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# Calculating NPV, IRR and incremental IRR

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1. Front up cost of plant is \$100 million. Profits of \$30million at the end of every year. Calculate the NPV if the cost of capital is 8%. Should you take the investment? Calculate the IRR and use it to determine the maximum deviation allowable in the cost of capital estimate to leave the decision unchanged.

2. Upfront costs \$5 million. Profits expected \$1million for 10 yrs. The company will provide support expected to cost \$100,000/year in perpetuity. Assume all profits and expenses occur at end of year.

a. What is the NPV if cost of capital is 6%? Should firm take project? Repeat for discount rates of 2% and 12%.
b. How many IRRs does this investment opportunity have?
c. Can the IRR rule be used to evaluate this investment? Explain

Year end Cash Flow (\$thousands)
Project 0 1 2 IRR
Playhouse -30 15 20 10.4%
Fort -80 39 52 8.6%

You can undertake only one project. If your cost of capital is 8% use the incremental IRR rule to make the correct decision.

#### Solution Preview

Please refer attached file for better clarity of tables and graphs.

1.
Discount rate=r=8%
Annual Cash inflow=C=\$30
PV of perpetuity =C/r=30/8%=\$375 million
But this is value at the end of year 1,

PV of cash inflows=375/(1+8%)=\$347.22 million
PV of outflows=\$100

NPV of project=PV of inflows-PV of outflows=347.22-100=\$247.22 million.
It is positive value, it should be accepted.

Now calculate IRR
At IRR, NPV=0 i.e. PV of cash inflows=PV of cash outflows
So, PV of Inflows=PV of cash outflows=\$100

Let IRR=r
PV of inflows=(30/r)/(1+r)
(30/r)/(1+r)=100
30/[r*(1+r)]=100
30=100r+100r^2
10r^2+10r-3=0
r=(-10+sqrt(10^2-4*10*-3))/(2*10)=0.2416

Internal rate of return=24.16%

If the cost of capital estimate is off by 16.16% (24.16%-8%), then the decision might change from accept to reject.

2.

Year End Cash Outflow Cash Inflow Net Cash flow PV of cash Flows at (PV=C/(1+r)^n)
(n) C ...

#### Solution Summary

There are three problems. Solutions to these problems depict the methodology to calculate NPV, IRR and incremental IRR.

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