Question

A two-year coupon bond with a 5% coupon rate is valued at $916.79 and another two-year coupon bond with a 10% coupon rate is valued at $1,007.13. Given this information, what will be the value of a two-year bond with an 8% coupon rate? The par values of all three bonds are $1,000.

	A.	$1,076.95
	B.	$1,039.63
	C.	$970.99
	D.	$1,004.36
	E.	$937.89

Answer 1

Answer;

Option C $970.99

Alternative 1

Bond1 & Bond 2 Present value diffrence = $1007.13 - $916.79 = $90.34

Bond1 & Bond 2 Coupon Rate  diffrence = 10% - 5% = 5%

Present value Diffrence per 1% = $90.34/5 = $18.068

Bond 3 Present value = Bond 1 Present value + {(bond 3 coupon rate - Bond 1 Coupon rate ) x (Present value diffrence per 1%)}

= $916.79 + 3 x $18.068

= $916.79 + $54.204

= $970.99

Alternative 2

Step 1 calculate bond 1 & bond 2 IRR

Bond 1

Coupon rate = 5%

Coupon payment = $50

Redemption amount = $1000(at Par)

Present value = $916.79

Bond 2

Coupon rate = 10%

Coupon payment = $100

Redemption amount = $1000(at Par)

Present value = $1007.13

Step 2 Simple Average of IRR = 9.78% + 9.59%/2 = 9.68

Bond 3 Present value

Coupon rate = 8%

Coupon payment = $80

Discounting rate = 9.68%

Redemption Price = $1000

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