How is present value index calculated?

Congratulations! You have just become the new head of your department. Upon arriving to move into your new office, you find a memo on your desk. You have your first assignment. You have been asked to develop a proposal for a new piece of equipment that your superiors believe will make your area much more efficient and effective. There are three possible alternatives that you are to consider.

Having had an amazing Managerial Accounting class in your MBA program, you know exactly what to do. You will compare these three alternative purchases using the following and develop a table to compare them, highlighting the strongest in each measure. Then you will write a memo to the CFO with your recommendation, your rationale, a table showing the results, and an appendix that shows each computation in full detail.

a. Present value index (how is this calculated?)

You are excited about this opportunity and cannot wait to get started, because you know that you will make a polished presentation and make a great impression!

Use a discount rate of 12%.

	Alternative A	Alternative B	Alternative C
Cost	$1,000,000	$1,250,000	$2,000,000
Setup Costs	$0	$50,000	$50,000
Training costs	$10,000	$25,000	$35,000
Annual maintence costs	$10,000	$15,000	$16,000
Anticipated annual savings	$125,000	$190,000	$225,000
Annual labor savings	$25,000	$0	$40,000
Expected useful life in years	8	9	7
Overhaul costs in year 4	$45,000	$50,000	$35,000

Calculation of payback period:

Particulars	Alternative-A (in $)	Alternative-B (in $)	Alternative-C (in $)
Initial Investment
Cost	10,00,000	12,50,000	20,00,000
Setup Cost	0	50,000	50,000
Training cost	10,000	25,000	35,000
Total Initial Investment	10,10,000	13,25,000	20,85,000
Net Annual Cash Inflows
Annual savings	1,25,000	1,90,000	2,25,000
Annual Labor Savingd	25,000	0	40,000
Total savings (A)	1,50,000	1,90,000	2,65,000
Annual maintenance cost (B)	10,000	15,000	16,000
Net Annual Cash Inflows (A)-(B)	1,40,000	1,75,000	2,49,000
Payback Period =Net investment/Annual Cash flow	7.21	7.57	8.37
Ranking	1	2	3

Calculation of Net Present value

Particulars	Alternative-A (in $)	Alternative-B (in $)	Alternative-C (in $)
Initial Cash Outflow (Step-1)	10,10,000	13,25,000	20,85,000
Overahall expesnes in 4th year	45,000	50,000	35,000
PVF @ 12%	0.636	0.636	0.636
PV of ovehall expenses	28,620	31,800	22,260
PV of total cash outflows	10,38,620	13,56,000	21,07,260
PV of Net cash Inflows
Net Annual Cash Inflows (Step-1) (A)	1,40,000	1,75,000	2,49,000
No of Years	8	8	7
PVAF @12% (B)	4.967	4.967	4.564
PV of cash in flows (A)*(B)	6,95,380	8,69,225	11,36,436
Net Present value=PV of cash inflows-PV of cash outflows	(3,43,240)	(4,86,775)	(9,70,824)
Ranking	1	2	3

Calculation of Accounting rate of return:

Particulars	Alternative-A (in $)	Alternative-B (in $)	Alternative-C (in $)
Average Annual Profit:
Annual Cash Inflows	1,40,000	1,75,000	2,49,000
No of Years	8	9	7
Total Inflow over period	11,20,000	15,75,000	17,43,000
Less: Overhaul cost	45,000	50,000	35,000
Less: Depreciation (No salvage value)	10,10,000	13,25,000	20,85,000
Total Profit/(loss) of project	65,000	2,00,000	(3,77,000)
Useful life	8	9	7
Average Annual Profit	8125	22,222	Nil
Average Investment
Initial Investment	10,10,000	13,25,000	20,85,000
At the end salvage value	0	0	0
Average Investment=(initial investment+ At the end salvage value)/2	5,05,000	6,62,500	10,42,500
Accounting rate of return=Average Annual Profit/Average investment	1.6%	3.35%	O%
Ranking	2	1	3

Internal Rate of Return:

Particulars	Alternative-A (in $)	Alternative-B (in $)	Alternative-C (in $)
NPV @ 10%
Initial Outflows	10,10,000	13,25,000	20,85,000
Overhall expense at the end of 4th year	45,000	50,000	35,000
PVF @10%	.683	0.683	0.683
PV of Overhall expense	30,735	34,150	23,905
Total Initial outflows	10,40,735	13,59,150	21,08,905
Net annual cash flows	1,40,000	1,75,000	2,49,000
Annuity factor@10%	5.3349	5.7590	4.8684
Annuity cashflows	7,46,886	1007825	12,12231
NPV @10%	(293849)	(351325)	(8,96,674)
NPV @12%	(3,43,240)	(4,86,775)	(9,70,824)
IRR=10%+NPV1*(R2-R1)/(NPV1-NPV2)	10.93%	10.83%	10.96%
Ranking	2	3	1