As a first step let's calculate the series of cash flows for investment.
Discount rate, R = 10%
PV factor for year N = (1 + R)(-N)
Let's put all these into a table. Please see the table below:
Tax rate |
T |
30% |
|||||
Year, N |
0 |
1 |
2 |
3 |
4 |
5 |
|
Investment in land |
A |
(2,120,000) |
2,320,000 |
||||
Investment in new plant & equipment |
B |
(5,420,000) |
|||||
Post tax Salvage value of plant & equipment |
C |
364,000 |
|||||
Investment in working capital |
D |
(620,000) |
(52,000) |
(52,000) |
(52,000) |
(52,000) |
828,000 |
Net cash flows towards investment |
E = A + B + C + D |
(8,160,000) |
(52,000) |
(52,000) |
(52,000) |
(52,000) |
3,512,000 |
Required return |
R |
10% |
|||||
PV factor |
(1+R)^(-N) |
1.0000 |
0.9091 |
0.8264 |
0.7513 |
0.6830 |
0.6209 |
PV of net investment |
F = E x PV factor |
(8,160,000) |
(47,273) |
(42,975) |
(39,068) |
(35,517) |
2,180,676 |
NPV of investments |
Sum of all F |
(6,144,157) |
|||||
Sum of PV factors from year 1 to 5 |
Sum of PV factor for years 1 to 5 only |
3.7908 |
NPV of all the investments = -6,144,157
Sum of PV factors for year 1 to 5 = 3.7908
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 = 52 cents = $ 0.0052
Nos. of stamps to be supplied annually = 102 mn = 102,000,000
Fixed cost per annum = 1,070,000
Annual depreciation = Cost of Plant & machinery / Life = 5,420,000 / 5 = 1,084,000
Annual Post tax operating cash flow = [(S - 0.0052) x 102,000,000 - 1,070,000 - 1,084,000] x (1 - 30%) + 1,084,000 = 71,400,000 x S - 795,080
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 = (71,400,000 x S - 795,080) x 3.7908
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, (71,400,000 x S - 795,080) x 3.7908 - 6,144,157 = 0
Hence, S = $ 0.03383604
So, please enter a value of 0.03384 (rounded off to 5 places of decimal)
Consider a project to supply 102 million postage stamps per year to the U.S. Postal Service...
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