Question $1(15$ marks$)$

$1\mathrm{.}1$ Mr Shikale has decided to sell a small mini market building that he has been her main business premises situated in a prime area in Rehoth town. There is a buyer who is willing to pay N$$1000000$ at closing of the transaction or will pay the amounts at the beginning of each of the next five years as follows:

Beginning of year Cash flow

$1$ N$$160000$

$2200000$

$3240000$

$4280000$

$5260000$

Because Mr Shikale really doesn$$t need the money today he plans to let it accumulate in an account that earns $7\%$ annual interest. Given his desire to buy a residential building at the end of $5$ years after closing on the sale of the mini market building, he has two payment options: N$$1000000$ lump sum or mixed stream of payments as shown in the table.

Required

$1\mathrm{.}1\mathrm{.}1$ What is the future value of the lump sum at the end of year five? $[1$ mark$]$

$1\mathrm{.}1\mathrm{.}2$ What is the future value of the mixed stream at the end of year five? $[3$ marks$]$

$1\mathrm{.}1\mathrm{.}3$ Based on your findings in $1\mathrm{.}1\mathrm{.}1$ and $1\mathrm{.}1\mathrm{.}2$ which alternative should Mr Shikale a take? $[1$ mark$]$

$1\mathrm{.}1\mathrm{.}4$ If Mr Shikale could earn $10\%$ rather than $7\%$ on the funds, would your recommendation in $1\mathrm{.}1\mathrm{.}3$ change? Explain. $[4$ marks$]$