Question

Your company is considering whether to invest in a new machine that costs $6m but will save the company $2.5m per year for the three years of its expected life. It will require an additional investment in inventory of $200 000. The marginal tax rate for companies 30% and depreciation for tax purposes is calculated on a straight line basis over three years. The machinery has an expected salvage value of $500 000. To keep the calculations simple, you decide to ignore inflation and use a real discount rate of 10%. Show that the machine project's NPV, IRR and Payback Periods are $83 621, 10.74% and 2.51 years respectively.

Answer 1

Please note: I think that the above given answers for NPV and IRR are incorrect except for payback period,so I have calculated the same and arrived at different answers which have been presented below:

Initial investment=machine+inventory=$(60,00,000+2,00,000)=$62,00,000

Pre-tax savings=$25,00,000

Tax rate=30%

Post tax savings=$25,00,000(1-0.3)=$17,50,000

depreciation on machine=$60,00,000/3=$20,00,000

tax shield on depreciation=$6,00,000

Expected salvage value=$5,00,000

Expected post tax salvage value=$5,00,000(1-0.3)=$3,50,000

Investment in inventory will be recovered at end of third year so it is an inflow.

Accordingly the cash flows for each period are as follows:

Year 0=-$(60,00,000+2,00,000)=-$62,00,000

Year 1 and 2=$(17,50,000+6,00,000)=$23,50,000

Year 3=$(17,50,000+6,00,000+3,50,000+2,00,000)=$29,00,000

Accordingly, NPV, IRR and Payback Period are calculated as follows:

1	2	3	4=2*3	5
year	cash flow($)	df @ 10%($)	pv	cumulative cash flow($)
0	-6200000	1.0000	-6200000	-6200000
1	2350000	0.9091	2136364	-3850000
2	2350000	0.8264	1942149	-1500000
3	2900000	0.7513	2178813	1400000
		NPV	57325
		IRR	10.51%
		payback	2.517

Notes:

1. To calculate DF the function power has been used in Excel where DF=POWER(1/1+rate,years)
2. For IRR we have used IRR function in Excel which has considered cash flows in column 2.
3. For payback we have made a separate column cumulative cash flow which is column 5. Then we calculated payback as:

Payback=2+(0+15,00,000)/(14,00,000+15,00,000)

=2+15,00,000/29,00,000

=2+0.517

=2.517 years