The Desreumaux Company has two bonds outstanding. Both bonds pay $100 annual interest plus $1,000 at...

The Desreumaux Company has two bonds outstanding. Both bonds pay $100 annual interest plus $1,000 at maturity. Bond L matures in 10 years, whereas Bond S matures in one year. One interest payment remains on Bond S. What will be the values of these bonds when the going rate of interest is (a) 4 percent and (b) 6 percent?

Expert Solution

(a) Calculation of price of bond @ 4% YTM

Bond L
Annual coupon =	100
Maturity	10	Years

Annual Interest received =		100.00
Cumulative P.V.F. @ 4 % for 10 periods=
(1- ((1/(1.04)^10)))/0.04		8.11089578

Present value of interest received			$811.09

Maturity amount received =		1000
P.V.F. @ 4% for 10th period =
(1/(1+0.04)^10)		0.67556417
Present value of Maturity amount			$675.56

Price of bond			$1,486.65


Bond S
Annual coupon =	100
Maturity	1	Years

Annual Interest received =		100.00
Cumulative P.V.F. @ 4 % for 1 periods=
(1- ((1/(1.04)^1)))/0.04		0.96153846

Present value of interest received			$96.15

Maturity amount received =		1000
P.V.F. @ 4% for 1st period =
(1/(1+0.04)^1)		0.96153846
Present value of Maturity amount			$961.54

Price of bond			$1,057.69

So, at 4% interest price of bond L is$1,486.65 and Bond S is $1,057.69.


(b) Calculation of price of bond @ 6% YTM

Bond L
Annual coupon =	100
Maturity	10	Years

Annual Interest received =		100.00
Cumulative P.V.F. @ 6 % for 10 periods=
(1- ((1/(1.06)^10)))/0.06		7.36008705

Present value of interest received			$736.01

Maturity amount received =		1000
P.V.F. @ 6% for 10th period =
(1/(1+0.06)^10)		0.55839478
Present value of Maturity amount			$558.39

Price of bond			$1,294.40


Bond S
Annual coupon =	100
Maturity	1	Years

Annual Interest received =		100.00
Cumulative P.V.F. @ 6 % for 1 periods=
(1- ((1/(1.06)^1)))/0.06		0.94339623

Present value of interest received			$94.34

Maturity amount received =		1000
P.V.F. @ 6% for 1st period =
(1/(1+0.06)^1)		0.94339623
Present value of Maturity amount			$943.40

Price of bond			$1,037.74

So, at 6% interest price of bond L is $1,294.40 and Bond S is $1,037.74.

jeff jeffy answered 1 year ago

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