Question

A question from Corporate Finance, by Berk&Demarzo

Galt Motors currently produces 500,000 electric motors a year and expects output levels to remain steady in the future. It buys a part from an outside supplier at a price of $2.50 each. The plant manager believes that it would be cheaper to make the part rather than buy it. Direct in-house production costs are estimated to be only $1.80 per the part. The necessary machinery would cost $700,000 today (year 0) and can produce output from the following year (year 1). It would be obsolete in 10 years (in year 10). This investment would be depreciated to zero for tax purposes using a 10-year straight line depreciation. The plant manager estimates that the operation would require additional working capital of $40,000 from ‘year 0’ (even though there is no production at year 0) but argues that you do not need the net working capital for the last year of operation (year 10). The expected proceeds from scrapping the machinery after 10 years are estimated to be $10,000. Galt Motors pays tax at a rate of 35% and has an opportunity cost of capital of 14%.

b) How much is the incremental cash flow that Galt Motors will incur in year 4 if they elect to manufacture the part in house is closest to:

c) How much is the incremental cash flow that Galt Motors will incur in year 10 if they elect to manufacture the part in house?

The answers for (b) and (c) are 500,000*(2.50-1.80)+0.35*70,000=374,500 and 500,000*(2.50-1.80)+0.35*70,000+40,000=414,500 each. My question is why the tax rate is not applied to the amount of CoGS(which is 500,000*(2.50-1.80)). As gross profit increases when CoGS decreases, I thought that a decrease in CoGS would lead to an increase in income tax, and the answer should have been 500,000*(2.50-1.80)*(1-0.35)+70,000*0.35. Why are the answers like that? I'd appreciate if anyone gives reply to this question.

Answer 1

The concept of this question is based on RELEVANT COSTING causing INCREMENTAL CASH FLOWS

First lets see the correct solution

	Current situation (buys part from outside) A	New option (in house production) B	Incremental flow (per unit) B-A positive savings
Price	2.5	1.8	+0.7
depreciation savings tax savings (700000/10)=70000	No depreciation savings	70000*0.35=24500	+0.049
			=0.7+0.049=0.749
Total Savings = 0.749*500000 =$374500
Tax	Currently also paying 35%	In new situation also paid 35%	Incremental effect would be increase in tax only due to the above savings

Now as per your DOUBT in the question answer should be$252000 which is incorrect.

"As gross profit increases when CoGS decreases, I thought that a decrease in CoGS would lead to an increase in income tax, and the answer should have been 500,000*(2.50-1.80)*(1-0.35)+70,000*0.35. Why are the answers like that? I'd appreciate if anyone gives reply to this question."

ok so,

Lets see after tax effect

	A	B	B-A
Lets put the values of tax and understand for clarity	Eg     Assume                Selling price is 10 Price=10 Cost=(2.5)           =7.5 Tax=(2.625) ProfitAfter tax =4.875	Price=10        Cost =(1.8) CASH PROFIT BEFORE TAX =8.2. Tax=(2.87) +depreciation=0.049Cash Profit After ta x=5.379	Savings Price=0 Cost=0.7 Cash profit diff=0.7 Tax diff=-0.245 +Depreciation=0.049 0.504
0.504*500000=$252000

Now as per your query the correct inflow of the project should be 252000 but its 374500So what is this difference of 374500-252000=122500

=122500/500000=0.245per unit

Hence it is the tax effect. So your analysis is correct but your value as per concept of relevant costing is incorrect hence, it is important to understand the concept of relevant costing

to clear why in question tax effect is not taken.

In relevant costing only those cost are taken which impact our decision in some way or another hence their impact can affect the "choice of decision".So we calculate incremental cash flows to find the positive or negative impact of such relevant cash flows.Tax is being paid every year and increase in profit or decrease in profit will change the TAX AMOUNT but tax will not change the profit until its rate is changed eg (35% and in year 4 it is 45% then tax will be taken) TAX IS NOT EXCLUSIVELY IMPACTING ANY FLOW HENCE ANY RELEVANT CHANGE HAS TO BE ANALYSED IN YEAR4

HERE YOU ARE REQUIRED TO CALCULATE INCREMENTAL CASH FLOW FOR YEAR 4

WHAT IS THE ADDITIONAL OR ANY EXTRA CHANGE THAT IS HAPPENING IN COST IN YEAR 4

IT IS COST $1.8 per unit OF IN HOUSE PRODUCTION

AND DEPRECIATION $70000 OF MACHINERY REST IS HAPPENING IN EVERY YEAR HENCE REST ARE NOT RELEVANT FOR YEAR 4 ONLY TWO COST ARE RELEVANT

1.PRODUCTION

2DEPRECITION

THEREFORE ONLY THEIR IMPACT HAS BEEN TAKEN

Same goes for year 10

See for any extra cost or savings impacting the incremental cash flow

Working capital recovered

Hence

374500+40000=414500.