Question

Q. 4 Langley Co is considering two projects that will each cost $1,500,000 initially and both projects will last 5 years: Project A This project will require $125,000 of initial working capital, and will generate $420,000 cash inflows per year for the 5 years, at the end of which time it will be scrapped with no residual value. The working capital will also be released at the end of the 5-year period to be used for other new projects. Project B In addition to the original investment, Project B will need $125,000 in Year 3 in order to maintain the equipment at peak capacity, and will generate $450,000 in annual cash inflows. It will be scrapped and sold as salvage for $75,000 in its final year. The after-tax discount rate is 8%. CCA rate 20% Tax rate 30% Required: 1) Use net present values to determine the more acceptable of the two projects. 2) Determine the internal rate of return of each project: Is it above [ ], or below[ ] 8%]. Does the IRR support your recommendation in 1)? 3) Explain the tax shield, and why it is important that it be included in this analysis? Would you come to the same conclusion with/without the tax shield calculation?

Answer 1

Project A

Statement showing depreciation

Year	Opening balance	Depreciation Rates	Depreciation (opening balance x Depreciation rates)	Closing Balance
1	1500000	10%	150000	1350000
2	1350000	20%	270000	1080000
3	1080000	20%	216000	864000
4	864000	20%	172800	691200
5	691200	20%	138240	552960

Statement showing NPV

Particulars	0	1	2	3	4	5	NPV = Sum of PV
Initial investment	-1500000
WC requirement	-125000
Annual cash inflows		420000	420000	420000	420000	420000
Less : Depreciation		150000	270000	216000	172800	138240
PBT		270000	150000	204000	247200	281760
Tax @ 30%		81000	45000	61200	74160	84528
PAT		189000	105000	142800	173040	197232
Add: Depreciation		150000	270000	216000	172800	138240
Annual cash flow		339000	375000	358800	345840	335472
Release of WC						125000
Total cash flow	-1625000	339000	375000	358800	345840	460472
PVIF @ 8%	1.0000	0.9259	0.8573	0.7938	0.7350	0.6806
PV	-1625000.00	313888.89	321502.06	284827.01	254202.72	313389.51	-137189.82

Thus NPV = -137189.82$

IRR is the rate at which NPV is 0

Assume r = 4% then NPV

Particulars	0	1	2	3	4	5	NPV = Sum of PV
Total cash flow	-1625000	339000	375000	358800	345840	460472
PVIF @ 4%	1.0000	0.9615	0.9246	0.8890	0.8548	0.8219
PV	-1625000.00	325961.54	346708.58	318971.89	295625.48	378474.42	40741.91

Assume r = 5% then NPV

Particulars	0	1	2	3	4	5	NPV = Sum of PV
Total cash flow	-1625000	339000	375000	358800	345840	460472
PVIF @ 5%	1.0000	0.9524	0.9070	0.8638	0.8227	0.7835
PV	-1625000.00	322857.14	340136.05	309944.93	284523.42	360791.86	-6746.59

Now using interpolation one can find IRR

Rate	NPV
4%	40741.91
5%	-6746.59
1%	47488.5
?	40741.91

=40741.91/47488.5

=0.86

Thus IRR = 4%+0.86% = 4.86%

Project B

Statement showing depreciation

Year	Opening balance	Depreciation Rates	Depreciation (opening balance x Depreciation rates)	Closing Balance
1	1500000	10%	150000	1350000
2	1350000	20%	270000	1080000
3	1080000	20%	216000	864000
4	864000	20%	172800	691200
5	691200	20%	138240	552960

