MAN321 – QUIZ 3 – SPRING 2020
Student Name / ID: Ismail Eren Ozsoy 21702985
1. A bond with a face value of $1,000 has 10 years until maturity, carries a coupon rate of 8.7%, and sells for
$1,130. Coupons are paid annually.
a.
If the bond has a yield to maturity of 9.3% one year from now, what will its price be at that time?
After a year, N = 9,
Coupon payment = 8.7% x 1000 = 87
FV = 1000
Yield of maturity = 9.3%
Compute PV = $964.46 is the price after a year
b.
Using your answer given in a., find the annual rate of return on the bond in the first year?
Annual Rate of Return = (P1 + C) / P0 - 1 = (964.46 + 87) / 1130 - 1 = -6.95%
c.
If the inflation rate during the first year is 3%, what is the real annual rate of return on the bond?
Real Rate = Nominal Rate - Inflation = -6.95% - 3% = -9.95%
2. Suppose today, there are three zero coupon bonds that are selling in the market each with a face value of
$1000. The first bond has one-year maturity with the price of $925.9. The second bond has two years maturity
with a price of $907. The third bond has three years of maturity with a price of $839.6. Suppose that there exists
a fourth bond which has a coupon rate of 4% (paid annually), a face value of $1000, and has a time to maturity
of three years. Calculate this bond’s price.
Yield rate of maturity = normal rate of return
We use 3rd bond to find YTM
YTM = (par value/price)1/ maturity year – 1
= (1000/839.6) – 1
= 0.060 or 6%
4th bond has same maturity so we use same YTM
BP = Cp (1-(1+YTM)maturity year) / YTM + Par value (1+ YTM) maturity year
Cp = 4% x 1000 = 40, YTM = 0.06, years to maturity = 3 and par value 1000
4th bond = 40 (1/0.06 – 1/0.06(1.06)3 ) + 1000 / (1.06)3 = 946.54