Question

You bought a 25-year ABC bond that has a coupon rate of 9 percent and sells at a yield to maturity of 8 percent. You hold this bond for 1 year before selling.

a. If in one year the yield to maturity for this bond is 10 percent, what is your rate of return?

b. What is your real rate of return if the inflation rate is 3%?

Answer 1

face value = 1000

Yield to maturity(i)= 8%

Coupon rate = 9%

Coupon Amount = 1000*9%= 90

Years to maturity (n)= 25

Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n

90*(1-(1/(1+8%)^25))/8% + 1000/(1+8%)^25

1106.747762

So, purchase price shall be $1106.747762

Calculation of sales price (Price after 1 year)

face value = 1000

Yield to maturity(i)= 10%

Coupon rate = 9%

Coupon Amount = 1000*9%= 90

Years to maturity (n)= 25-1= 24

Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n

90*(1-(1/(1+10%)^24))/10% + 1000/(1+10%)^24

910.1525598

Bond sale price will be $910.1526

Rate of return formula = (Sale price - purchase price+coupon received)/Purchase price*100

(910.1526-1106.7478+90)/1106.7478*100

-9.631390277

Rate of return is -9.63%

(b) real rate of return =((1+Nominal rate of return)/(1+Inflation rate)) -1

((1+(-9.6314%))/(1+3%) ) -1

-0.1226349515 or -12.26%

So, real rate of return is -12.26%