Question

4. Two years ago, you purchased a zero coupon bond with a 5-year time to maturity, a 6% YTM, and a par value of $1,000. The bond’s YTM today is 5%. If you sell the bond today, what is the annual rate of return on your investment?

Answer 1

The price of zero coupon bond 2 years back can be calculated using the PV function in excel

2 years back,

Rate = 6%

NPER = 5years

PMT = Coupon = 0

Future Value = Par Value = $1000

Type = 0

PV =PV(6%,5,0,1000,0)

= - $747.26 (Negative sign is indicative of Cash outflow to purchase the bond)

Today,

Rate = 5%

NPER = 3 years

PMT = No coupons = 0

FV = 1000

Type = 0

PV =PV(5%,3,0,1000,0)

= - $863.84

If you were sell the bond today, the returns can be calculated using compound interest formula

FV= PV (1+r)^t

here,

PV = Purchase price of the bond = 747.26

t = 2 years

FV = Selling Price of bond 2 years later = 863.84

Rate r = (FV/PV) ^(1/t) -1

= (863.84/747.26)^(1/2) - 1

= 1.156^0.5 -1

= 1.0752 -1

= 7.52%

The annual rate of return would be 7.52%