Question

Suppose there is a 3-year bond with a $1000 face value, 30% annual coupon payments and a 20% annual yield to maturity. 4) 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

price of bond is calculated using the PV function of EXCEL

duration of bond = sum of product of weight of cash flows from bonds and time until the cash flow is received

for part d) new price of bond when the interest rate increases is calculated using the duration rule

according to which:

% change in price = -d*% increase in interest rate

where d = modified duration = duration calculated in part c/(1+y)

y = YTM(yield to maturity) of bond