Question

You bought a 10-year zero-coupon bond with a face value of $1,000 and a yield to maturity of 3.4% (EAR). You keep the bond for 5 years before selling it.

The price of the bond today is P0=F(1+r)T=1,0001.03410=P0=F(1+r)T=1,0001.03410= 715.8

If the yield to
maturity is still 3.4% when you sell the bond at the end of year-5,
what is your personal *annual rate* of return?

Answer #1

Price of a zero-coupon bond is the present value of future cash flows discounted at required rate of return. As far as a zero-coupon bond is concerned, it does not pay any coupon payments, it pays only a lump sum amount on its maturity.

**Value of zero-coupon bond =
Face vale / (1+required return) ^{time to
maturity}**

= 1000 / (1+.034)^10

= 1000 / 1.39702889108

= **$715.80**

**P5 =** 1000 /
(1+.034)^5

= 1000 / 1.18195976712

= **$846.05**

**Investor's total return** comprises of 2
elements-**capital gain/loss** (change in market
price) and **coupon payment.**

**Rate of Return = (Sale value
- cost of acquisituion + coupon pay) / cost of
acquisituion**

**=**
(846.05-715.80)/715.80

**HPR =**
**18.20%**

annual rate of return = (1+HPR)^(1/5)-1

= 1.1820^(1/5) -1

= 1.0340070392-1

= **3.40%**

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