Question

With the ground broken for the construction of its new home (the Nicol Building), the Sprott School of Business needs someone to supply it with 250 customized computers per year for the next 5 years, and you have decided to bid on the contract. It will cost you $125,000 to install the equipment necessary to start production. The equipment will be depreciated at 30 percent (class 10), and you estimate that it can be salvaged for 20.00% (of the original cost) at the end of the 5- year contract. Your fixed production costs will be $50,000 per year, and your variable production costs should be $600 per computer. You also need an initial investment in net working capital of $13,000. Assuming that your tax rate is 34 percent and you require a 12 percent return on your investment:

1. a) What is the depreciation tax shield in the third year of this project?

2. b) What is the present value of the CCA tax shield?

3. c) What is the minimum price that your company should bid per single computer?

Assuming you believe that Sprott School of Business will pay $975.00 per customized computer, what is the NPV of this project? Should you submit a bid given this new information?

Answer 1

1. The depreciation tax shield

first we need to find the depreciation of the third year

Depreciation schedule
year	opening balance	Depreciation (30%)	closing balance
1	125,000	37,500	87,500
2	87,500	26,250	61,250
3	61,250	18,375	42,875
4	42,875	12,863	30,013
5	30,013	9,004	21,009

depreciation tax shield for the 3rd year is:
depreciation for 3rd year	18,375
tax rate =	34%
tax shield = dep. * tax rate	$       6,248

                                 

2. PV of the CCA tax shield

PV of tax shield =(C-Spv)[(d*t)/(k+d)] * [(1+0.5k)/(1+k)]
c= cost od asset =	125,000
Spv = present value of salvage value
salvage value= 20% * 125000=	25,000
Present value =	Future value/ (1+r)^n
PV of salvage value =	=25000/(1+0.12)^5 =14815.67
d= depreciation rate =	30.00%
t= tax rate =	34%
k= cost of capital=	12%

=	(125000-14815.67)((0.30*0.34)/(0.12+0.30)) * ((1+0.5*0.12)/(1+0.12))
	=110814.33(0.102/0.42)*(1.06/1.12)
	=25470.33

So the PV of tax shield= $25,470.33

3. Now, the maximum they should pay is:

We need to calculate the total cost of the computers to estimate the break even value where they will incur no loss

This will be trial and error where we will see the rate at which the NVP will be closest to 0

Because the situation where NPV is 0 will be where the cost of the project is recovered and it will be the minimum rate

If we keep the rate as $1000

		years
Particulars	0	1	2	3	4	5
initial cost	125000
net working cap required	13000
total initial requirement	138000
sales (250*1000)		250,000	250,000	250,000	250,000	250,000
fixed cost		-50,000	-50,000	-50,000	-50,000	-50,000
Depreciation		-37,500	-26,250	-18,375	-12,863	-9,004
variable cost= 250*600		-150,000	-150,000	-150,000	-150,000	-150,000
salvage value recovered						25,000
EBT		12,500	23,750	31,625	37,138	65,996
tax= EBT*34%		4,250	8,075	10,753	12,627	22,439
Net profit		8,250	15,675	20,873	24,511	43,558
Discount factor (1/(1+r%)^n	for r= 12% 1/(1+12%)^n	1/(1+0.12)^1	1/(1+0.12)^2	1/(1+0.12)^3	1/(1+0.12)^4	1/(1+0.12)^5
DF		0.89	0.80	0.71	0.64	0.57
PV of the profit = DF* net profit	-138000	7,366.07	12,496.01	14,856.63	15,577.02	24,715.71

NPV= sum total = -62988.55

Which is less than 0, so we will increase the rates.

By keeping the rate as $1100

		years
particulars	0	1	2	3	4	5
initial cost	125000
net working cap required	13000
total initial requirement	138000
sales (250*975)		275,000	275,000	275,000	275,000	275,000
fixed cost		-50,000	-50,000	-50,000	-50,000	-50,000
Depreciation		-37,500	-26,250	-18,375	-12,863	-9,004
variable cost= 250*600		-150,000	-150,000	-150,000	-150,000	-150,000
salvage value recovered						25,000
EBT		37,500	48,750	56,625	62,138	90,996
tax= EBT*34%		12,750	16,575	19,253	21,127	30,939
Net profit		24,750	32,175	37,373	41,011	60,058
Discount factor (1/(1+r%)^n	for r= 12% 1/(1+11%)^n	1/(1+0.12)^1	1/(1+0.12)^2	1/(1+0.12)^3	1/(1+0.12)^4	1/(1+0.12)^5
DF		0.89	0.80	0.71	0.64	0.57
PV of the profit = DF* net profit	-138000	22,098.21	25,649.71	26,601.01	26,063.07	34,078.25

NPV= -3509.7

So we keep is closer to $1100, as $1106, the NPV= $59 so we can assume that if we keep the price as $1106, the cost is covered.

4. Now if the price is $975

		years
particulars	0	1	2	3	4	5
initial cost	125000
net working cap required	13000
total initial requirement	138000
sales (250*975)		243,750	243,750	243,750	243,750	243,750
fixed cost		-50,000	-50,000	-50,000	-50,000	-50,000
Depreciation		-37,500	-26,250	-18,375	-12,863	-9,004
variable cost= 250*600		-150,000	-150,000	-150,000	-150,000	-150,000
salvage value recovered						25,000
EBT		6,250	17,500	25,375	30,888	59,746
tax= EBT*34%		2,125	5,950	8,628	10,502	20,314
Net profit		4,125	11,550	16,748	20,386	39,433
Discount factor (1/(1+r%)^n	for r= 12% 1/(1+11%)^n	1/(1+0.12)^1	1/(1+0.12)^2	1/(1+0.12)^3	1/(1+0.12)^4	1/(1+0.12)^5
DF		0.89	0.80	0.71	0.64	0.57
PV of the profit = DF* net profit	-138000	3,683.04	9,207.59	11,920.54	12,955.51	22,375.07

NPV= -77858.25

Which shows loss for the company and so the company should not accept this proposal.