Financial Mathematics - Assignment Example

Fundamentals of Corporate Finance

Question 1

Main assumptions

Rate of inflation for the four years =3.25%

Market sizing

Original equipment manufacturer

Production: 6.2 million cars annually

Growth rate 2.5% per a year

Market share:11%

Replacement market

Production: 32 million tires

Growth rate: 2%

Market share: 8%

Revenue calculations

Annual price growth 100%+1%+3.25%= 104.25%

OEM market growth index 100%+2.5% = 102.5%

Replacement market growth index 100%+2% = 102%

ORIGINAL EQUIPMENT MANUFACTURER

Year 1

Year 2

Year 3

Year 4

price per a unit

$ 41.0000

$41*104.25% =$42.7425

$42.7425 *104.25% =$44.5591

$44.5591 *104.25% =$46.4528

Total manufactured cars

6,200,000.0000

6,200,000.0000* 102.5% =6,355,000.0000

6,355,000.0000*102.5% =6,513,875.0000

6,513,875.0000*

102.55 =6,676,721.8750

Total number of tires needed

6,200,000.0000*4 =24,800,000.0000

6,355,000.0000*4 =25,420,000.0000

6,513,875.0000 *4 =26,055,500.0000

6,676,721.8750* 4 =26,706,887.5000

Market share/tires sold

24,800,000.0000*11%= 2,728,000.0000

25,420,000.0000* 11% =2,796,200.0000

26,055,500.0000*11% =2,866,105.0000

26,706,887.5000*11% =2,937,757.6250

Sales revenue

2,728,000.0000 *$41 =$111,848,000.0000

2,796,200.0000*$42.7425= $119,516,578.5000

2,866,105.0000*$44.5591 =$127,710,933.9134

2,937,757.6250 *46.4528 =$136,467,114.8198

REPLACEMENT MARKET

Year 1

Year 2

Year 3

Year 4

price per a unit

$62.0000

$62.0000*104.25% =$64.6350

$64.6350*104.25% =$67.3820

$67.3820 *104.25% =$70.2457

Total Market size

32,000,000.0000

32,000,000.0000 *102% =32,640,000.0000

32,640,000.0000*102% =33,292,800.0000

33,292,800.0000*102% =33,958,656.0000

Market share/ units sold

32,000,000.0000 *8% =2,560,000.0000

32,640,000.0000*8%

=2,611,200.0000

33,292,800.0000*8% =2,663,424.0000

33,958,656.0000*102% =2,716,692.4800

Sales revenue

2,560,000.0000 *$62 =$158,720,000.0000

2,611,200.0000*64.6350 =$168,774,912.0000

2,663,424.0000*$67.3820 = $179,466,802.6752

2,716,692.4800*$70.2457= $190,836,024.6247

Total sales revenue

$111,848,000.0000 + $158,720,000.0000 =270,568,000.0000

$$119,516,578.5000 + $168,774,912.0000

=288,291,490.5000

$$127,710,933.9134 + 179,466,802.6752 =307,177,736.5886

$$136,467,114.8198 + $190,836,024.6247 =327,303,139.4445

Expenses calculation

Assumptions

Variable costs growth index 104.25%

Marketing cost growth index 103.25%

Variable costs

Year 1

Year 2

Year 3

Year 4

Cost per a unit

$18.0000

$18.0000*104.25% =$18.7650

$18.7650*104.25% =$19.5625

$19.5625* 104.25% =$20.3939

OEM units

2,728,000.0000

2,796,200.0000

2,866,105.0000

2,937,757.6250

Replacement market units

2,560,000.0000

2,611,200.0000

2,663,424.0000

2,716,692.4800

Total units manufactured

2,728,000.0000 +2,560,000.0000 =5,288,000.0000

2,796,200.0000 + 2,611,200.0000 =5,407,400.0000

2,866,105.0000 + 2,663,424.0000 =5,529,529.0000

2,937,757.6250 + 2,716,692.4800 =5,654,450.1050

Variable costs

5,288,000.0000*$18 =$95,184,000.0000

5,407,400.0000 *$18.7650 =101,469,861.0000

5,529,529.0000* $19.5625 =108,171,480.1816

5,654,450.1050* $20.3939 =115,316,399.0212

Marketing and Admin costs

$ 25,000,000.0000

$25,000,000.0000 *103.25% =$25,812,500.0000

$25,812,500.0000* 103.25% =$26,651,406.2500

$26,651,406.2500 * 103.25% =$27,517,576.9531

Depreciation calculation

Initial cost of equipment $120,000,000

Salvage value $65,000,000

Life of asset 4 years

Deprecation annually

FREE CASH FLOW FOR YRAR 0 TO 4

Year 0

Year 1

Year 2

Year 3

Year 4

Revenues

$270,568,000.0000

$288,291,490.5000

$307,177,736.5886

$327,303,139.4445

Cost of goods sold

($95,184,000.0000)

($101,469,861.0000)

($108,171,480.1816)

($115,316,399.0212)

Gross profit

$175,384,000.0000

$186,821,629.50

$199,006,256.4070

$211,986,740.4233

Cash operating expenses

($25,000,000.0000)

($25,812,500.0000)

($26,651,406.2500)

($27,517,576.9531)

