**Difficulty: **Easy

**Prize: **Free access to our FAST Financial Modelling online training course worth £395, plus the self-respect and admiration of your peers

__Introduction__

Net present Value (NPV) is a key metric used by investors to calculate the attractiveness of a potential investment. Investopedia defines NPV as follows:

Net Present Value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows. NPV is used in capital budgeting to analyze the profitability of a projected investment or project.

The following is the formula for calculating NPV:

where

Ct = net cash inflow during the period t

Co = total initial investment costs

r = discount rate, and

t = number of time periods

__The Challenge__

Whilst the concept of NPV is generally well understood by modellers and investors alike, it is amazing how often in our model review work we find NPV’s calculated incorrectly which have a material impact on the viability of the project (To find out more about how to model NPV try the Financial Modelling Handbook website).

The challenge is simple, based upon the simple cashflow model provided, calculate the NPV of the future pre-tax, pre-financing cashflows of the project.

Assume NPV base date of 30^{th} June 2016 and nominal discount rate of 8%.

__Instructions and Guidelines__

- 1. Download the template model from here (or above).
- 2. Based on the cashflows in the model, found on the ‘Cashflow’ sheet, calculate the NPV as per above.
- 3. If you are brave enough, post your answer (the calculated NPV plus your decision to invest or not) as a comment otherwise you can e-mail me your answer and calculations to danny.leitch@f1f9.com
- 4. The winner will be selected using a complex Excel based randomiser algorithm.
- 5. The answer will be posted next week on this blog.

[…] thanks to those of you who took the time to complete my NPV modelling challenge #4. And special thanks to those that had the bravery to go public with their […]

NPV is EUR90.958 mil

Invest given that NPV is positive

Hi Tanja Groth, your comments on the conversion of the discount rate are spot on. We’ll have a little to say on that topic soon but I would raise the question now: what does “nominal discount rate 8%” actually mean? And so how should you convert it to a semi annual rate.

Equally, what does “semi annual” mean? A lot of the solutions we received effectively assumed 180 days in each semi annual period…Watch this space – more to come.

Thanks for the responses so far guys. I’ve received an interesting spread of results so far…….

I’ll now be marking homework next week, so still time for any more responses.

I’ve calculated NPV as 90,958 (EUR k). We should invest given IRR of 11.2% is higher than discount rate of 8.0%?

Fascinating little exercise. A nominal (annual) discount rate of 8% gives a semi-annual discount rate of 4% and a NPV of 85,074 EURk for the base date of 30th June 2016.

Conversely, aggregating the biannual values into annual ones and using the nominal discount rate of 8% gives you a NPV of 92,854 EURk for the base year of 2016 – throwing some doubt over the standard approach of dividing the discount rate by number of periods… any insight you can provide on the implications for financial modelling of annual versus monthly cashflow statements?

And yes – if I had 200,000EURk to invest, and a financing cost of less than 3% in real terms, this would appear to be a good investment.

Adjusting for the effective discount rate (rather than simply dividing by number of periods) gives an NPV of £91,185 which is my final answer. Still gives a discrepancy against the annual value, although a smaller one. May the force be with us all!

There were three other challenges? Were are those at?

Ken, you’re the first person to ask…….

It was a cynical ploy on my part to create intrigue (star wars style) by going straight to 4.

I’ll be coming back to do 1, 2 and 3 at some point soon (probably wont be as good as 4,5 and 6).

5 and 6 are in the pipeline and will be out in the next few weeks. I’ll make sure you get them.