Question

An Investment of 2.5 million is spread evenly over two years and is followed by revenues of $750,000 in year 1,increasing 10% each year thereafter, against constant cost of $150,000 per year. what are the project balance over the life of the project,which runs,for seven year,after the investment is completed, assuming a 15% interest? Is the progect risky? why or why note?

Answer 1

Answer :-

Given investment is spread evenly over a 2 year span
ie. The investment in first and second years is $ 1.25 million
The revenues are $ 750000 in year 1 while increasing by 10% every year for 7 years

Years	1	2	3	4	5	6	7
Revenue	$ 750000	$ 825000	$ 907500	$ 998250	$ 1098075	$ 1207882.5	$ 1328670.75
Present Value	$ 568181.81	$ 542763.16	$ 518571.43	$ 496641.8	$ 475357.14	$ 511814.62	$ 435629.75

The present value can be calculated by discounting the Revenues at 15% and the first year revenue of $ 750000 should be discounted by (1+0.15)² since the revenues are followed after two years of investment and the project has started 2 years back.

The table shown above are the revenues and the discounted values which are added to get the total revenues for 7 years after the investment period of 2 years.
= $ 750000 / (1.15)² + $ 825000 / (1.15)³  + $ 907500 / (1.15)⁴ + $ 998250 / (1.15)⁵ + $ 1098075 / (1.15)⁶+ $ 1207882.5 / (1.15)⁷+ $ 1328670.75 / (1.15)⁸
= $ 750000 / 1.32 + $ 825000 / 1.52  + $ 907500 / 1.75 + $ 998250 / 2.01+ $ 1098075 / 2.31 + $ 1207882.5 / 2.36 + $ 1328670.75 / 3.05
The Present values are given above in the table
The sum of all the present values of revenues = $ 3548959.71
Thus the total cash inflow at present value = $ 3548959.71

The first year investment = 1.25 million (cash outflow)

The second year investment of $ 1.25 million cash outflow should also be discounted by 15% as (1+0.15)¹

Therefore the cash outflows = - $ 1.25 m - $ 1.25 / (1.15) = -1,25m - 1.087m = - 2.337 million = - 2337000

The constant cost is $ 150000 / year, so the cost for 7 years is discounted at the rate of 15%, the first year cost will be discounted by (1+0.15)² since the project has started two years back
= $ 150000 / (1.15)² + $ 150000 / (1.15)³+ $ 150000 / (1.15)⁴​​​​​​​+ $ 150000 / (1.15)⁵​​​​​​​+  $150000 / (1.15)⁶​​​​​​​+ $ 150000 / (1.15)⁷​​​​​​​+  $150000 / (1.15)⁸​​​​​​​
= $ 150000 / 1.32 + $ 150000 / 1.52 + $ 150000 / 1.75 + $ 150000 / 2.01 + $ 150000 / 2.31 + $ 150000 / 2.66 + $ 150000 / 3.05  
= $ 113636.36 + $ 98684.21 + $ 85714.29 + $74626.87 + $ 64935,06 + $ 56390.98 + $ 49180.32
= $ 543168.09
Thus is the Present value of the constant cost of $ 150000 / year = $ 543168.09 which is a cash outflow
Therefore the Present value of the total cash outflow is equal to -$ 2337000 - $ 543168 = - $ 2880168  

The total cash inflow - Total cash outflow = $ 3548959.71 - $ 2880168 = $ 668791.71

Thus the project profit after 7 years = $ 668791.71
The project is not risky as the NPV is positive and can be undertaken.