Question

A firm is considering an investment in a new machine with a price of $18.18 million to replace its existing machine. The current machine has a book value of $6.18 million and a market value of $4.68 million. The new machine is expected to have a four-year life, and the old machine has four years left in which it can be used. If the firm replaces the old machine with the new machine, it expects to save $6.88 million 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 an investment of $268,000 in net working capital. The required return on the investment is 11 percent, and the tax rate is 39 percent. Assume the company uses straight-line depreciation.       a. What is the NPV of the decision to purchase a new machine? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16. Enter your answer in dollars, not millions of dollars, e.g., 1,234,567.)    b. What is the IRR of the decision to purchase a new machine? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)       c. What is the NPV of the decision to keep the old machine? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16. Enter your answer in dollars, not millions of dollars, e.g., 1,234,567. A negative answer should be indicated by a minus sign.)       d. What is the IRR of the decision to keep the old machine? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16. A negative answer should be indicated by a minus sign.)

Answer 1

Solution a) Calculation of NPV of the decision to purchase new machine

	$
Cost of New Machine	18,18,00,000
Increase in Working Capital	2,68,000
	18,20,68,000
Less: Scrap Value of Old Machine	4,68,00,000
Initial Cash Outflow	13,52,68,000

Depreciation for New Machine

Depreciation as per Straight Line Method = (Cost – Scrap value) / No of years

                                                                            = (18,18,00,000 – 0) / 4

                                                                            = $4,54,50,000 per annum

Depreciation for Old Machine = Current Book Value – Scrap value / no. of years

                                                     = 6,18,00,000 / 4
                                                     = $1,54,50,000 per annum

Therefore, Incremental Depreciation = Depreciation of new machine - Depreciation of old machine

                                                                  = $4,54,50,000 - $1,54,50,000

                                                                  = $3,00,00,000

Calculation of Incremental cash inflows:

	Year 1	Year 2	Year 3	Year 4
Savings in operating Costs	6,88,00,000.00	6,88,00,000.00	6,88,00,000.00	6,88,00,000.00
Less: Incremental Depreciation	3,00,00,000.00	3,00,00,000.00	3,00,00,000.00	3,00,00,000.00
Net Savings before Tax	3,88,00,000.00	3,88,00,000.00	3,88,00,000.00	3,88,00,000.00
Tax @ 39%	1,51,32,000.00	1,51,32,000.00	1,51,32,000.00	1,51,32,000.00
Net Saving after Tax	2,36,68,000.00	2,36,68,000.00	2,36,68,000.00	2,36,68,000.00
Cash Inflows (Net savings after tax + Incremental Depreciation)	5,36,68,000.00	5,36,68,000.00	5,36,68,000.00	5,36,68,000.00
Recovery of Additional Working Capital				2,68,000.00
Total Cash Inflows	5,36,68,000.00	5,36,68,000.00	5,36,68,000.00	5,39,36,000.00
Discounting Factor @ 11%	0.90	0.81	0.73	0.66
Present Value of Cash Inflows	4,83,49,549.55	4,35,58,152.75	3,92,41,579.05	3,55,29,313.82
Total Present Value of Cash Inflows	16,66,78,595.17
Less: Initial Cash Outflows	13,52,68,000.00
Net Present Value after Purchasing New Machine	3,14,10,595.17

As the NPV for the purchase of New machine is positive, it is recommended that new machine should be purchased.

Solution 2: Calculation of Internal Rate of Return for the purchase of new machine:

For calculation of IRR, we require a two discounting rate, one with a positive NPV and one with a negative NPV.

As we have seen that at 11% discounting rate, we have a positive NPV, Hence, we will try calculating NPV with a higher discounting rate so that we get a negative NPV.

Let us try calculating NPV at 13% discount rate

Year	Cash Inflows	Df @ 13%	PVCI @ 13%
1	4,83,49,549.55	0.88	4,27,87,211.99
2	4,35,58,152.75	0.78	3,41,12,422.86
3	3,92,41,579.05	0.69	2,71,96,382.73
4	3,55,29,313.82	0.61	2,17,90,793.55
		PVCI	12,58,86,811.13
		(-) Initial Investment	13,52,68,000.00
		NPV	-93,81,188.87

IRR = Discount Rate with positive NPV + (Positive NPV / Difference in NPV * Difference in rates)At 13% Discount Rate, we are getting a negative NPV. So, we can apply the following formula to calculate IRR

= 11% + [31410595.17 / 31410595.17-(-93,81,188.87) x (13-11)

= 11% + (31410595.17 / 40791784.04 x 2)

= 11% + 1.54

= 12.54 %

hence, the IRR of the new machine is 12.54 %

Solution 3: Calculation of NPV of the decision to keep old machine

	Year 1	Year 2	Year 3	Year 4
Depreciation	1,54,50,000.00	1,54,50,000.00	1,54,50,000.00	1,54,50,000.00
Cash Inflows	-1,54,50,000.00	-1,54,50,000.00	-1,54,50,000.00	-1,54,50,000.00
Discounting factor @ 11%	0.90	0.81	0.73	0.66
Net Present Value	-1,39,18,918.92	-1,25,39,566.59	-1,12,96,906.84	-1,01,77,393.55
Total NPV of Old Machine	-4,79,32,785.90

The old machine has a negative NPV -4,79,32,785.90.