Question

Consider a project to supply 107 million postage stamps per year to the U.S. Postal Service for the next five years. You have an idle parcel of land available that cost $1,740,000 five years ago; if the land were sold today, it would net you $1,815,000 aftertax. The land can be sold for $1,755,000 after taxes in five years. You will need to install $5.7 million in new manufacturing plant and equipment to actually produce the stamps; this plant and equipment will be depreciated straight-line to zero over the project’s five-year life. The equipment can be sold for $730,000 at the end of the project. You will also need $610,000 in initial net working capital for the project, and an additional investment of $57,000 in every year thereafter. Your production costs are .55 cents per stamp, and you have fixed costs of $1,120,000 per year. If your tax rate is 23 percent and your required return on this project is 9 percent, what bid price should you submit on the contract? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., 32.16161.)

Answer 1

As a first step let's calculate the series of cash flows for investment.

1. Investment in land at t=0 will be opportunity cost of land today = - sale price of land today = - $ 1,815,000
2. Return of investment in land at the end of year 5 = sale price of land at the end of year 5 = $ 1,755,000
3. Investment in plant and equipment at t=0 will be -$ 5,700,000
4. Salvage value at the end of year 5 = $ 730,000
5. Tax basis at the end of year 5 = 0 (as asset will be fully depreciated by then)
6. Gain on sale of plant & equipment = Salvage value - tax basis = 730,000 - 0 = 730,000
7. Tax on gain = Tax rate, T x Gain on sale = 23% x 730,000 = 167,900
8. Post tax salvage value = Salvage value - tax on gain on sale = 730,000 - 167,900 = 562,100
9. Initial investment in working capital = -610,000
10. Subsequent investment in working capital per year for next four year = - 57,000
11. Release of working capital at the end of year 5 = cumulative investment in working capital = 610,000 + 4 x 57,000 = $ 838,000

Discount rate, R = 9%

PV factor for year N = (1 + R)^(-N)

Let's put all these into a table. Please see the table below:

Tax rate	t	23%
Year, N		0	1	2	3	4	5
Investment in land	A	(1,815,000)					1,755,000
Investment in new plant & equipment	B	(5,700,000)
Post tax Salvage value of plant & equipment	C						562,100
Investment in working capital	D	(610,000)	(57,000)	(57,000)	(57,000)	(57,000)	838,000
Net cash flows towards investment	E = A + B + C + D	(8,125,000)	(57,000)	(57,000)	(57,000)	(57,000)	3,155,100
Required return	R	9%
PV factor	(1+R)^(-N)	1.0000	0.9174	0.8417	0.7722	0.7084	0.6499
PV of net investment	F = E x PV factor	(8,125,000)	(52,294)	(47,976)	(44,014)	(40,380)	2,050,599
NPV of investments	Sum of all F	(6,259,066)
Sum of PV factors from year 1 to 5	Sum of PV factor for years 1 to 5 only	3.8897

NPV of all the investments = - 6,259,066

Sum of PV factors for year 1 to 5 = 3.8897

Now, let's say S is the bid price per stamp in $. Then annual operating post tax cash flow will be:

[(Sale Price - production cost ) x Nos. of stamps to be supplied annually - Fixed Cost - Depreciation] x (1 - Tax rate) + Depreciation

Production cost = 0.55 cents = $ 0.0055

Nos. of stamps to be supplied annually = 107 mn = 107,000,000

Fixed cost per annum = 1,120,000

Annual depreciation = Cost of Plant & machinery / Life = 5,700,000 / 5 = 1,140,000

Annual Post tax operating cash flow = [(S - 0.0055) x 107,000,000 - 1,120,000 - 1,140,000] x (1 - 23%) + 1,084,000 = 82,390,000 x S - 1,053,345

Sum of PV of all annual operating cash flows over year 1 to 5 = Annual Operating cash flow x Sum of PV factor over 5 years = (7 82,390,000 x S - 1,053,345) x 3.8897

If we bid at a price such that NPV of the project is 0 then

Sum of PV of all annual operating cash flows over year 1 to 5 + NPV of investments = 0

Hence, ( 82,390,000 x S - 1,053,345) x 3.8897 - 6,259,066 = 0

Hence, S = $ 0.032315858

So, please enter a value of 0.03232 (rounded off to 5 places of decimal)