Question

Big Maple Corp. wants to buy a new, more efficient sawmill. After their market research they have found three possible options. Sawmill A would cost $130,000 today, enjoy annual savings of $54,000 and last for 6 years. Sawmill B would cost $320,000, enjoy annual savings of $78,000 and last for 10 years. Sawmill C would cost $382,000, enjoy annual savings of $76,000 and last for 14 years. Assuming a discount rate of 11.7%, which sawmill should Big Maple purchase?

Answer 1

In case of different lifes, selet the project with higher equated NPV.

Equated NPV = NPV / PVAF(r%, n)

NPV :
NPV is the difference between Present value of Cash Inflows and Present value of cash outflows.

NPV = PV of Cash Inflows - PV of Cash Outflows
If NPV > 0 , Project can be accepted
NPV = 0 , Indifference point. Project can be accepted/ Rejected.
NPV < 0 , Project will be rejected.

PVAF = SUm [ PVF(r%, n) ]
PVF(r%, n) = 1 / ( 1 + r)^n
r = Int rate per period
n = No. of periods

How to calculate PVAF using Excel:
=PV(Rate,NPER,-1)
Rate = Disc Rate
NPER = No.of periods

Sawmiil A:

Year	Cash Flow	PVF @11.7 %	Disc CF
0	$            -130,000.00	1.0000	$           -130,000.00
1 - 6	$                54,000.00	4.1466	$            223,915.25
NPV			$              93,915.25

Equated NPV = NPV / PVAF(r%, n)

= $ 93915.25 / 4.1466

= $ 22648.85

Sawmiil B:

Year	Cash Flow	PVF @11.7 %	Disc CF
0	$            -320,000.00	1.0000	$           -320,000.00
1 - 10	$                78,000.00	5.7203	$            446,182.70
NPV			$            126,182.70

Equated NPV = NPV / PVAF(r%, n)

= $ 126182.70 / 5.7203

= $ 22058.79

Sawmiil C:

Year	Cash Flow	PVF @11.7 %	Disc CF
0	$            -382,000.00	1.0000	$           -382,000.00
1 - 14	$                76,000.00	6.7312	$            511,571.31
NPV			$            129,571.31

Equated NPV = NPV / PVAF(r%, n)

= $ 129571.31 / 6.7312

= $ 19249.36

Sawmill A is selected as it has higher equated NPV.