Question

Consider a bond with a market price of $1049.73, a face value of $1,000, maturity of 3 years and a coupon rate of 12%. The YTM on this bond is 10%. What is the realized annualized rate of return on this investment if all cash flows are reinvested at 20% per year for the next three years? Please put your answer on the blank line on the answer sheet. Round your answer to 4 places to the right of the decimal.

Answer 1

Coupon = Face Value*Coupon Rate = 1000*12% = $120

FV of All Coupons at the end of 3rd year = FV of Annuity = P*[{(1+i)^n}-1]/i

Where, P = Annuity = 120, i = Interest Rate = 0.2, n = Number of Periods = 3

Therefore, FV = 120*[{(1+0.2)^3}-1]/0.2 = 120*0.728/0.2 = $436.8

Holding Period Return = [Maturity Value or Face Value-Purchase Price+FV of All Coupons]/Purchase Price = [1000-1049.73+436.8]/1049.73 = 387.07/1049.73 = 0.368733 = 36.8733%

Note: Realized Annualized Rate of Return is calculated UNDER 2 DIFFERENT ASSUMPTIONS.

Realized Annualized Rate of Return(Average Annual Return) = Holding Period Return/Holding Period = 0.368733/3 = 0.122911 = 12.2911%

Realized Annualized Rate of Return(Compounded Annual Return):

Holding Period Return = [(1+Compounded Annual Return)^Holding Period]-1

Therefore,

0.368733 = [(1+R)^3]-1

1.368733^1/3 = 1+R

Therefore, R = 1.110298-1 = 0.110298 = 11.0298%