Depreciation

($13,750,000.0000)

($13,750,000.0000)

($13,750,000.0000)

($13,750,000.0000)

Net operating income

$136,634,000.0000

$147,259,129.50

$158,604,850.1570

$170,719,163.4702

Taxes 35%

$47,821,900.0000

$51,540,695.3250

$55,511,697.5549

$59,751,707.2146

Net operating profit

$88,812,100.0000

$95,718,434.18

$103,093,152.6020

$110,967,456.2556

Add back depreciation

$13,750,000.0000

$13,750,000.0000

$13,750,000.0000

$13,750,000.0000

operating cash flow

$102,562,100.0000

$109,468,434.1750

$116,843,152.6020

$124,717,456.2556

Less Capital expenditure

($120,000,000.0000)

Less Net working capital

($11,000,000.0000)

($67,642,000.0000)

($72,072,872.6250)

($76,794,434.1472)

($81,825,784.8611)

Add salvage value

$65,000,000.0000

Return of Working capital

($11,000,000.0000)

Free cash flow

($131,000,000.0000)

$34,920,100.0000

$37,395,561.5500

$40,048,718.4549

$96,891,671.3945

Question 2

In capital budgeting, depreciation is considered only to the extent that is affects taxable income and thus the amount of tax liability. It is, however, a non-cash expense. This means that there is no real transfer of cash and thus it does treated as a negative cash flow and has no effect on the free cash flow (Bertoni, Colombo & Croce, 2010).

On the other hand, depreciation is tax deductible. This means that it is recognized as an expense. It is thus subtracted from the gross income to get the net operating income before tax. This provides a depreciation tax shield because the taxable income is less the depreciation charge. It is however, added back to get the operating cash flows.

Question 3

I would use 12% as the discount rate for the project

The additional risk associated with SuperTread is a non-systematic. These risks are specific to an industry or a company and do not affect all market players as a whole. The 2% additional risk is specific to SuperTread tires and does not affect the other tires produced by the company.

Unlike systemic risks, non-systemic risks are not accounted for in the rate of return. They are mitigated through investment diversification. They however form part of the total risk of a particular investment (Savvides, 1989).

Question 4

Net present Value

Year 0 cash flows

NPV = ($131,000,000) + ++ + = $20,072,468.9940

The net present value is the value of all future cash flows expected from the investment discounted to the present period less the initial capital investment. It is an estimate of the change in value of a company with the adoption of a new project. A positive NPV of $20,072,468.9940 indicates that the project is profitable since there is residue left after subtracting the initial capital investment (Bierman & Smidt, 2007).

Payback period

Period/Year

cash flow

Accumulated cash flow

0

$ (131,000,000.0000)

$ (131,000,000.0000)

1

$ 34,920,100.0000

$ (96,079,900.0000)

2

$ 37,395,561.5500

$ (58,684,338.4500)

3

$ 40,048,718.4549

$ (18,635,619.9951)

4

$ 96,891,671.3945

$ 78,256,051.3994

= = 3.1923

Payback period is 3 years 2 months. The company desires a payback period of less than 3 3 years and thus based on this appraisal method, the investment should be rejected.

The payback period estimates how long it would take for the initial investment to be recovered from the net cash flows that the project generates. The Acceptable payback period is set by the company and thus varies from one company to another. The shorter the payback period the more desirable the investment. This method of appraisal however does not consider the time value of money and favors projects whose cash flows are more closer to the onset of the project than later on.

Discounted payback period

Period/Year

cash flow

Discounting factor

Discounted cash flows

Accumulated cash flow

0

$ (131,000,000.0000)

1

$ (131,000,000.0000)

$ (131,000,000.0000)

1

$ 34,920,100.0000

0.892857143

$ 31,178,660.7143

$ (99,821,339.2957)

2

$ 37,395,561.5500

0.797193878

$ 29,811,512.7152

$ (70,009,826.5705)

3

$ 40,048,718.4549

0.711780248

$ 28,505,886.7464

$ (41,503,939.8240)

4

$96,891,671.3945

0.635518078

$ 61,576,408.8181

$ 20,072,468.9940

Payback period is 3 years 8 months which is within the 4-year discounted payback period that is acceptable by the company.

The discounted payback period indicates the amount of time it would take to recover the initial investment from discounted cash flows generated by the investment (Gervais, 2011). It takes into consideration the time value of money.

Internal rate of return

NPV at 12% discount rate is $20,072,468.9940

NPV at a higher discount rate

NPV = ($131,000,000) + ++ + = ($199,252.2048)

IRR= 12% + = 0.179402

IRR= 17.9410%

The internal rate of return is the rate that equates the net present value of all future cash flows to zero. The fact that it is an internal rate means that this appraisal method does not take into consideration external factors such as inflation. It presents the percentage earnings per an investment unit invested and thus allows investors to compare potential investments based on the yield to be realized (Magni, 2010).

With an IRR of 17.9410%, the project is viable because the rate is higher than the discounting rate, which stands at 12%.

Profitability index

= [ ++ + ] /$131,000,000 =1.1532

A positive profitability index of 1.1532 means the project is viable and the company should invest. This index shows the ratio of discounted cash flows to the initial investment. The ratio quantifies the amount of value per unit that the investment yields.