# Finance Assignment Answer

**(Question number 1-9)**

** Ans: 1** Yield to Maturity on the Mortgage Bond.

Face Value = $1000

Coupon Rate = 8%

Therefore, semi-annual rate = 4%

Coupon payment = 0.04 * 1000 = $ 40

Let half a year be1 time period.

End of Period | Cash Flow ($) |

1 | 40 |

2 | 40 |

3 | 40 |

---- | |

---- | |

19 | 40 |

20 | 1000 + 40 = 1040 |

Let the annual Yield to Maturity be R. => Semi-annual yield = R/2 = r

Present Value of Bond = CF1/(1+r) + CF2/(1+r)^2 + …… CF20/(1+r)^20

875 = 40/(1+r) + 40/(1+r)^2 + ….. 40/(1+r)^19 + 1040/(1+r)^20

Solve this equation for r using a financial calculator or Microsoft Excel.

r = 5%

R = 2r = 10%

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** Ans 2:** Let k be the cost of equity.

Using the dividend discount model.

P = D1/(k-g)

=> 27 = D0 * (1+g) / (k-g)

=> 27 = 1.215*1.08/(k- 0.08)

=> k = 0.1286 = 12.86%

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** Ans 3:** Total Debt (long-term) = 5,143,000

Total Equity = 500,000 + 2,000,000 + 8,640,210 = 11,140,210

D/(D+E) = 0.3158

E/(D+E) = 0.6842

Overall cost of capital = D/(D+E) * YTM + E/(D+E) * k

0.3158 * 0.1 + 0.6842* 0.1286

=0.03158 + 0.08799

= 0.1196 = 11.96%

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** Ans 4:** Cash Flows for automated mixer

Cost of Mixer = $240,000

MACRS Depreciation schedule:

End of year | Cost of Asset | MACRS | Depreciation | Accumulated | Book Value |

factor | for the year | Depreciation | at end of year. | ||

1 | 240000 | 0.3333 | 79992 | 79992 | 160008 |

2 | 240000 | 0.4445 | 106680 | 186672 | 53328 |

3 | 240000 | 0.1481 | 35544 | 222216 | 17784 |

4 | 240000 | 0.0741 | 17784 | 240000 | 0 |

The Revenues and Expenses both increase by 5%.We assume that the Marginal Revenues brought in by the mixer and the savings in expenses obtained also increase at 5% per annum..

The change in Working Capital is assumed to increase by 20% of the given estimates due to the mixer. Only changes due to the mixer i.e. 20% of the given estimates have been used for calculating the mixer's cash flows.

The Cash flow calculations have been shown below.

Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | |

Revenues | 62500 | 65625 | 68906.25 | 72351.5625 | 75969.14 |

Expenses | -22500 | -23625 | -24806.25 | -26046.5625 | -27348.9 |

Gross Profit | 85000 | 89250 | 93712.5 | 98398.125 | 103318 |

Depreciation | 79992 | 106680 | 160008 | 53328 | 0 |

Profit Before Tax | 5008 | -17430 | -66296 | 45070 | 103318 |

Tax | 35% | 35% | 35% | 35% | 35% |

Profit after Tax | 3255 | -11330 | -43092 | 29296 | 67157 |

PAT + Depreciation | 83247 | 95351 | 116916 | 82624 | 67157 |

Change in Working Capital |
|||||

Inventory | 3200 | 3200 | 3200 | 3200 | 3200 |

Acc. Receivable | 800 | 800 | 800 | 800 | 800 |

Acc. Payable | 1200 | 1200 | 1200 | 1200 | 1200 |

Total change | 2800 | 2800 | 2800 | 2800 | 2800 |

Capital Expenditure | 0 | 0 | 0 | 0 | 0 |

Cash Flow | 80447 | 92551 | 114116 | 79824 | 64357 |

** Ans 5:** NPV = -240,000 + 80447/1.1196 + 92551/(1.1196^2) + 114116/(1.1196^3) +

79824/(1.1196^4) + 64357/(1.1196^5)

= $66438.97

** Ans 6:** IRR is the rate used for discounting such that the NPV becomes 0.

Let the IRR be r.

