Question

Central Food Inc., is considering replacing its current production line to improve efficiency. The new production line will cost $650,000 plus $50,000 for shipping and installation. The current production line has a book value of $74,000 and an estimated market value of $95,000. CF uses straight-line depreciation method and has a marginal tax rate of 25% for net income and capital gain.

CF’s current annual sales is $433,000 and by estimation, the new production line can increase CF’s annual sales by about 28%. NWC will rise by $35,000. And due to higher maintenance cost, the operating costs will rise by $15,000 each year. In 11 years the production line currently under consideration can be sold for $110,000. CF’s require rate of return is 11%. For this replacement project:

1) Find initial investment and all the future incremental cash flows.

2) Put all cash flows in #1 on a timeline.

3) Find the discounted payback period. If the threshold is 4.5 years, should CF accept his project?

4) Find the net present value. Should CF accept this project?  

5) Find the profitability index. Should CF accept this project?  

6) Find the modified internal rate of return. Should CF accept this project?

Answer 1

Part (1)

Calculation of Initial Investment
Total Cash Outflow:
Purchase of New Production Line (Purchase Cost + Shipping and Installation)	$                                                    700,000
Net Increase in Working capital	$                                                      35,000
Total Cash Inflow:
Sale of Current Production Line	$                                                      89,750
Net Initial Investment	$                                                    645,250

Calculation of Future Incremental Cash Flows
	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6	Year 7	Year 8	Year 9	Year 10	Year 11	Year 11
Increase in Sales	121,240	121,240	121,240	121,240	121,240	121,240	121,240	121,240	121,240	121,240	121,240	-
Increase in Operating Costs	15,000	15,000	15,000	15,000	15,000	15,000	15,000	15,000	15,000	15,000	15,000	-
Increase in Depreciation	46,909	46,909	46,909	46,909	46,909	46,909	46,909	46,909	46,909	46,909	46,909	-
Sale of New Producation Line	-	-	-	-	-	-	-	-	-	-	-	110000
Recovery of Working Capital	-	-	-	-	-	-	-	-	-	-	-	35,000
Net Increase in Income before Tax	59,331	59,331	59,331	59,331	59,331	59,331	59,331	59,331	59,331	59,331	59,331	145,000
Less: Tax @25%	14,833	14,833	14,833	14,833	14,833	14,833	14,833	14,833	14,833	14,833	14,833	27,500
Net Increase in Income after tax	44,498	44,498	44,498	44,498	44,498	44,498	44,498	44,498	44,498	44,498	44,498	117,500
Add: Depreciation	46,909	46,909	46,909	46,909	46,909	46,909	46,909	46,909	46,909	46,909	46,909	0
Net Cash Flow After Tax	91,407	91,407	91,407	91,407	91,407	91,407	91,407	91,407	91,407	91,407	91,407	117,500

Working Note:

Calculation of Cash Inflow from Sale of Current Production Line
Sale Value	$                                                      95,000
Book Value	$                                                      74,000
Capital Gain	$                                                      21,000
Tax on Capital Gain (25%)	$                                                        5,250
Net Cash Inflow (Sale Proceeds - Tax on Capital Gain)	$                                                      89,750

Depreciation
	Current Production Line	New Production Line
Book Value	74,000	700,000
Salvage Value	-	110,000
Usefule Life	11 Years	11 Years
Depreciation	6,727	53,636

Calculation of capital Gain tax on sale of Production Line in Year 11
Sale Value	110,000
Book Value	-
Capital Gain	110,000
Capital Gain Tax @25%	27,500

Part (3)

Discounted Pay Back Period:

Year	Cash Flow	Present Value Factor @11%                     (1/(1+i)^n)	Discounted Cash Flow	Cumulative Discounted Cash Flow
0	(645,250)	1	(645,250)	(645,250)
1	91,407	0.9009	82,349	(562,901)
2	91,407	0.8116	74,188	(488,713)
3	91,407	0.7312	66,836	(421,877)
4	91,407	0.6587	60,213	(361,665)
5	91,407	0.5935	54,246	(307,419)
6	91,407	0.5346	48,870	(258,549)
7	91,407	0.4817	44,027	(214,522)
8	91,407	0.4339	39,664	(174,858)
9	91,407	0.3909	35,733	(139,125)
10	91,407	0.3522	32,192	(106,933)
11	208,907	0.3173	66,283	(40,650)

Positive cash flows do not arise during the useful life of product line, therefore discounted payback period exceeds 11 years. The threshold for Discounted paybacj period is 4.5 years, so CF should not accept this project.

Part (4)

Net Cash Inflow:

Year	Cash Flow	Present Value Factor @11%                     (1/(1+i)^n)	Discounted Cash Flow
1	91,407	0.9009	82,349
2	91,407	0.8116	74,188
3	91,407	0.7312	66,836
4	91,407	0.6587	60,213
5	91,407	0.5935	54,246
6	91,407	0.5346	48,870
7	91,407	0.4817	44,027
8	91,407	0.4339	39,664
9	91,407	0.3909	35,733
10	91,407	0.3522	32,192
11	208,907	0.3173	66,283
			$604,600

Net cash Outflow: $645,250

Net Present Value:

Net Cash Inflow - Net Cash Outflow

$604,600 - $645,250
($40,650)

As the Net Present value is nefative, CF should not accept this project.

Part (5)

CF should not accept this project as the Profitability index is less than 1.

Part (6)

Modified Internal Rate of Return: Rate of return at which Net Cash Inflow is equals to Net Cash Outflow.

Net Cash Inflow if discounted at 11%:

Year	Cash Flow	Present Value Factor @11%                     (1/(1+i)^n)	Discounted Cash Flow
1	91,407	0.9009	82,349
2	91,407	0.8116	74,188
3	91,407	0.7312	66,836
4	91,407	0.6587	60,213
5	91,407	0.5935	54,246
6	91,407	0.5346	48,870
7	91,407	0.4817	44,027
8	91,407	0.4339	39,664
9	91,407	0.3909	35,733
10	91,407	0.3522	32,192
11	208,907	0.3173	66,283
			$604,600

Net Cash Inflow if discounted at 9%:

Year	Cash Flow	Present Value Factor @9%                       (1/(1+i)^n)	Discounted Cash Flow
1	91,407	0.9174	83,860
2	91,407	0.8417	76,935
3	91,407	0.7722	70,583
4	91,407	0.7084	64,755
5	91,407	0.6499	59,408
6	91,407	0.5963	54,503
7	91,407	0.5470	50,003
8	91,407	0.5019	45,874
9	91,407	0.4604	42,086
10	91,407	0.4224	38,611
11	208,907	0.3875	80,958
			667,577

Therefore, by applying Interpolation we can calculate MIRR as:

9.71%

The Modified Internal Rate of Return is less than the required rate of Return So CF should not accept this project.