Can anyone help?? I do not really understand what both of them mean either?
If the initial cost of an investment is £10 mil with annual rental of £1m, annual maintenance of £100,000. Over 3yrs with nominal rate of interest of 5% and annual rate of inflation at 2%. How would you work out the annual rate of return? And also the real rate of return after allowing for inflation. I am stuck please help.

For proper guidance, first clarify exactly what those cash flows are. I can see that the initial investment is 10M--no problem there.

The "annual rental" of 1M--I'd assume this is the annual income produced by the investment. Just confirm or correct that one for me.

"Annual maintenance" of 0.1M: Sounds like an expense item. Are we thus saying (in conjunction with the "rental" item above) that the investment is producing a NET return of 900K per year?

The "over 3 years" part is a little unclear--I doubt you're describing an investment that costs 10M to get into, then returns just 900K per year for 3 years, and then it's game over (unless you were talking about an investment in a dot-com start-up a few years ago). Or maybe the "maintenance" expense only lasts for 3 years, but the income goes on indefinitely?

So re-describe the scenario a bit and let us see exactly what kind of cash flows you're describing.

As to the latter part of your question, an investment's "real" rate of return , given a particular nominal rate and expected inflation rate , is given by

. Check back in and we'll deal with the investment.

Thanks for that it is an exam question so it is not a real life scenario I will write you the full question as it may explain it better.

A developer funds a £10m office development in the city centre which has a current annual rental of £1m. This is expected to rise in line with inflation, as are annual maintenance costs of £100,000 which are the responsibility of the developer under the term of the lease.

The lease runs out in three years time, and the current tenants have indicated they will probably be looking for larger premises at that time. The current nominal rate of interest is 5% and the annual rate of inflation is 2%.

You are require to find:
1. the annual rate of return on the original investment
2. the real rate of return after allowing for inflation
3. the present value of the three year project
4. the net present value of the three year project
5. the estimated value of the building in three years time if offered for sale.

I hope this is a bit clearer. I just do not understand this at all and my lecturer as not given any notes on this topic apart from npv and pv so I am unsure on the others. Your help greatly appreciated.

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!

Thank you for making this a lot clearer I will put this into practice and see if I understand better. Thank you.