Question

Please show work, don't give me an excel based response, thank you! Consider a capital expenditure project to purchase and install new equipment with an initial cash outlay of $25,000. The project is expected to generate net after-tax cash flows each year of $6800 for ten years, and at the end of the project, a one-time after-tax cash flow of $11,000 is expected. The firm has a weighted average cost of capital of 12 percent and requires a 3-year payback on projects of this type. Determine whether this project should be accepted or rejected using NPV, IRR, PI, and PB.

Answer 1

Initial cash outlay	(25,000.00)	$
Annual after tax cash inflow	6,800.00	$
Life	10	years
Salvage	11,000.00	$
Rate	12%
Pay back period (PB)=	Initial outlay / Annual cash inflow
	25000/6800
	3.68	Years

	Project	1.12
	a	b	a*b
Year	Cashflow	PV factor 12% [1/(1+r)]^n	PV
0	(25,000.00)	1.000	(25,000.00)
1	6,800.00	0.893	6,071.43
2	6,800.00	0.797	5,420.92
3	6,800.00	0.712	4,840.11
4	6,800.00	0.636	4,321.52
5	6,800.00	0.567	3,858.50
6	6,800.00	0.507	3,445.09
7	6,800.00	0.452	3,075.97
8	6,800.00	0.404	2,746.41
9	6,800.00	0.361	2,452.15
10	17,800.00	0.322	5,731.12
		NPV of project	16,963.22
		Discounted inflow (a)	41,963.22
		Initial outflow (b)	25,000.00
		NPV of project (a-b)	16,963.22	$
		Profitability index(PI)	Discounted inflow/Outflow
			41963.22/25000
		PI	1.68

For IRR two different rates are taken to get negative and positive NPV
Here, we have taken 25% and 26% rates
	Project	1.25
	a	b	a*b
Year	Cashflow	PV factor 25% [1/(1+r)]^n	PV
0	(25,000.00)	1.000	(25,000.00)
1	6,800.00	0.800	5,440.00
2	6,800.00	0.640	4,352.00
3	6,800.00	0.512	3,481.60
4	6,800.00	0.410	2,785.28
5	6,800.00	0.328	2,228.22
6	6,800.00	0.262	1,782.58
7	6,800.00	0.210	1,426.06
8	6,800.00	0.168	1,140.85
9	6,800.00	0.134	912.68
10	17,800.00	0.107	1,911.26
		NPV of project	460.54
		Discounted inflow (a)	25,460.54
		Initial outflow (b)	25,000.00
		NPV of project (a-b)	460.54	$

	Project	1.26
	a	b	a*b
Year	Cashflow	PV factor 26% [1/(1+r)]^n	PV
0	(25,000.00)	1.000	(25,000.00)
1	6,800.00	0.794	5,396.83
2	6,800.00	0.630	4,283.19
3	6,800.00	0.500	3,399.36
4	6,800.00	0.397	2,697.91
5	6,800.00	0.315	2,141.19
6	6,800.00	0.250	1,699.36
7	6,800.00	0.198	1,348.70
8	6,800.00	0.157	1,070.40
9	6,800.00	0.125	849.52
10	17,800.00	0.099	1,764.88
		NPV of project	(348.66)
		Discounted inflow (a)	24,651.34
		Initial outflow (b)	25,000.00
		NPV of project (a-b)	(348.66)	$

IRR of the project is when NPV of project = 0
NPV of the project at 25%	460.54
NPV of the project at 26%	(348.66)
Difference	809.20
IRR	25% + 1%*(460.54/809.2)
IRR	25.56%

Project is giving postive NPV

IRR is higher than required rate of return

PI is greater than 1

PB is 3.68 years

From the above results, everything regarding the project is positive

SO project should be undertaken

Notes:

Salvage value is adjusted with last year cash outflow

NPV = Discounted inflow - Initial investment

IRR of the project is when NPV of project = 0

For IRR two different rates are taken to get negative and positive NPV