Zero-Coupon Bond Valuation

EXERCISE 01

Face value is €1,000, maturity is 20 years and annual YTM is 6%.

P=\frac{1{,}000}{1.06^{20}}

Price = €311.80.

With a positive yield and no coupons, the price is below par. A negative yield would imply a price above par.

EXERCISE 02

A zero-coupon bond has face value €100 and matures in 8 years. The required annual yield is 4.00%.

P=\frac{F}{(1+y)^n},\quad y=\left(\frac FP\right)^{1/n}-1

P=\frac{100}{1.04^8}

€73.07.

EXERCISE 03

A zero-coupon bond has face value €100 and matures in 5 years. Its price is €78.35.

P=\frac{F}{(1+y)^n},\quad y=\left(\frac FP\right)^{1/n}-1

y=\left(\frac{100}{78.35}\right)^{1/5}-1

5.0007%