-240,000 + 80447/(1+r) + 92551/(1+r)^2 + 114116/(1+r)^3 +

79824/(1+r)^4 + 64357/(1+r)^5 = 0

IRR = 24.13%

** Ans 7:** The depreciation schedule for the continuous oven is as follows.

End of year | Cost of Asset | MACRS | Depreciation | Accumulated | Book Value |

factor | for the year | Depreciation | at end of year. | ||

1 | 685000 | 0.1429 | 97886.5 | 97886.5 | 587113.5 |

2 | 685000 | 0.2449 | 167756.5 | 265643 | 419357 |

3 | 685000 | 0.1749 | 119806.5 | 385449.5 | 299550.5 |

4 | 685000 | 0.1249 | 85556.5 | 471006 | 213994 |

5 | 685000 | 0.0893 | 61170.5 | 532176.5 | 152823.5 |

6 | 685000 | 0.0892 | 61102 | 593278.5 | 91721.5 |

7 | 685000 | 0.0893 | 61170.5 | 654449 | 30551 |

8 | 685000 | 0.0446 | 30551 | 685000 | 0 |

The Oven does not bring in Marginal Revenues but saves operating costs. These Savings have been assumed to grow to 5% more than today over the next 10 years. Assuming a constant increase at 1.1746%.

The estimated change in working capital is $14000 per annum. We assume 5% of this (=$700) to be because of the oven.

The Cash flow calculations are shown below.

Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Year 6 | Year 7 | Year 8 | Year 9 | Year 10 | |

Revenues | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

Expenses | -105000 | -106833.3 | -108699 | -110596 | -112528 | -114492 | -116491 | -118525 | -120595 | -122700 |

Gross Profit | 105000 | 106833.3 | 108699 | 110596.5 | 112528 | 114492 | 116491 | 118525 | 120595 | 122700 |

Depreciation | 97886.5 | 167756.5 | 119807 | 85556.5 | 61170.5 | 61102 | 61171 | 30551 | 0 | 0 |

Profit Before Tax | 7113.5 | -60923.2 | -11108 | 25039.99 | 51357 | 53390.2 | 55321 | 87974.2 | 120595 | 122700 |

Tax | 35% | 35% | 35% | 35% | 35% | 35% | 35% | 35% | 35% | 35% |

PAT | 4623.775 | -39600.08 | -7220.1 | 16275.99 | 33382.1 | 34703.7 | 35958 | 57183.2 | 78386.5 | 79755 |

PAT + Depreciation | 102510.28 | 128156.42 | 112586 | 101832.5 | 94552.6 | 95805.7 | 97129 | 87734.2 | 78386.5 | 79755 |

Change in Working Capital |
||||||||||

Inventory | 800 | 800 | 800 | 800 | 800 | 800 | 800 | 800 | 800 | 800 |

Acc Receivable | 200 | 200 | 200 | 200 | 200 | 200 | 200 | 200 | 200 | 200 |

Acc Payable | 300 | 300 | 300 | 300 | 300 | 300 | 300 | 300 | 300 | 300 |

Total Change | 700 | 700 | 700 | 700 | 700 | 700 | 700 | 700 | 700 | 700 |

Cap Ex. | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -30000 |

Cash Flows | 101810.28 | 127456.42 | 111886 | 101132.5 | 93852.6 | 95105.7 | 96429 | 87034.2 | 77686.5 | 109055 |

