Real Rate and IRR

Hi, This is quite a tricky one…. I think you’ve / question has missed out that the contribution of $20000 (4000 units x $5) is in current terms ( real cash flows).

It does use the Fisher equation ( real/ nominal) but is also about the sensitivity of cost of capital – e.g. what rate would the discount rate have to change by before the project is non viable.

We know we find the sensitivity of the cost of capital by using an IRR – because we find at what discount rate the NPV becomes zero.

So we need to find the annuity rate that would make NPV zero in this case – i.e. where:
Annual real cashflows ($20,000) * annuity discount factor = Investment outlay ($50,000)

Rearrange this to find approximate annuity discount rate = 50000/20000= 2.5
The annuity rate which is approx 2.5 is somewhere between 9% and 10%.
IRR calc using these two rates then tells us its 9,7%.

Note that this the real rate because we applied it to real cashflows of $20000 per year.
To convert it to a nominal money rate we need to apply Fisher equation:
=(1+nominal rate) = (1 + real rate) x (1 + inflation rate).

Nominal rate = (1+ .097) x (1.04) =1.141
Nominal rate = 1.141 -1 = 14.1%

This is the maximum nominal rate (if inflation is 4%) that would allow the project to be viable using inflated cashflows….if the nominal rate exceeds this e.g. 14.5% then you should find the NPV turns negative.

Hopefully thats the answer showing in you book (please can you post the book answer when you ask the question in future so I can be sure I’m guiding you correctly for the requirement of that question).

ps) You should go in for your exam – I doubt youll get much which is as complicated as this one.
The exam itself is an experience and it doesnt matter if you are not successful
Have you tried the Pearson practice assessment – that gives you a score under
timed conditions?

Cath