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I can't seem to get the correct answer as the back of the course reader.

+2 votes
44 views
asked Oct 18, 2016 in BUS 2016H - Financial Mathematics by Nolwazi
The question number is 2.22 and the answer is supposed to be R76.77. Please could somebody help.

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1 Answer

+2 votes
answered Oct 18, 2016 by Richard van Gysen (3,020 points)
 
Best answer

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 receied 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 and begin at the end of year 10.

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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