**NPV = **-685000 + CF1/(1.1196) + CF2/(1.1196^2) +…… CF10/(1.1196^10)

= - $93,193.24

Even without the Working Capital assumption the NPV = -$89,655.02

** Ans 8:** The depreciation schedule for the semi-automated packer is as follows.

End of year | Cost of Asset | MACRS | Depreciation | Accumulated | Book Value |

factor | for the year | Depreciation | at end of year. | ||

1 | 390000 | 0.1429 | 55731 | 55731 | 334269 |

2 | 390000 | 0.2449 | 95511 | 151242 | 238758 |

3 | 390000 | 0.1749 | 68211 | 219453 | 170547 |

4 | 390000 | 0.1249 | 48711 | 268164 | 121836 |

5 | 390000 | 0.0893 | 34827 | 302991 | 87009 |

6 | 390000 | 0.0892 | 34788 | 337779 | 52221 |

7 | 390000 | 0.0893 | 34827 | 372606 | 17394 |

8 | 390000 | 0.0446 | 17394 | 390000 | 0 |

The Oven does not bring in Marginal Revenues but saves operating costs. These Savings have been assumed to grow to 5% more than today over the next 10 years. Assuming a constant increase at 1.1746%.

The estimated change in working capital is $14000 per annum. We assume 5% of this (=$700) to be because of the oven.

The Cash flow calculations are shown below.

We assume that the previous packer was sold at its market value when the semi-automated packer was installed.

Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Year 6 | Year 7 | Year 8 | Year 9 | Year 10 | |

Revenues | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

Expenses | -90000 | -91571.4 | -93170.2 | -94797 | -96452 | -98136 | -99850 | -101593 | -103367 | -105172 |

Gross Profit | 90000 | 91571.4 | 93170.24 | 94796.99 | 96452.1 | 98136.2 | 99849.7 | 101593 | 103367 | 105172 |

Depreciation | 97886.5 | 167756.5 | 119806.5 | 85556.5 | 61170.5 | 61102 | 61170.5 | 30551 | 0 | 0 |

Profit Before Tax | -7886.5 | -76185.1 | -26636.3 | 9240.489 | 35281.6 | 37034.2 | 38679.2 | 71042 | 103367 | 105172 |

Tax | 0.35 | 0.35 | 0.35 | 0.35 | 0.35 | 0.35 | 0.35 | 0.35 | 0.35 | 0.35 |

PAT | -5126.225 | -49520.3 | -17313.6 | 6006.318 | 22933.1 | 24072.2 | 25141.5 | 46177.3 | 67188.5 | 68361.6 |

PAT + Depreciation | 92760.275 | 118236.2 | 102492.9 | 91562.82 | 84103.6 | 85174.2 | 86312 | 76728.3 | 67188.5 | 68361.6 |

Change in Working Capital |
||||||||||

Inventory | 800 | 800 | 800 | 800 | 800 | 800 | 800 | 800 | 800 | 800 |

Acc Receivable | 200 | 200 | 200 | 200 | 200 | 200 | 200 | 200 | 200 | 200 |

Acc Payable | 300 | 300 | 300 | 300 | 300 | 300 | 300 | 300 | 300 | 300 |

Total Change | 700 | 700 | 700 | 700 | 700 | 700 | 700 | 700 | 700 | 700 |

Cap Ex. | -20000 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

Cash Flows | 112060.28 | 117536.2 | 101792.9 | 90862.82 | 83403.6 | 84474.2 | 85612 | 76028.3 | 66488.5 | 67661.6 |

NPV = -390000 + CF1/1.1196 + CF2/(1.1196^2) + …. CF10/ (1.1196^10)

= -$29367.55

However, without the Working Capital assumption the Cash flows are

Cash Flows | 112760.28 | 118236.2 | 102492.9 | 91562.81783 | 84103.6 | 85174.22925 | 86312 | 76728.3 | 67188.5 | 68361.6 |

And the NPV = $128624.53

** Ans 9:** Mike should undertake the automated mixer as it has a NPV = $66438.97 and an IRR of 24% i.e. greater than the overall cost of capital. Therefore, Mike should invest the $240,000 in the automated mixer.

The Continuous Oven has a negative NPV ( = -$93,193) and therefore should not be undertaken.

The Semi-automated packer has an NPV of $128,624.53. (However, the effects on Working Capital should be studied carefully as they turn the NPV negative) . The investment worth $ 390,000 should be made.

Therefore, Total Capital Expenditure for Mike = $240,000 + $390,000 = $630,000 which is less than his budget of $1,000,000.

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