Question

Consider a bond with one year remaining to maturity, a $1,000 face value, an 8 percent coupon rate (paid semiannually), and an interest rate (either required rate of return or yield to maturity) of 10 percent.

a.How much is the present value of the bond?

b.How much is the Duration of the bond?

c.How much is the modified Duration of the bond?

d.Use the duration computed above, calculate the change of the bond price in percentage if the required return moves up by 50 basis points.

Answer 1

Solution :

The calculation is done on the excel sheet and screenshot is attached

Method:

1. Find the Cash flow for all the periods
2. Find the discounting factor using formula DF = 1/ (1+yield )^time
3. Find the discounted cash flow and add the CF this will give the price of the bond
4. Multiply discounted CF with time and add all the values and then divide with the price of the bond to find the duration
5. Divide Duration with (1+ effective yield) to get modified duration

Part A ) Price of the bond = 983.59

Part B ) Duration = 0.98

Part C ) Modified duration = 0.93

Part D ) Since Modified duration is 0.93, it means if the yield goes up by 100 basis points then the bond price will fall by 0.933 %.

Here yield is moving up by 50 bps so chance in price = 0.933 / 2 % = 0.47%

Price will fall by 0.47%