Question

Suppose you purchased a ten year, 8% coupon code (annual coupon payment) at $980. Two years later, you decide to take a vacation and sell the bond to acquire the necessary funds. At the time you sell the bond, 8 year bonds with similar characteristics sell for yields 9%. What is your realized yield on the bond?

Answer 1

Given:

for 10 year bond

coupon rate = 8%= 0.08

assuming par value of bond = $1000

purchase price of bond = $980

coupon value = coupon rate*par value of bond = 8%*1000 = 0.08*1000 = $80

Now in the first year only the coupon yield will be received since the holding period of bond is 2 years and the bond will be sold at the end of 2 years

Return in 1 st year from bond, R1 = coupon value/purchase price of bond = 80/980 = 0.081632653 = 8.1632653%

in the second year of the bond since the bond will be sold at the end of this year, the return will include both the coupon and the capital gain from selling the bond

for selling price of bond

it is given that , another bond with maturity of 8 years coupon 8% sells for yield 9%

we will calculate the price of this bond

Price of bond,P =

Where Y = yield on the bond = 9% = 0.09

n = maturity of bond = 8 years

C = coupon value =$ 80

M = par value of bond = $1000

P = C*(PVIFA) + M/(1+Y)ⁿ

PVIFA = present value interest rate factor

PVIFA for 9% yield and maturity 8 years =

putting the values in the above mentioned formula

PVIFA =

= 0.992563/0.179331 = 5.534819

substituting the value to calculate price of bond

P = 80*5.534819 + 1000/((1.09)⁸) = 442.7855 + 501.8663 = 944.6518

Now calculating the 2nd year return on the 10-year bond purchased

Return in 2nd year, R2 = (coupon value + (selling price of bond - purchase price of original bond))/purchase price of bond

=( 80 + (944.6518 - 980))/980 = (80 - 35.3481911)/980 = 0.045563 = 4.5563%

Holding period return for 2 years = [(1+R1)*(1+R2)] - 1 = [(1.081633)*(1.045563)] - 1 = 0.130915 = 13.09152%

This is the realized yield on the bond after 2 years