Question

Your company has been approached to bid on a contract to sell 5,700 voice recognition (VR) computer keyboards a year for four years. Due to technological improvements, beyond that time they will be outdated and no sales will be possible. The equipment necessary for the production will cost $4.9 million and will be depreciated on a straight-line basis to a zero salvage value. Production will require an investment in net working capital of $485,000 to be returned at the end of the project, and the equipment can be sold for $485,000 at the end of production. Fixed costs are $660,000 per year, and variable costs are $93 per unit. In addition to the contract, you feel your company can sell 15,000, 17,100, 19,700, and 12,200 additional units to companies in other countries over the next four years, respectively, at a price of $206. This price is fixed. The tax rate is 23 percent, and the required return is 10 percent. Additionally, the president of the company will undertake the project only if it has an NPV of $150,000. What bid price should you set for the contract?

Note:Bid price of $162.16 is incorrect

Answer 1

Lets find the present value of each of the other variables given except the primary sales

a. Additional Sales to companies in other countries:

Particulars	Year 1	Year 2	Year 3	Year 4	Working
Additional sales	15,000	17,100	19,700	12,200	Given in question
Selling Price for the additional unit	206	206	206	206	Given in question
Total Sales (before tax)	3,090,000	3,522,600	4,058,200	2,513,200	Additional sales*Selling Price for the additional unit
Tax at 23%	710,700	810,198	933,386	578,036	Total Sales (before tax) * 23%
Total Sales (after tax)	2,379,300	2,712,402	3,124,814	1,935,164	Total Sales (before tax) - Tax at 23%
Discount factor at 10%	0.909	0.826	0.751	0.683	Year 1 = (1/(1.10)^1 Year 2 = (1/(1.10)^2 Year 3 = (1/(1.10)^3 Year 4 = (1/(1.10)^4
Present Value of annual cash flows	2,163,000	2,241,655	2,347,719	1,321,743	Total Sales (after tax)* Discount factor at 10%
Present Value of all annual additional sales	8,074,117				sum of all Present Value of annual cash flows

b. Variable & Fixed Costs

Particulars	Year 1	Year 2	Year 3	Year 4	Working
Variable cost per unit	93	93	93	93	Given in question
Sales units of the bid	5,700	5,700	5,700	5,700	Given in question
Additional sales to companies in other countries	15,000	17,100	19,700	12,200	Given in question
Total Variable cost	1,925,100	2,120,400	2,362,200	1,664,700	Variable cost per unit*(Sales units of the bid+Additional sales to companies in other countries)
Fixed Costs	660,000	660,000	660,000	660,000	Given in question
Total Costs (before tax)	2,585,100	2,780,400	3,022,200	2,324,700	Total Variable cost + Fixed costs
Tax at 23%	594,573	639,492	695,106	534,681	Total Costs (before tax) * 23%
Total Costs (after tax)	1,990,527	2,140,908	2,327,094	1,790,019	Total Costs (before tax) - Tax at 23%
Discount factor at 10%	0.909	0.826	0.751	0.683	Year 1 = (1/(1.10)^1 Year 2 = (1/(1.10)^2 Year 3 = (1/(1.10)^3 Year 4 = (1/(1.10)^4
Present Value of annual costs	1,809,570	1,769,345	1,748,380	1,222,607	Total Sales (after tax)* Discount factor at 10%
Present Value of all annual costs	6,549,903				sum of all Present Value of annual costs

c. Depreciation

Cost of the equipment = $4,900,000 (given in question)

Life of the equipment = 4 years (given in question)

Particulars	Year 1	Year 2	Year 3	Year 4	Working
Depreciation per annum	1,225,000	1,225,000	1,225,000	1,225,000	Straight line basis to a zero salvage value = cost of the equipment / project life = 4900000/4
Tax shield at 23%	281,750	281,750	281,750	281,750	Depreciation per annum* 23%
Discount factor at 10%	0.909	0.826	0.751	0.683	Year 1 = (1/(1.10)^1 Year 2 = (1/(1.10)^2 Year 3 = (1/(1.10)^3 Year 4 = (1/(1.10)^4
Present Value of annual depreciation tax shield	256,136	232,851	211,683	192,439	Tax shield at 23%* Discount factor at 10%
Present Value of all annual depreciation tax shield	893,110				sum of all Present Value of annual depreciation tax shield

d. Working Capital:

Net working Capital in Year 0 = $485,000 (given in question)

Net working Capital in Year 4 = $485,000 to be recovered (given in question)

Present value of  Net working Capital in Year 4 = $485,000*discounting factor of 10% at 4th year = $485,000*0.6830135 ((1/(1.10)^4) = $331,262

Present value of all net working capital = Net working Capital in Year 0 - Present value of  Net working Capital in Year 4 = $485,000 - $331,262 = $153,738

e. Sale of equipment at the end of production

Equipment sale value at the end of year 4= $485,000 (given in question)

Book value (salvage value) at the end of year 4 = 0 (given in question)

Thus, capital gain on sale of equipment = $485,000-$0 = $485,000

Tax on Capital gain = $485,000 * 23% = $111,550

Net Sale value of equipment at the end of year 4 = $485,000-$111,550=$373,450

Present value of net sale value of equipment = $373,450**discounting factor of 10% at 4th year = $373,450*0.6830135 ((1/(1.10)^4) = $255,071

f. Original investment in the equipment = $4,900,000 (given in question).

g. Net Present Value = Present Value of all annual additional sales - Present Value of all annual costs + Present Value of all annual depreciation - Present value of all net working capital + Present value of net sale value of equipment - Original investment

Applying each of the value from above, we get

NPV = 8,074,117-6,549,903+893,110-153,738+255,071-4,900,000 = -2,381,343 (without the bid sales)

h. Desired NPV = $150,000

To get the Desired NPV, current NPV to increase by $150000+2,381,343 = 2,531,343

Let sale price of the bid be Y

Sales revenue per annum = 5,700 unit per annum * Y

After tax sales revenue = 5700*Y*(1-23% tax rate) = 4,389*Y

PV factor of year 1 - 4 = (1/(1.10)^1+(1/(1.10)^2+(1/(1.10)^3+(1/(1.10)^4 = 3.16987

Thus, 4,389*Y*3.16987 = $2,531,343(required NPV)

Thus, Y = 2,531,343/(4,389*3.16987) = $181.9

Thus, to get the NPV of $150,000, bid price for the contract should be $181.9 per VR computer keyboards.