Question

Yield to maturity Moe’s Inc. has bonds outstanding with a par value of $1000 and 10 years to maturity. These bonds pay a coupon of $45 every six months. Current market conditions are such that the bond sells for $938. Calculate the yield to maturity on the issue.

Duration A newly issued 5-year Altec Corp. bond has a price of $1,095.99, a par value of $1,000, and pays annual interest at a 12% coupon rate. Find the duration of the bond.

Answer 1

Solution:

Yield to maturity

Face Value (F) = $1,000

Coupon rate (C) = $45 per six months = $45 * 2 = $90 per year

Current Yield (P)= $938

Years (n) = 10

Yield to maturity = {C + [(F - P) / n]} / [(F + P) /2]

= {90 + [(1000 – 938) / 10]} / [(1000 + 938) / 2]

= 10%

Duration

Duration = {SUM[(t * c) / (1 + t)ⁱ] + [(n * m) / (1 + t)ⁿ} / P

t = time in years until maturity = 5 years

c = coupon payment amount = $120 ($1,000 * 12%)

i = interest rate = 12% = 0.12

n = no. of coupon payments made = 1

m = par value = $1,000

P = bond’s current market price = $1,095.99

Duration = {[(5 * 120) / (1 + 0.12)⁵] + [(4 * 120) / (1 + 0.12)⁴] + [(3 * 120) / (1 + 0.12)³] + [(2 * 120) / (1 + 0.12)²] + [(1 * 120) / (1 + 0.12)¹] + [(5 * 1000) / (1 + 0.12)⁵]} / $1,000

= (340.46 + 305.05 + 256.25 + 191.33 + 107.14 + 2837.20) / $1,000   

= 4.037 years