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

Thanks

Login

0 votes

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 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

- All categories
- BUS 1003H - Introduction to Financial Risk (41)
- BUS 2016H - Financial Mathematics (50)
- BUS 3018F - Models (69)
- BUS 3024S - Contingencies (57)
- BUS 4028F - Financial Economics (20)
- BUS 4027W - Actuarial Risk Management (39)
- BUS 4029H - Research Project (5)
- Mphil (1)
- Calculus and Pure Mathematics (3)
- Statistics (16)

...