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-Initial investment: The initial investment (I) is the sum of the invest in plant and equipment.

I = $1,000,000

-Working Capital: The additional net investment in inventory and receivables is the working capital needed for the project:

WC = $200,000

There is no additional info about the WC, so we can assume that it will not change over the project's life. Then Working Capital Change for each year Yi is: ChWCi = Previous Year WC - Current WC = 0 (for i=1 to 7) and ChWC0 = -$200,000

The working capital is recovered, this means that for the end of the year 8 it will be zero or: ChWC8 = $200,000

-Depreciation: For the first five years Yi (i = 1 to 5):

Di = (Invest in plant and equipment)/5 = $1,000,000/5 = $200,000

For the years 6 to 8 the depreciation will be zero.

-Revenues: For the first year the expected revenues will be: R1 = $950,000

For the years Yi (i=2 to 8): Ri = $1,500,000

 

-Expenses: Indirect incremental costs will be $80,000 all the eight years. For each year the direct costs will be 0.55*Ri . Then for each year Yi (i=1 to 8), the expenses (Ei) will be:

Ei = $80,000 + 0.55*Ri , then:

E1 = $80,000 + 0.55*$950,000 = $602,500

For i=2 to 8: Ei = $80,000 + 0.55*$1,500,000 = $905,000

-Taxes: The firm's marginal tax rate is 35%, then the taxes will be:

Ti = T * (Ri - Ei - Di) with T = 0.35 (i=1 to 8)

T1 = 0.35*($950,000-$602,500-$200,000) = $51,625

For i=2 to 5 Ti = 0.35*($1,500,000-$905,000-$200,000) = $138,250

For i=6 to 8 Ti = 0.35*($1,500,000-$905,000-$0) = $208,250

 

The Cash Flow Statement would be as under:

 

YEARS

0 1 2 3 4 5 6 7 8

1.Revenues 0 950 1500 1500 1500 1500 1500 1500 1500

2.Expenses 0 602.5 905 905 905 905 905 905 905

3.Depreciation 0 200 200 200 200 200 0 0 0

4.Income before 0 147.5 395 395 395 395 595 595 595 tax, [1-(2+3)]

5.Taxes 0 51.6 138.2 138.2 138.2 138.2 238.2 238.2 238.2

6.Net Income 0 95.9 256.8 256.8 256.8 256.8 356.8 356.8 356.8 [4-5] 7.Cash flow from operation 0 295.9 456.8 456.8 456.8 456.8 356.8 356.8 356.8 [1-2-5]

--------------------------------------------------------------

8.Investments -1000 0 0 0 0 0 0 0 0

9.Change in WC -200 0 0 0 0 0 0 0 200

10.Total cash -1200 0 0 0 0 0 0 0 200 flow from investment [8+9]

--------------------------------------------------------------

11.Total cash -1200 295.9 456.8 456.8 456.8 456.8 356.8 356.8 556.8 flow [7+10]

 

Payback Period

Payback (PB) calculation will give us an idea on how long it will take for a project to recover the total initial investment. Then if: Y = the year before full recovery of total investment TI; U = Unrecovered cost at the start of last year; CFi = CF of the year Y+1; PB = Y + U/CFi

We will consider the total initial investment (TI) as the sum of the invest in plant and equipment plus the initial Working Capital required.

TI = $1,200,000

At the end of the year 2 we have recovered: $295,875 + $456,750 = $752,625

And U is: U = $1,200,000 - $752,625 = $447,375 (less than CF3, then Y = 2)

PB = 2 + 447,375/456,750 = 2.98 years or 2 years, 11 months and 23 days.

 

NPV

 

First we need to define the Present Value (PV):

CF1 CF2 CF8 PV = --------- + ---------- + .... + ---------- (1 + R) (1 + R)^2 (1 + R)^8

where R is the required return.

Net Present Value:

NPV = PV - TI where TI = Total Initial Investment

Using a calculator we find that:

PV = $2,229,365.07

NPV = PV - TI = $2,229,365.07 - $1,200,000 = $1,029,365.07

 

 

Regarding the Acceptance the project, this can be accepted because it is rule to Accept a project if its payback period is less than maximum acceptable payback period.

 

The NPV is positive and very atractive. The NPV criterion has considerable merits: - it takes in to account the time value of money - it considers the cash flow stream in its project life The NPV Decision Rule says: -Accept a project if NPV >= 0. So by this criterion the project is also acceptable.

 

Additional investment in land and building is a relevant cash flow, so it must be added to the initial investment, and depending on the amount of money invested on this topic the NPV could become negative and in that case the project will be rejected via the NPV criterion. Also note that the current payback period is very close to the limit of 3 years, so any additional investment will increase the payback period to a number greater than 3 and the project will be rejected, despite of the possibility that the NPV remains positive.