2015 test 1 question 2

Question

could you please explain where the 0.5 used in the calculation for j comes from.

and the two n values 2/12 an 3 4\12

Answer 1

The coupons are paid on the 1st of June and the 1st of December. You know this because there is always a coupon on the redemption date and can therefore work backwards. (Coupons are not necessarily paid on valuation date). So draw a timeline with this information and see if you can see where those n figures come from. If this still doesn't help just comment below and I'll explain it fully. 

The 0.5 for the interest rate, remember that the annuity formula has to have the interest rate that relates to the time period of payments. ie since the coupons are paid every 6 months you need an effective 6 months (0.5 of a year) interest rate. 

Comments

Can you please explain further?

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So using the annuity in arrears it takes the PV back to the 1st of June 2014 but you need the evaluation on the 1st of August. Therefore you have to take it forward for 2 months. That's how you get the 2/12 

For the 3 4/12 n value: if you count the number of years and months between the 1st of August 2014 and 1st of December 2017 you get 3 years 4 months which is how long you have to discount the redemption value by. 

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So one does not need to take it back all the way to the start of the coupons and then bring it forward to the present value?

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Are you talking about the redemption value?

If you are, you can do that but you'll get the same answer. But it's just easier to take it back straight to the valuation date. 

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I took the coupons and the redemption back and then brought them forward as one value.

On that note about taking everything back, would the coupons then be in advance?

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That's perfectly fine. Did you get the right value?

No because the payments are still only being starting on the 1st of December(end of the 6 months). There is no payment on the 1st of June 2014. 

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Okay, so that is where I went wrong.  When I looked at the memo I didn't understand why it wasn't in advance. Now I do.

Thank you very much.