$($From the CT$1$ exam, Sept $\text{'}08)$ An insurance company is considering two

possible investment options.

The first investment option involves setting up a branch in a foreign coun$-$

try. This will involve an immediate outlay of $0\mathrm{.}25m,$ followed by invest$-$

ments of $0\mathrm{.}1m$ at the end of one year, $0\mathrm{.}2$m at the end of two years,

$0\mathrm{.}3m$ at the end of three years and so on until a final investment is made

of $1m$ in ten years time. The investment will provide annual payments

of $0\mathrm{.}5m$ for twenty years with the first payment at the end of the eighth

year. There will be an additional incoming cash flow of $5m$ at the end

of the $27$ th year.

The second investment option involves the purchase of $1$ million shares in

a bank at a price of $4\mathrm{.}20$ per share. The shares are expected to provide

a dividend of $21p$ per share in exactly one year, $22\mathrm{.}05$p per share in two

years and so on$,$ increasing by $5\%$ per annum compound. The shares are

expected to be sold at the end of ten years, just after a dividend has been

paid, for $5\mathrm{.}64$ per share.

Determine which of the options has the higher net present value at a rate

of interest of $7\%$ per annum effective.$($From the CT$1$ exam, Sept $\text{'}08)$ An insurance company is considering two

possible investment options.

The first investment option involves setting up a branch in a foreign coun$-$

try. This will involve an immediate outlay of $0\mathrm{.}25m,$ followed by invest$-$

ments of $0\mathrm{.}1m$ at the end of one year, $0\mathrm{.}2$m at the end of two years,

$0\mathrm{.}3m$ at the end of three years and so on until a final investment is made

of $1m$ in ten years time. The investment will provide annual payments

of $0\mathrm{.}5m$ for twenty years with the first payment at the end of the eighth

year. There will be an additional incoming cash flow of $5m$ at the end

of the $27$ th year.

The second investment option involves the purchase of $1$ million shares in

a bank at a price of $4\mathrm{.}20$ per share. The shares are expected to provide

a dividend of $21p$ per share in exactly one year, $22\mathrm{.}05$p per share in two

years and so on$,$ increasing by $5\%$ per annum compound. The shares are

expected to be sold at the end of ten years, just after a dividend has been

paid, for $5\mathrm{.}64$ per share.

Determine which of the options has the higher net present value at a rate

of interest of $7\%$ per annum effective.