Question

1. Explain the implication of M & M (1963) propositions I, II and III in tax world using appropriate diagram.  

2. Zaffers Ltd. Is considering buying a new machine with a price of $18M to replace its existing machine. The current machine has a book value of $6M and a market value of $4.5M. The new machine is expected to have a four-year life, the old machine has four years left in which it can be used. If the firm replaces the old machine with a new one. It expects to save $6.7M in operating costs each year over the next four years. Both machines will have no salvage value in four years. If the firm purchases the new machine it will also need and investment of $2.5M in net working capital. The replaced rate on the investment is 10% and the tax rate is 30%.

1. The initial cash flow at year 0.

2. The net cash flows in year 1 to 3.

3. The net cash flow in year 4.

4. The NPV.

5. Whether the firm should replace the old machine with new machine?

Answer 1

1. Purchase of new machine = $18 Million = Cash-outflow (shown as negative) in Year 0

2. Net Sale of existing machine:

Particulars	$ Million
Sale of existing Machine	4.50
Book Value of existing Machine	6.00
Loss on Sale (4.5-6)	(1.50)
Tax saving on loss (1.5*30%)	(0.45)
Net Sale of existing machine (4.5+0.45)	4.95

Net Sale of existing machine = $4.95 Million =  Cash-inflow (shown as positive) in Year 0

3. Net working capital = $2.5 Million = Cash-outflow (shown as negative) in Year 0

4. Recovery of net working capital = $2.5 Million = Cash-inflow (shown as positive) in Year 4.

It is assumed that the net working capital will be recovered at the end of year 4 (though the question is silent on this).

5. After tax saving in operating costs:

Saving in operating costs per annum = $6.7 Million

Tax rate = 30%

Tax on Saving in operating costs per annum = $6.7*30% = $2.01 Million

Net Saving in operating costs per annum = $6.7-$2.01 = $4.69 Million = Cash-inflow (shown as positive) in Year 1,2,3 & 4.

6. Depreciation on old machine = Book value now / number of useful life remaining = $6/4 years = $1.5 Million per annum (assumed on straight line basis)

Tax shield on depreciation = $1.5*30% = $0.45 Million = Cash-inflow (shown as positive) in Year 1,2,3 & 4.

Depreciation on new machine = Cost of new machine / number of useful life remaining = $18/4 years = $4.5 Million per annum (assumed on straight line basis)

Tax shield on depreciation = $4.5*30% = $1.35 Million = Cash-inflow (shown as positive) in Year 1,2,3 & 4.

7. Discount factor at 10%

Year 1 = 1/(100%+10%)^1 = 0.909

Year 2 = 1/(100%+10%)^2 = 0.826

Year 3 = 1/(100%+10%)^3 = 0.751

Year 4 = 1/(100%+10%)^4 = 0.683

Net Present Value:

(Numbers in $ Million)

Particulars		Years	Cash-flows		Present Value of Cash-flows
Working Reference	New Machine	Existing Machine	Discount factor at 10%	New Machine	Existing Machine	Incremental
Purchase cost	1	0	(18.00)	-	1.000	(18.00)	-	(18.00)
Net Sale of existing machine	2	0	4.95	-	1.000	4.95	-	4.95
Net Working Capital	3	0	(2.50)	-	1.000	(2.50)	-	(2.50)
Net Working Capital-recovery	4	4	2.50	-	0.683	1.71	-	1.71
After tax saving in operating costs	5	1	4.69	0	0.909	4.26	-	4.26
After tax saving in operating costs	5	2	4.69	-	0.826	3.88	-	3.88
After tax saving in operating costs	5	3	4.69	-	0.751	3.52	-	3.52
After tax saving in operating costs	5	4	4.69	-	0.683	3.20	-	3.20
Tax shield on depreciation	6	1	1.35	0.45	0.909	1.23	0.41	0.82
Tax shield on depreciation	6	2	1.35	0.45	0.826	1.12	0.37	0.74
Tax shield on depreciation	6	3	1.35	0.45	0.751	1.01	0.34	0.68
Tax shield on depreciation	6	4	1.35	0.45	0.683	0.92	0.31	0.61
Total			11.11	1.80		5.30	1.43	3.88

Net Present Value (total of present value of cash flows of all years) of the new machine is $5.3 Million, old machine is $1.43 Million. Thus, New Machine generates incremental NPV of $3.88 Million. Thus the firm should replace the old machine with the new one.

Net working capital is assumed to be recovered at the end of year-4 in above NPV calculation. Since the question is silent on that, below is the NPV scenario if the net working capital is not recovered at the end of year 4.

(Numbers in $ Million)

Particulars	Working Reference	Years	Cash-flows		Present Value of Cash-flows
New Machine	Existing Machine	Discount factor at 10%	New Machine	Existing Machine	Incremental
Purchase cost	1	0	(18.00)	-	1.000	(18.00)	-	(18.00)
Net Sale of existing machine	2	0	4.95	-	1.000	4.95	-	4.95
Net Working Capital	3	0	(2.50)	-	1.000	(2.50)	-	(2.50)
After tax saving in operating costs	5	1	4.69	-	0.909	4.26	-	4.26
After tax saving in operating costs	5	2	4.69	-	0.826	3.88	-	3.88
After tax saving in operating costs	5	3	4.69	-	0.751	3.52	-	3.52
After tax saving in operating costs	5	4	4.69	-	0.683	3.20	-	3.20
Tax shield on depreciation	6	1	1.35	0.45	0.909	1.23	0.41	0.82
Tax shield on depreciation	6	2	1.35	0.45	0.826	1.12	0.37	0.74
Tax shield on depreciation	6	3	1.35	0.45	0.751	1.01	0.34	0.68
Tax shield on depreciation	6	4	1.35	0.45	0.683	0.92	0.31	0.61
Total			8.61	1.80		3.60	1.43	2.17

Even in this scenario, new machine has incremental NPV of $2.17 Million over old machine and hence old machine should be replaced with new one.