Question

Part A Bank ABC is offering a bond that pays $100 in interest at the end of each of the next three years and repays $1,000 in principal at the end of the 3'd year. The interest rate is I2%. Calculate the bond's selling price. Part B Is this bond being offered at a discount, at a premium or at par?

Part C What is the coupon rate on this bond?

Part D What is the return on this bond if it is sold within 2years when the YTM decreases down to 10%?

Answer 1

Ans Let coupon be C = $100

Par value of the bond, F = $1000

Years to maturity, n = 3 years

Yield to maturity, y = 12% or 0.12

A) Price of the bond from bond price formula,

P = C*[(1-1/(1+y)^n)/y] + F/(1+y)^n

=> P = 100*[(1-1/(1+0.12)^3] + 1000/(1+0.12)^3

=> P = 240.183 + 711.780 = $951.963

B) As the selling price if the bond, $951.963, is less than its par value, $1000, so, the bond is selling at a discount.

C) Coupon rate on the bond = C/F = 100/1000 = 0.1 or 10%
D) When yield to maturity, y' = 10% or 0.1

Years to maturity = 1 year

So, price at which the bond was sold, P' = 100*[(1-1/(1+0.1)^2)/0.1] + 1000/(1+0.1)^2

=> P' = $1000

So, interest earned, i, can be calculated using bond price formula for keeping the bond for 2 years,

P = C*[1-1/(1+i)^2)/i] + P'/(1+i)^2

=> 951.963 = 100*[1-1/(1+i)^2)/i] + 1000/(1+i)^2

=> i = 12.875%
So, the interest earned if the bond is sold in the market within 2 years is 12.875%

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