CFA Level 1: Spot and Forward Rates

Calculating the Price of a 3-Year Zero-Coupon Bond

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Question

Given the following spot and forward rates, how much should an investor pay for a 3-year, annual zero-coupon bond with a face value of $1,000?

The investor should pay approximately:

Answers

Explanations

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A. B. C. D.

B

The yield to maturity on an N-year zero coupon bond is equivalent to the N-year spot rate.Thus, to determine the present value of the zero-coupon bond, we need to calculate the 3-year spot rate.

Using the formula: (1 + Z3)3= (1 +1f0) + (1 +1f1) + (1 +1f2)

Where Z = spot rate andnfm= The n year rate m periods from today, (1f0= the 1 year spot rate now)

(1 + Z3)3= (1.035) * (1.115) * (1.1975)

Z3= 1.38191/3- 1 = 0.11386, or 11.39%

Then, the value of the zero coupon bond = 1,000 / (1.1139)3= 723.62, or approximately$724. or, using a financial calculator, N = 3, I/Y = 11.39, FV = 1,000, PMT = 0, Compute PV = 723.54, or approximately$724.

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