The numbers provided are in millions of dollars and reflect market values:
-The short-term debt consists of 4-year bonds paying an annual coupon of 4 percent and selling at par.What is the duration of the short-term debt?
A)3.28 years
B)3.53 years
C)3.78 years.
D)4.03 years.

Question

The numbers provided are in millions of dollars and reflect market values: 
-The short-term debt consists of 4-year bonds paying an annual coupon of 4 percent and selling at par.What is the duration of the short-term debt?
A)3.28 years 
B)3.53 years 
C)3.78 years. 
D)4.03 years.

Quizplus · Accepted Answer

11efb87c_f0d9_68af_9137_b19ce6e3712a_TB1314_00 The duration of a bond is the weighted average of the times to maturity of its cash flows. The cash flows of a bond are its coupon payments and its face value. The weights are the present values of the cash flows divided by the present value of the bond.The present value of a cash flow is the amount of money that would have to be invested today at a given interest rate to grow to the amount of the cash flow at the time it is received. The present value of a bond is the sum of the present values of its cash flows.The duration of a bond can be calculated using the following formula:Duration = (PV1 / V) * (T1) + (PV2 / V) * (T2) + ... + (PVn / V) * (Tn)where:PV1, PV2, ..., PVn are the present values of the cash flowsV is the present value of the bondT1, T2, ..., Tn are the times to maturity of the cash flowsIn this case, the bond has a face value of $1,000, a coupon rate of 4%, and a maturity of 4 years. The bond is selling at par, which means that its present value is $1,000.The present value of the coupon payments is:PV1 = $40 / (1 + 0.04)^1 + $40 / (1 + 0.04)^2 + $40 / (1 + 0.04)^3 + $40 / (1 + 0.04)^4 = $150.99The present value of the face value is:PV2 = $1,000 / (1 + 0.04)^4 = $851.36The duration of the bond is:Duration = (PV1 / V) * (T1) + (PV2 / V) * (T2) = ($150.99 / $1,000) * (1) + ($851.36 / $1,000) * (4) = 3.28 yearsTherefore, the duration of the short-term debt is 3.28 years.

The Numbers Provided Are in Millions of Dollars and Reflect