Question

You just bought a 7-year zero coupon bond for $742.77. What is the (expected) taxable capital gain on this bond a year from now?

Question 7 options:

	$14.33
	$18.51
	$22.47
	$32.23
	None of the above.

Answer 1

Years to maturity = 7

Price = 742.77

Face value = $1,000

Price = Face value * 1 / (1 + YTM)⁷.

742.77 = $1000 * 1 / (1 + YTM)⁷.

(1 + YTM)⁷ = 1.346312

Apply 'log' on both sides

Log(1 + YTM)⁷ = Log (1.346312)

7 * Log(1 + YTM) = 0.129145

Log(1 + YTM) = 0.0184493

Apply 'Antilog' on both sides

Antilog[Log(1 + YTM)] = Antilog (0.0184493)

1 + YTM = 1.0433963

YTM = 0.0433963 or 4.33963%

Years remaining a year from now = 6

Price of the bond one year from now = Face value * 1 / (1 + YTM)⁶.

Price of the bond one year from now = $1,000 * 1 / (1 + 0.0433963)⁶

Price of the bond one year from now = $1,000 * 0.775

Price of the bond one year from now = $775

Capital Gain = $775 - 742,77

Capital Gain = $32.23