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A particular annuity will make payments of $1M every 8 months for a total of 20...

A particular annuity will make payments of $1M every 8 months for a total of 20 payments, with the first payment occurring 8 months from the start. The price of this instrument is $15 183 575.00. Determine its: (a) yield to maturity (b) Macaulay duration (c) modified duration.

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Answer #1

Create a timeline in excel from 0 to 160, put the value of $(15,183,575) in period 0 and 1,000,000 for everry 8 months of the payment and calculate the IRR which will be the YTM, in this case its calculated as 0.34%.

Time (t) Cash Flow Discount Factor Present Value %PV %PV x t
1 0.996577

So first column in the time period, second column is the cash flow, discount factor is calculated as 1/(1+0.34%)^Time period. Present Value is Discount factor * Cash Flow. % PV is the present value of that line divided by the total PV value. The sum of the column %PV*t gives the Macalaulay duration which in this case comes out to be 76.74.

Modified duration =Macaulay duration/(1+YTM)=76.477

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