Question

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1.

A zero-coupon bond has a face value of $1,000 and matures in 2 years. An auction reveals that investors require a(n) 7.0% annual return on this bond. What should be the price of this bond? Round to the nearest cent. Numeric Answer:

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Answer 1

For a zero coupon bond,

F Zero Coupon Bond Value (1r) F face value of bond T rate or yield t time to maturity

a)

$Value = \frac{1000}{(1 + 0.07)^2}$

Value = 1000/1.1449

Value = $873.4

b)

$80 = \frac{100}{(1 + r)^8}$

(1 + r)⁸ = 1.25

1 + r = 1.0283

r = 2.8%

c)

YTM = 3%

$P_1 = \frac{1000}{(1 + 0.03)^4}$

$P_1 = 888.49$

YTM = 6%

$P_2 = \frac{1000}{(1 + 0.06)^4}$

$P_2 = 792.09$

% Change = (P2 - P1)/P1 = (792.09 - 888.49)/888.49 = -10.8%