Financial Exercises 3: NPV and IRR

by Clemens Werkmeister

1. NPV and NPV-function

Project I requires an investment of 500 € and has expected cash flows of 300 € both in year 1 and 2.
a. Calculate the net present value (NPV) assuming a cost of capital of 10 %.
b. Plot a graph (NPV-function) showing the investment’s NPV for costs of capital between 0 % and 20 %.
c. Estimate the cost of capital that corresponds to a NPV of zero (the internal rate of return – IRR).
d. A similar project II requires an investment of 600 € and has expected cash flow of 360 € in year 1 and 350 € in year 2. Plot its NPV-function and estimate its IRR.

2. Calculating IRRs

The following table shows the investments (in year 0) and expected cash flows (years 1 to 3) for the projects A to D:

year	A	B	C	D
0	-500	-600	-600	-600
1	600	400	300	400
2		350	300	400
3			200	-50

a. Calculate the exact internal rates of return of projects A and B.
b. Estimate the IRR of projects C and D using the Newton-method or the trial-and-error approach.
c. Which one is the best project assuming a cost of capital of 10 %?
d. You have to choose between A and B. What is the critical cost of capital for changing from B to A?

3. IRR and Effective annual rate

Your bank offers you a special credit over 20.000 €, paid out with a discount (disagio) of 2 %. Interest is 6 % per year, amortization is due after two years. The bank charges annual service fees of 200 € in year 1 and 2.
a. Determine the payments associated with that credit.
b. Calculate the effective annual rate (internal rate of return).
c. The bank offers you a floating rate credit with 12-months-Euribor + 3 % as interest rate. In the first year this results in an interest rate of 5 %. What is the maximum Euribor rate for the second year that results in the same average effective rate than the 6%-fixed-rate-credit of a?

4. Nominal and real rates

A project requires an initial investment of 500 €. The expected cash flows of 300 € in year 1 and 316 € in year 2 already reflect an expected inflation rate of 3 % per year.
a. Calculate the IRR and the NPV assuming a cost of capital of 10 %.
b. Calculate the inflation-adjusted (“real”) cash flows and the real cost of capital.
c. Calculate the IRR and the NPV based on the inflation-adjusted figures.
d. Adjust the original IRR for the inflation rate and compare it to the IRR of the inflation-adjusted cash flows.

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References:
For some useful formulae you might have a look at our Financial Resources Formulary.
For further exercises we suggest our Financial Exercises.