Question

Suppose there is a 3-year bond with a $1000 face value, 30% annual coupon payments and a 20% annual yield to maturity.

a) Without any calculation, briefly explain whether this bond will be selling a premium or a discount.

b) Calculate the price of this bond.

c) Calculate the duration of this bond.

d) Suppose the interest rates in the economy rise by 5 percentage points immediately after someone bought this bond. Show a calculation using duration for what should happen to the price of this bond immediately.

e) Suppose now one year passes and the interest rates in the economy are still 5 percentage points higher. If the person that owns this bond sells it for fair value, what would be their one year rate of return? Show a calculation.

Answer 1

Answer:

A. Here, coupon rate is greater than the yield to maturity thus the bond will be selling for a premium.

B. Price of bond can be calculated using the following formula

P = C(P/A,i%,3) +M(P/F,i%,3)

P = 300(P/A,20%,3) + 1,000(P/F,20%,3)

P = 631.944 + 578.7037

Price of bond = $ 1,210.65

C. Duration of bond = 2923.61/1210.65 = 2.4149

D. Price of bond will decline by = duration of bond*percent Change in interest rate

= 2.4149 *0.05 = 0.12074

= 12.074%

New price of Bond = $ 1210.65(1-0.12074)

Price of bond = $ 1,064.48

As soon as interest rate increases the price of bond decreases.

E. Price after 1 year = 300(P/A,25%,2)+1000(P/F,25%,2)

= 432 + 640

= $ 1072

So the person will be selling it for a price of $ 1072.

The person has purchased the bond at a price of

1. When price = $ 1210.65

Return = (1072-1210.65)/1210.65 = - 11.45%

2. When price = $ 1064.48

Return = (1072-1064.48)/1064.48 = 0.706%