Much clearer... thanks.
With a test question (as with homework), we can't land the plane for you, but we'll help you get the plane lined up with the runway as you make your approach.
You've got an initial outlay of 10 M, and then a NET annual
inflow starting at 900 K (1 M of income, and 100K of expense). Since both the income (rent) and expense (maintenance) are expected to rise with inflation, it's the same as saying that the NET inflow of 900K will increase each year with inflation. So from here on we can treat the rent (IN) and maintenance (OUT) as a single net "IN" amount.
The fact that the current tenants will probably bail after 3 years is kind of a wild card here. In most situations of this nature, the analysis assumes that replacement tenants will be obtained, and the inflation-growth cash flows will continue indefiitely. I'm going with that premise, but check your text carefully to see if the author assumes a different approach, as other assumptions could also be considered valid.
For Question (1), find in your text a discussion for something called the
Gordon Growth model, or the
constant-growth model. It'll have this form, with possibly different notation:
where
P is the Present value of an investment;
is the cash flow occurring one year away;
r is the rate of return; and
g is the expected annual growth of the cash flows. This model gives the value of an investment in which the annual cash returns are growing by a constant factor each year, and are expected to continue indefinitely. (Do you see how this fits your scenario?)
Notice that in your case,
P = 10 M;
= 900 K;
g = 0.02 (inflation rate); and
r is what your question is asking for. Usually when you use this model, you know
,
r, and
g, and you're trying to find
P. But in this case we know
P (10M), and we want to find the
rate of return r. So solving this equation for
r rearranges it to
. Hit the ol' calculator with that one to find
r, which will be the project's annual rate of return, assuming the cash flows continue to grow at 2% indefinitely.
The answer you got for Q (1) is called the
nominal rate of return. To turn that nominal return into a
real return, see my earlier post. That'll take care of Q (2).
Answering Q (3) is simply a matter of discounting the first 3 years' cash flows by the given discount rate of 5%. Remember that the first year's CF is 900K, but that it grows by 2% each year for Years 2 and 3.
Your Q (3) answer is the
Present Value of the first three years' cash flows. To get the project's 3-year NET present value (Q (4)), deduct the project's initial outlay from the Q(3) present value. Hint: It'll be large and negative.
For Q (5), the value of the building three years away will be the value of a growing cash flow stream, so you'll go back to that Gordon growth formula I gave you earlier in this post. Now you're using it to find
P, the value of the building 3 years from today, so use the formula in its original form. Remember that
will now be the Year 4 cash flow--which you can easily determine, recalling that Year 1 cash flow = 900K, and it grows by 2% per year thereafter. Also in the formula,
g is still 2%, and use the given 5% discount rate for
r.
Best of luck with it!