Question

PROBLEM #2
You are considering purchasing bonds to add to your investment portfolio. Bond
A is a 15 year bond that pays a 12% annual coupon. Bond B is a 20 year bond that pays a
8% annual coupon. Assume both bond terms started 2 years ago and that the discount rate
is 10%.

A. What are both bonds worth today?

B. What is the total return on both bonds?

C. Would you purchase both, neither, or one of the bonds to add to your
portfolio? Why?

Answer 1

A) Value of bond today = Annual interest * ((1 - (1/(1+i)^n)) / i) + Par value * (1/(1+i)^n)

Assumed $100 bond par value

Bond A :

i (disount rate) = 10% or 0.10

Par value of bond (assumed) = $100

Annual coupon = Par value*Rate = $100*12%=$12

n (remaining years to maturity) = 13 years

Value of bond A today = $12 * ((1 - (1/(1+0.10)^13)) / 0.10) + $100 * (1 /(1+0.10)^13)

Value of bond A today = $12 * ((1 - 0.2897)/0.10) + $100 * 0.2897

Value of bond A today = ($12 * 7.1030) + $28.97

Value of bond A today = $85.2360 + $28.97

Value of bond A today = $114.2060

Bond B :

i (discount rate) = 10% or 0.10

Par value of bond (assumed) = $100

Annual coupon = Par value * Coupon rate = $100 * 8% = $8

n (balance years to maturity) = 18 years

Value of bond B today = $8 * ((1 - (1/(1+0.10)^18)) / 0.10) + $100 * (1/(1+0.10)^18)

Value of bond B today = $8 * ((1 - 0.1799)/0.10) + $100 * 0.1799

Value of bond B today = ($8 * 8.2010) + $17.99

Value of bond B today = $65.6080 + $17.99

Value of bond B today = $83.5980

B) Total return on bonds (YTM)

YTM = (C + ((P - M) /n)) / ((P + M) /2)

Bond A:

Here, C (Coupon) = $100 * 12% = $12

P (Par value) = $100

M (Market price) = $114.21

n (year to maturity) = 13 years

YTM = ($12 + (($100 - $114.21)/13)) / (($100 + 114.21)/2)

YTM = ($12 - $1.0931) / $107.1050

YTM (return on bond A) = 0.1018 or 10.18%

Bond B :

P (Par value) = $100

M (Market price) = $83.60

n (years to maturity) = 18 years

C (Coupon) = $100 * 8% = $8

YTM = ($8 + (($100 - $83.60)/18)) / (($100 + $83.60)/2)

YTM = ($8 + 0.9111) / 91.80

YTM (return on bond B) = 0.0971 or 9.71%

C) Bond B is to be choosen.

As lower price of bond than it's par value means it is issued at discount & it's yield is higher than coupon rate. Hence this type of bond is to be choosen.

Bond B price $83.60 than it's par value $100 which means issued at discount & having higher yield @ 9.71% than coupon rate @ 8%.

Bond A price $114.21 than par value $100 which means issued at premium & hence it should not be hold for longer time.