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Question regarding increasing annuities.

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asked May 7 in BUS 1003H - Introduction to Financial Risk by anonymous

This is from our course reader and the answer is R76,77. I keep on getting 72.64, please help:

image

Thanks

1 Answer

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answered May 8 by Richard van Gysen (2,680 points)
 
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This question is best done with a timeline and breaking the cashflows into three separate parts.

1) At the end of the 5th year, we receive R12 and it increases by 10% for the next 5 years (6 payments in total). I interpret this as R12 received at the start of year 6 and increases (annuity in advance) by 10% and I can create a geometric increasing annuity and PV it to end of year 5 (start of year 6).

2)The dividends are constant at \(R12*(1.1)^5\) for five more years after year 10. They start at the end of year 11 and end at the end of year 15.

3) The R150 redeemed at the end of year 15.


Thus,

\( PV = (12*\ddot{a}_{\bar{6|}j}) *v^5 + 12*(1.1)^5*({a}_{\bar{5|}i})v^{10} + 150v^{15} \)

where j = (i-g)/(1+g) = (13.5% - 10%)/(1+10%) = 3.1818%

Subbing in i and j,

PV = R76.77

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