$($c$)$ Determine from this plot the approximate internal rate of return of for each flat sep$-$

arately and for the combined project. Determine also the cross$-$over rate for the two

flats.

Task $3$: Compare the investments in the two flats. Suppose the investor decides to

buy only one of the two flats, not both. Which flat would you recommend to the investor to

buy? Your analysis should be based on considerations such as

the size of the investment and the return for each flat;

the present value for each flat, whether these are positive or negative at the given

Interest rate, and how the present values depends on interest rate;

the yields from each of the two flats and the cross$-$over rate;

the payback period;

and any other considerations you think are relevant.

You should explain carefully how you came to your conclusion on which flat to chose. Any

relevant calculations, tables and$/$or charts for this task should be included in the 'Comparison

of Investments' worksheet.Task $1$: Compute the Net Present Value $(NPV)$ of the cash flow at the given

Interest rate.

$($a$)$ In the worksheet 'Cash flow and $NPV\text{'},$ create a table in which, for each flat, the

following are displayed: monthly rental income, monthly maintenance costs, monthly

tax payment, net monthly income, present value at time zero of net monthly income,

for months starting from time zero to the end of the cash flow. There should be one

row in the table for each month. Calculate the NPV of the rental income streams $($after

income tax$)$ from flat $1$ and from flat $2,$ separately.

$($b$)$ Compute the NPV of the sale of each of the two flats, after capital gains taxes.

$($c$)$ Compute the NPV of total cash flow for each of the two flats separately, and the NPV

of the investment project as a whole.

Be careful about how you apply rent increases on the two flats: one has a percentage increase

and the other has a total annual increase that is a fixed amount of money. Similarly, be

careful about the increases in maintenance payments: one has a percentage $($of the previous

maintenance$)$ increase, whereas the other increases by a percentage of the amount that the

rent increases.

Task $2$: Compute the approximate Internal Rate of Return $($IRR$)$ for the invest$-$

ment project. The investor wants to assess the sensitivity of the investment project to shifts

in the interest rate. Put these calculations in the worksheet labelled $\text{'}$NPV vs interest rate'.

$($a$)$ Create a table in which you consider interest rate values ranging from $0\mathrm{.}5\%$ p$.$a$.$ effective

to an appropriate level, with increments of $0\mathrm{.}5\%($the template considers up to $10\%$

but you may consider a larger range if necessary$).$ Your table should include the NPV

of the initial investment in each flat, the NPV of the rental income streams $($net of

maintenance and taxes$)$ and the NPV of the sale of each flat $($net of capital gains tax$).$

And, for each value of the interest rate, compute the total NPV for each flat, and the

total NPV of the project.

Hint: there are several different ways you could do this. Excel functions like $=NPV$

or $=$SUMPRODUCT might be useful, but be careful, and be sure to check that your

table in this task is consistent with the NPV calculation you did in Task $1.$

$($b$)$ Make a chart of the NPV for flats $1$ and $2,$ and of the grand total for the whole

project, as a function of interest rate over an appropriate range. Include this chart in

your report.