Question

You are considering opening a new plant. The plant will cost $97.4 million upfront and will take one year to build. After​ that, it is expected to produce profits of $28.5 million at the end of every year of production. The cash flows are expected to last forever. Calculate the NPV of this investment opportunity if your cost of capital is 7.5%. Should you make the​ investment? Calculate the IRR. Does the IRR rule agree with the NPV​ rule?

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Calculate the NPV of this investment opportunity if your cost of capital is 7.5%.

You are considering opening a new plant. The plant will cost $97.4 million upfront and will take one year to build. After that, it is expected to produce profits of $28.5 million at the end of every year of production. The cash flows are expected to last forever. Calculate the NPV of this investment opportunity if your cost of capital is 7.5%. Should you make the investment? Calculate the IRR. Does the IRR rule agree with the NPV rule? Here is the cash flow timeline for this problem: Years 0 1 2 2 3 4 Forever Cash Flow ($ million) -97.4 28.5 28.5 28.5 28.5 Calculate the NPV of this investment opportunity if your cost of capital is 7.5%.

Answer 1

Calculation of NPV
Cashflow from Year 2 in millions	$                                                           28.50
Cost of capital	7.50%
Horizon value at year 1=	Annual cash flow/cost of capital
Horizon value at year 1=	28.50/7.5%
Horizon value at year 1=	$                                                         380.00
PV of horizon value at Year 0=	Horizon value/(1+cost of capital)
PV of horizon value at Year 0=	380/(1+7.5%)
PV of horizon value at Year 0=	$                                                         353.49
Initial investment	$                                                           97.40
NPV=	PV of inflows - PV of initial investment
NPV=	353.49-97.40
NPV=	$                                                         256.09
Since NPV is positive, the project should be selected
Calculation of IRR
Cashflow from Year 2 in millions	$                                                           28.50		$                                                           28.50
Cost of capital-Assumed	23.00%		24.00%
Horizon value at year 1=	Annual cash flow/cost of capital		Annual cash flow/cost of capital
Horizon value at year 1=	28.50/23%		28.50/24%
Horizon value at year 1=	$                                                         123.91		$                                                         118.75
PV of horizon value at Year 0=	Horizon value/(1+cost of capital)		Horizon value/(1+cost of capital)
PV of horizon value at Year 0=	123.91/(1+23%)		118.75/(1+24%)
PV of horizon value at Year 0=	$                                                         100.74		$                                                           95.77
Initial investment	$                                                           97.40		$                                                           97.40
NPV=	PV of inflows - PV of initial investment		PV of inflows - PV of initial investment
NPV=	100.74-97.40		95.77-97.40
NPV=	$                                                             3.34		$                                                            (1.63)
IRR	=Lower rate + Difference in rates*(NPV at lower rate)/(Lower rate NPV-Higher rate NPV)
IRR	'=23%+ (24%-23%)*(3.34231/(3.34231-(-1.6338)
IRR	23.67%
IRR is higher than the cost of capital and hence project should be selected. Both rules agree.