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Question 1 from tut test 3

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asked Apr 17 in BUS 1003H - Introduction to Financial Risk by anonymous

A bond pays a coupon of R15 every 6 months and has a term of 10 years, at which time it will be redeemed at R100. The next coupon is due in 6 months’ time. The interest rate is 6% per 6 months. Calculate the price you would be willing to pay for this bond.

Solution :PV = R15 × 1 − 1.06−20 0.06 + R100v^20

              = R172.05 + R31.18

              = R203.23

Can someone please explain why the 6% interest rate that's payable per 6 months was used to calculate PV of the redemption value

3 Answers

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answered Apr 18 by Richard van Gysen (2,680 points)
 
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Following on from Pandy's description,

When in doubt about the interest rate, if they have not stated whether it is effective or nominal convertible (usually they do), assume it is the effective rate to the time unit given. So here it is just 6% effective half-yearly with Basic Time Units being every 6 months.

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answered Apr 17 by Daniel Campbell (140 points)

In this case they have present valued the R100 redemption payment using the 6% interest per 6 month period and since we are PV-ing for 10 years, they have raised v to the power of 20. (There are 20 6 month periods in 10 years). This is equivalent to calculating the yearly effective interest rate and using n = 10. 

+1 vote
answered Apr 17 by Pandy (1,620 points)

Hi there

In future please double-check your question before posting. Your formula doesn't seem to have come through correctly.

Given that the coupon pays R15 every 6 months for 10 years, we can consider 6 months to be our basic time unit, and so the 6% payable half-yearly is the correct interest rate to use. Effectively we're considering each half-year to be one time unit, thus 6% now applies to one of our time units, the same way an interest rate payable annually applies to one year. Importantly, don't forget to 'convert' the years into our new basic time unit i.e. 10 years in 6 month intervals is 20 basic time units. Thus, we get the formula:

\(PV=15a_{\overline{20|}@6\%}+100V^{20}=15\times \frac{1-(1+6\%)^{-20}}{6\%}+100(1+6\%)^{-20}=R203.23\)

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