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- February 12, 2015 at 11:38 pm #228186
I have a question that I can not solve even seeing an answer at my study question bank ,

question info are next:Debentures have $100 value at par

coupon rate/year of redemption/date of redemption/dates of int.payments/MP July 2005

6% 2010 1 April 1April/1October unlistedMarket evidence suggests that the 6% 2010 debentures have a six-monthly gross redemption yield (i.e. internal rate of return maturity) of 6% . The prevailing level of market interest rates can be assumed to remain unchanged over the next 6 years.

required:Estimate the price on 1 July 2005 that an investor should be prepared to pay for 6% 2010 debentures

answer :

PV=3/0.06(1-1/1.06^9)+$3How did they get to this formula, and is it a very basic , this is the first time i see it here , Can u give me some hint

February 13, 2015 at 9:26 am #228224The MV of debentures is the present value of the future receipts discounted at the required rate of return.

Here, the future receipts on $100 nominal are $6 a year, therefore $3 every six months (since the interest is payable six-monthly) for a total of 9 payments. The required return is 6% every six months. So the PV is $3 per period discounted for 9 periods at 6% per period. You can discount using the 6% annuity factor for 9 periods (from the tables). Instead of using the tables, the answer (for some reason!) has calculated the annuity factor by using the formula which is at the top of the tables (but will give the same figure as in the tables).

I don’t know which study text you got this from, but the question is rather ‘over-the-top’ for Paper F9. In F9 we assume generally that the interest is every year rather than every six months.

February 14, 2015 at 10:03 pm #228401Thank you for this reply , I have been confused with calculating PV using this formula , most of the time I like to use tables to get present values . Another thing that I have been questioning myself is the second part of this question or I could say an answer , the calculation of the interest have been done getting the figure of 23.41 and at par value of 56.19 and the question is what is the value in July 1st . Answer goes like this

(23.41+59.19) / 1.0296 = 80.23

Without any explanation how did they get to the figure of 1.0296

I get that 23.41+59.19 is the present value at the October 2005 and we want the present value in July 1 that is three months in reverse , how did they get to the figure of 1.0296 I really cant figure it outPlease Help

Thanks

February 15, 2015 at 8:57 am #2284192.96% is the 3-monthly interest.

If r is the 3 monthly interest, and 6% is the 6-monthly interest, then:

(1+r)^2 = 1.06

(squared, because there are two 3 month periods in 6 months)So (1+r) = square root of 1.06, which is 1.0296

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