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. |
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
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 |
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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