Statement showing NPV

Particulars	0	1	2	3	4	5	NPV = Sum of PV
Initial investment	-1500000
WC requirement
Annual cash inflows		450000	450000	450000	450000	450000
Less : Depreciation		150000	270000	216000	172800	138240
Less: Repairs				125000
PBT		300000	180000	109000	277200	311760
Tax @ 30%		90000	54000	32700	83160	93528
PAT		210000	126000	76300	194040	218232
Add: Depreciation		150000	270000	216000	172800	138240
Annual cash flow		360000	396000	292300	366840	356472
Cash flow from sale of machine						218388
Total cash flow	-1500000	360000	396000	292300	366840	574860
PVIF @ 8%	1.0000	0.9259	0.8573	0.7938	0.7350	0.6806
PV	-1500000.00	333333.33	339506.17	232037.16	269638.35	391240.06	65755.08

Thus NPV = 65755.08 $

IRR is the rate at which NPV is 0

Assume r = 9% then NPV

Particulars	0	1	2	3	4	5	NPV = Sum of PV
Total cash flow	-1500000	360000	396000	292300	366840	574860
PVIF @ 9%	1.0000	0.9174	0.8417	0.7722	0.7084	0.6499
PV	-1500000.00	330275.23	333305.28	225709.23	259878.70	373619.56	22788.00

Assume r = 10% then NPV

Particulars	0	1	2	3	4	5	NPV = Sum of PV
Total cash flow	-1500000	360000	396000	292300	366840	574860
PVIF @ 10%	1.0000	0.9091	0.8264	0.7513	0.6830	0.6209
PV	-1500000.00	327272.73	327272.73	219609.32	250556.66	356942.83	-18345.74

Now using interpolation one can find IRR

Rate	NPV
9%	22788
10%	-18345.74
1%	41133.74
?	22788

=41133.74/22788

=0.55

Thus IRR = 9% + 0.55% = 9.55%

1) Project B is more desirable as it's NPV is positive (i.e 65755.08 $) while project A should be rejected as it has negative NPV

2) For Project A , IRR is below cost of capital (IRR = 4.86%) , and For Project B , IRR is above cost of capital (IRR = 9.55%), as per IRR rule , project B should be selected and Project A should be rejected , thus IRR support your recommendation in 1

3) tax shield on depreciation means tax savings due to depreciation. Depreciation is non cash item, it is just debited in P&L account for accounting purpose. Because it is debited in P&L , comapny has to pay less tax because of depreciation. Tax so saved because of depreciation is tax shield

Statement showing NPV for project A

Particulars	0	1	2	3	4	5	NPV = Sum of PV
Initial investment	-1500000
WC requirement	-125000
Annual cash inflows		420000	420000	420000	420000	420000
Less : Depreciation
PBT		420000	420000	420000	420000	420000
Tax @ 30%		126000	126000	126000	126000	126000
PAT		294000	294000	294000	294000	294000
Add: Depreciation
Annual cash flow		294000	294000	294000	294000	294000
Release of WC						125000
Total cash flow	-1625000	294000	294000	294000	294000	419000
PVIF @ 8%	1.0000	0.9259	0.8573	0.7938	0.7350	0.6806
PV	-1625000.00	272222.22	252057.61	233386.68	216098.78	285164.36	-366070.35

Thus NPV = -366070.35 $

Statement showing NPV for project B

Particulars	0	1	2	3	4	5	NPV = Sum of PV
Initial investment	-1500000
WC requirement
Annual cash inflows		450000	450000	450000	450000	450000
Less : Depreciation
Less: Repairs				125000
PBT		450000	450000	325000	450000	450000
Tax @ 30%		135000	135000	97500	135000	135000
PAT		315000	315000	227500	315000	315000
Add: Depreciation
Annual cash flow		315000	315000	227500	315000	315000
Cash flow from sale of machine						218388
Total cash flow	-1500000	315000	315000	227500	315000	533388
PVIF @ 10%	1.0000	0.9259	0.8573	0.7938	0.7350	0.6806
PV	-1500000.00	291666.67	270061.73	180596.83	231534.40	363014.91	-163125.46

Thus NPV = -163125.46 $

Thus if we remove depreciation then we will not get tax shield and hence none of the project is acceptable now