Question

In: Finance

A company just issued a bond with the following characteristics: Maturity = 3 years Coupon rate...

A company just issued a bond with the following characteristics:

Maturity = 3 years

Coupon rate = 8%

Face value = $1,000

YTM = 10%

Interest is paid annually and the bond is noncallable.

Calculate the bond’s Macaulay duration ?Round "Present value" to 2 decimal places and "Duration" to 4 decimal place.?

Calculate the bond’s modified duration

Assuming the bond’s YTM goes from 10% to 9.5%, calculate an estimate of the price change without considering convexity

Calculate the convexity of the bond.

Solutions

Expert Solution

Macaulay Duration

Period Cash Flow Period * Cash flow PV @8% PV of cash flow
1 80 80 0.926 74.08
2 80 160 0.857 137.12
3 1080 3240 0.794 2572.56
Total 2783.76

Macaulay Duration = Sum of PV of cash flow / Face value of bond

= 2783.76 / 1000 = 2.7837 Years

Modified Duration

Modified Duration = Macaulay Duration / [1 + (YTM/2)]

= 2.7837 / [1 + (0.1 / 2)]

= 2.6511 years

Price Change

factor change in yield = 0.095 / 0.1 = 0.95

assuming price of bond is $1000

New price = 1000 / 0.95 = $1052.63

Change in price = $52.63

Covexity of bond

convexity of bond = [P(i decreases) + P(i Increases) - 2*FV] / [2 * FV * dY^2]

where P(i decreases) - price of bond in case of decrease in interest rate

P (i increases) - price when interest rate increases

FV - Face value of bond

dY = change in interest rate

dY = 0.5% = 0.005

if YTM increases from 10% to 10.5%, then

Price of bond = $952.38 (calculation is done as per above mentioned method and assumption)

Convexity of bond = [1052.63 + 952.38 - 2*1000] / [2*1000*0.005^2]

= 5.01 / 0.05 = 100.2


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