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 PeriodCash Flow ($)
140
240
340
----
----
1940
201000 + 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 yearCost of AssetMACRSDepreciationAccumulatedBook Value
factorfor the yearDepreciationat end of year.
12400000.33337999279992160008
22400000.444510668018667253328
32400000.14813554422221617784
42400000.0741177842400000

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 1Year 2Year 3Year 4Year 5
Revenues625006562568906.2572351.562575969.14
Expenses-22500-23625-24806.25-26046.5625-27348.9
Gross Profit850008925093712.598398.125103318
Depreciation79992106680160008533280
Profit Before Tax5008-17430-6629645070103318
Tax35%35%35%35%35%
Profit after Tax3255-11330-430922929667157
PAT + Depreciation83247953511169168262467157
Change in Working Capital
Inventory32003200320032003200
Acc. Receivable800800800800800
Acc. Payable12001200120012001200
Total change28002800280028002800
Capital Expenditure00000
Cash Flow80447925511141167982464357
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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 yearCost of AssetMACRSDepreciationAccumulatedBook Value
factorfor the yearDepreciationat end of year.
16850000.142997886.597886.5587113.5
26850000.2449167756.5265643419357
36850000.1749119806.5385449.5299550.5
46850000.124985556.5471006213994
56850000.089361170.5532176.5152823.5
66850000.089261102593278.591721.5
76850000.089361170.565444930551
86850000.0446305516850000

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 1Year 2Year 3Year 4Year 5Year 6Year 7Year 8Year 9Year 10
Revenues0000000000
Expenses-105000-106833.3-108699-110596-112528-114492-116491-118525-120595-122700
Gross Profit105000106833.3108699110596.5112528114492116491118525120595122700
Depreciation97886.5167756.511980785556.561170.561102611713055100
Profit Before Tax7113.5-60923.2-1110825039.995135753390.25532187974.2120595122700
Tax35%35%35%35%35%35%35%35%35%35%
PAT4623.775-39600.08-7220.116275.9933382.134703.73595857183.278386.579755
PAT + Depreciation102510.28128156.42112586101832.594552.695805.79712987734.278386.579755
Change in Working Capital
Inventory800800800800800800800800800800
Acc Receivable200200200200200200200200200200
Acc Payable300300300300300300300300300300
Total Change700700700700700700700700700700
Cap Ex.000000000-30000
Cash Flows101810.28127456.42111886101132.593852.695105.79642987034.277686.5109055

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 yearCost of AssetMACRSDepreciationAccumulatedBook Value
factorfor the yearDepreciationat end of year.
13900000.14295573155731334269
23900000.244995511151242238758
33900000.174968211219453170547
43900000.124948711268164121836
53900000.08933482730299187009
63900000.08923478833777952221
73900000.08933482737260617394
83900000.0446173943900000

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 1Year 2Year 3Year 4Year 5Year 6Year 7Year 8Year 9Year 10
Revenues0000000000
Expenses-90000-91571.4-93170.2-94797-96452-98136-99850-101593-103367-105172
Gross Profit9000091571.493170.2494796.9996452.198136.299849.7101593103367105172
Depreciation97886.5167756.5119806.585556.561170.56110261170.53055100
Profit Before Tax-7886.5-76185.1-26636.39240.48935281.637034.238679.271042103367105172
Tax0.350.350.350.350.350.350.350.350.350.35
PAT-5126.225-49520.3-17313.66006.31822933.124072.225141.546177.367188.568361.6
PAT + Depreciation92760.275118236.2102492.991562.8284103.685174.28631276728.367188.568361.6
Change in Working Capital
Inventory800800800800800800800800800800
Acc Receivable200200200200200200200200200200
Acc Payable300300300300300300300300300300
Total Change 700700700700700700700700700700
Cap Ex.-20000000000000
Cash Flows112060.28117536.2101792.990862.8283403.684474.28561276028.366488.567661.6

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 Flows112760.28118236.2102492.991562.8178384103.685174.229258631276728.367188.568361.6

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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