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.
---
References:
Financial Resources Formulary
Financial Exercises
Newton-Verfahren