Question
Asked Apr 14, 2019
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Compute the Macaulay duration under the following conditions:
a. A bond with a four-year term to maturity, a 10 percent coupon (annual payments), and a market yield of 8 percent.
b. A bond with a four-year term to maturity, a 10 percent coupon (annual payments), and a market yield of 12 percent.
c. Compare your answers to parts (a) and (b), and discuss the implications of this for classical immunization.  
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Expert Answer

Step 1

Part (a)

Let's assume that the bond has a face value of $ 1,000. (Please note that this assumption willm not have any impact on the final answers. This is just to facilitate our intermediate calculations).

Annual cashflows to bond holder per year for year 1, 2 & 3 = Annual coupon = 10% x Face Value = 10% x $ 1,000 = $ 100

Cash flows to the bond holder in year 5 = Annual coupon + Repayment of Face Value = 100 + 1,000 = $ 1,100

Yield = 8%

Discount factor for year N = (1+ yield)-N = 1.08-N

PV of cash flows, PV = Cash flows x Discount factor

Time weighted Present Value  of Cash flows, PVT = Present value of the cash flows x Year in which the cash flow occurs = PV x N

Step 2

Please see the table below. Please see the second row. That explains how each column has been calculated.

Year

Total Cash flows to the bond holder

Discount Factor

PV of cash flows

Time weighted PV of Cash flows

N

C

DF = 1.08^(-N)

PV = C x DF

PVT = PV x N

1

100.00

0.9259

92.59

92.59

2

100.00

0.8573

85.73

171.47

3

100.00

0.7938

79.38

238.15

4

1,100.00

0.7350

808.53

3,234.13

Total

1,400.00

 

1,066.24

3,736.34

Step 3

Price of the bond = Sum of Present value of the cash flows to the bond holder = $ 1,066.24

Macaulay's duration  =  Total...

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