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%