Homework Answers
Following is the calculation of CF:
| Particulars | Remark | Year 0 | Years 1-4 | Year 5 |
| Units | Given | 28000 | 28000 | |
| SP | Given | $344 | $344 | |
| Sales | 28000x344 | $ 96,32,000.00 | $ 96,32,000.00 | |
| Per unit vc | Given | $235.00 | $235.00 | |
| Variable cost | 28000x235 | $ 65,80,000.00 | $ 65,80,000.00 | |
| Fixed Cost | Given | $ 12,50,000.00 | $ 12,50,000.00 | |
| Depriciation | Calculated below | $ 10,40,000.00 | $ 10,40,000.00 | |
| EBT | Sales-VC-FC-DEP | $ 7,62,000.00 | $ 7,62,000.00 | |
| Tax | 0.24*EBT | $ 1,82,880.00 | $ 1,82,880.00 | |
| EAT | EBT-Tax | $ 5,79,120.00 | $ 5,79,120.00 | |
| OCF | EAT+DEP | $ 16,19,120.00 | $ 16,19,120.00 | |
| Fixed investment | Given | -5200000 | ||
| Working capital investment or recovery | -500000 | $500,000.00 | ||
| After tax salvage value | 625000 x (1-0.24) | $475,000.00 | ||
| CF |
OCF+Fixed investment+Working capital investment +After tax salvage value |
$-57,00,000.00 |
$16,19,120.00 |
$25,94,120.00 |
Depreciation = fixed investment/life = 5200000/5 = $10,40,000.00
NPV is calculated below:
| Year | CF | Discount Factor | Discounted CF | ||
| 0 | $ -57,00,000.00 | 1/(1+0.13)^0= | 1 | 1*-5700000= | $ -57,00,000.00 |
| 1 | $ 16,19,120.00 | 1/(1+0.13)^1= | 0.884955752 | 0.884955752212389*1619120= | $ 14,32,849.56 |
| 2 | $ 16,19,120.00 | 1/(1+0.13)^2= | 0.783146683 | 0.783146683373796*1619120= | $ 12,68,008.46 |
| 3 | $ 16,19,120.00 | 1/(1+0.13)^3= | 0.693050162 | 0.693050162277696*1619120= | $ 11,22,131.38 |
| 4 | $ 16,19,120.00 | 1/(1+0.13)^4= | 0.613318728 | 0.613318727679377*1619120= | $ 9,93,036.62 |
| 5 | $ 25,94,120.00 | 1/(1+0.13)^5= | 0.542759936 | 0.542759935999449*2594120= | $ 14,07,984.41 |
| NPV = Sum of all Discounted CF | $ 5,24,010.42 | ||||
Now if we increase the quantity by 1%, the CF for years 1-4 becomes:
| Particulars | Year 1-4 | Year 5 |
| Units | $ 28,280.00 | $ 28,280.00 |
| SP | $ 344.00 | $ 344.00 |
| Sales | $ 97,28,320.00 | $ 97,28,320.00 |
| Per unit vc | $ 235.00 | $ 235.00 |
| Variable cost | $ 66,45,800.00 | $ 66,45,800.00 |
| Fixed Cost | $ 12,50,000.00 | $ 12,50,000.00 |
| Depriciation | $ 10,40,000.00 | $ 10,40,000.00 |
| EBT | $ 7,92,520.00 | $ 7,92,520.00 |
| Tax | $ 1,90,204.80 | $ 1,90,204.80 |
| EAT | $ 6,02,315.20 | $ 6,02,315.20 |
| CF | $ 16,42,315.20 | $ 16,42,315.20 |
| Working capital investment or recovery | $500,000.00 | |
| After tax salvage value | $475,000.00 | |
| CF | $26,17,315.20 |
So the change in CF for 1-4 years
is $16,42,315.20/$16,19,120.00 -1 = 1.43%
So the change in NPV is $6,05,593.30/ $5,24,010.42
-1 = 16%
Now the minimum level of output below which you dont want to operate would be when NPV = 0, this can be found out using hit and trial or excel's goal seek function:
Using excel it comes out as 26,201.55 units, as it is tonnes, so fractional units is possible.
| Particulars | Year 1-4 | Year 5 |
| Units | $ 26,201.55 | $ 26,201.55 |
| SP | $ 344.00 | $ 344.00 |
| Sales | $ 90,13,332.43 | $ 90,13,332.43 |
| Per unit vc | $ 235.00 | $ 235.00 |
| Variable cost | $ 61,57,363.73 | $ 61,57,363.73 |
| Fixed Cost | $ 12,50,000.00 | $ 12,50,000.00 |
| Depriciation | $ 10,40,000.00 | $ 10,40,000.00 |
| EBT | $ 5,65,968.71 | $ 5,65,968.71 |
| Tax | $ 1,35,832.49 | $ 1,35,832.49 |
| EAT | $ 4,30,136.22 | $ 4,30,136.22 |
| CF | $ 14,70,136.22 | $ 14,70,136.22 |
| Working capital investment or recovery | $500,000.00 | |
| After tax salvage value | $475,000.00 | |
| CF | $24,45,136.22 |
| Year | CF | Discount Factor | Discounted CF | ||
| 0 | $ -57,00,000.00 | 1/(1+0.13)^0= | 1 | 1*-5700000= | $ -57,00,000.00 |
| 1 | $ 14,70,136.22 | 1/(1+0.13)^1= | 0.884955752 | 0.884955752212389*1470136.21735312= | $ 13,01,005.50 |
| 2 | $ 14,70,136.22 | 1/(1+0.13)^2= | 0.783146683 | 0.783146683373796*1470136.21735312= | $ 11,51,332.30 |
| 3 | $ 14,70,136.22 | 1/(1+0.13)^3= | 0.693050162 | 0.693050162277696*1470136.21735312= | $ 10,18,878.14 |
| 4 | $ 14,70,136.22 | 1/(1+0.13)^4= | 0.613318728 | 0.613318727679377*1470136.21735312= | $ 9,01,662.07 |
| 5 | $ 24,45,136.22 | 1/(1+0.13)^5= | 0.542759936 | 0.542759935999449*2445136.21735312= | $ 13,27,121.98 |
| NPV = Sum of all Discounted CF | $ -0.00 | ||||
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