Question

3) Consider a 5-year risk-free bond with annual coupons of 6% and a face value of $1,000. a) If this bond is currently priced at $1,068.94, what is its yield to maturity? b) If the yield to maturity on this bond increased to 5.2%, what would be the new price?

Answer 1

a) We have following formula for calculation of bond’s yield to maturity

Bond price P0 = C* [1- 1/ (1+YTM) ^n] /YMT + M / (1+YTM) ^n

Where,

M = value at maturity, or face value = $ 1,000

P0 = the current market price of bond = $1,068.94

C = coupon payment = 6% of $1000 = $60

n = number of payments = 5 (years)

YTM = interest rate, or yield to maturity =?

Now we have,

$1,068.94 = $60 * [1 – 1 / (1+YTM) ^5] /YTM + $1,000 / (1+YTM) ^5

By trial and error method we can calculate the value of YTM, which is 4.43% per annum

Therefore yield to maturity of the bond is 4.43%

b)

Bond price P = C* [1- 1/ (1+YTM) ^n] /YMT + M / (1+YTM) ^n

Where,

M = value at maturity, or face value = $ 1,000

P = the new market price of bond =?

C = coupon payment = 6% of $1000 = $60

n = number of payments = 5 (years)

YTM = interest rate, or yield to maturity =5.2%

Now we have,

P = $60 * [1 – 1 / (1+5.2%) ^5] /5.2% + $1,000 / (1+5.2%) ^5

= $258.34 + $776.11

= $1,034.45

Therefore new price of the bond is $1,034.45