.0		$900.0	$438.37
28	$900.0		$900.0	$426.84
29	$1,300.0		$1,300.0	$600.34
30	$1,300.0		$1,300.0	$584.56
31	$1,300.0		$1,300.0	$569.19
32	$1,300.0		$1,300.0	$554.23
33	$1,300.0		$1,300.0	$539.66
34	$1,300.0		$1,300.0	$525.47
35	$1,300.0		$1,300.0	$511.66
36	$1,300.0		$1,300.0	$498.20
37	$1,300.0		$1,300.0	$485.11
38	$1,300.0		$1,300.0	$472.35
39	$1,300.0		$1,300.0	$459.93
40	$1,300.0	$20,000.0	$21,300.0	$7,337.73
sum				$21,541.53
				Bond's Price↑

The current price of Bond M is $21,541.53

Bond N is like zero coupon bond

Bond N price = F/ (1+i) ^t

Where,

Price of the bond N =?

Face value or Maturity value of the bond F = $20,000

i = yield to maturity = 5.4% per year and six monthly yield to maturity = 5.4%/2 = 2.7% as compounded semiannually.

And time period for maturity t =20 year or 20* 2 = 40 six-months

Therefore

Price of the bond N = $20,000 / (1+2.7%) ^40

= $ 6,889.89

Current price of the bond N is $ 6,889.89