Principles of Finance

Principles of Finance

Assignment Module 1

Part I: Calculating Present Value.

Answer A:

The Present Value is given by

Present Value = Future Value/(1+i)n

Here

Future Value = $15000/-

Interest rate = 'i = 0.07

No of years = n = 1

Therefore our present value is given by

PV= 15000/ (1+.07)1

Present Value = $14018.7/-

If the discount rate is only 4% or 0.04, then our present value will become,

PV = 15000/(1+.04)1

Present Value = $ 15600/-

Answer B

Account A

Future Value = $6500/-

No of years = 1

Interest rate = 0.06 or 6%

Present Value = 6500 / (1+.06)1

PV = $6132.01/-

Account B

Future Value = $12,600/-

No of years = 2

Interest rate = 0.06 or 6%

Present Value = 12600 / (1+.06)2

PV = $11,214/-

Answer C

Present Value = Future Value year 1 / (1+i)0 + Future Value year 2 / (1+i)1 + Future Value year 3 / (1+i)2

FV1 = 49,000,000 , FV2 = 61,000,000, FV3 = 85,000,000 , interest (i) = 7%

PV = (49,000,000 / (1.07)0) + (61,000,000 / (1.07)1) + (85,000,000 / (1.07)2)

PV = 49,000,000 + 57,009,345.79 + 74,242,291.9

PV = $180,251,637.7/-

FV1 = 49,000,000 , FV2 = 61,000,000, FV3 = 85,000,000 , interest (i) = 5%

PV = (49,000,000 / (1.05)0) + (61,000,000 / (1.05)1) + (85,000,000 / (1.05)2)

PV = 49,000,000 + 58,095,238.1+ 77,097,505.67

PV = $184,192,743,76/-

FV1 = 49,000,000 , FV2 = 61,000,000, FV3 = 85,000,000 , interest (i) = 3%

PV = (49,000,000 / (1.03)0) + (61,000,000 / (1.03)1) + (85,000,000 / (1.03)2)

PV = 49,000,000 + 59,223,300,97 + 80,120,652,28

PV = $188,343,953,25/-

After comparing the values of the three present values we can see that the higher the discount rate, the lower the present value. The discount rate is representing the opportunity cost of the gold mine. If the discount rate is 7 % and someone offers us that he is willing to give us more than 0.180 billion $ for purchasing the gold mine then we can sell off this asset and invest the capital in a more lucrative asset which gives us a return of more than 7.6%.

Part II: Capital Budgeting Practice Problems

Answer A.

Net Present Value when Discount rate is 0.0%

Year

Cash flow

Discount rate

PVIF

PV

PV

0

-400000

0%

1/((1+0.0)0)

-400000 x 1/((1+0.0)0)

-400000

1

100000

0%

1/((1+0.0)1)

100000 x 1/((1+0.0)1)

100000

2

120000

0%

1/((1+0.0)2)

120000 x 1/((1+0.0)2)

120000

3

850000

0%

1/((1+0.0)3)

850000 x 1/((1+0.0)3)

850000

NPV

$670000/-

The NPV at Discount Rate 0% is $670,000/-

Net Present Value when Discount rate is 2%

Year

Cash flow

Discount rate

PVIF

PV

PV

0

-400000

02%

1/((1+0.02)0)

-400000 x 1/((1+0.02)0)

-400000

1

100000

02%

1/((1+0.02)1)

100000 x 1/((1+0.02)1)

98039.22

2

120000

02%

1/((1+0.02)2)

120000 x 1/((1+0.02)2)

115340.3

3

850000

02%

1/((1+0.02)3)

850000 x 1/((1+0.02)3)

800974

NPV

614353.5

The NPV at Discount Rate 2% is $614,353.5/-

Net Present Value when Discount rate is 6%

Year

Cash flow

Discount rate

PVIF

PV

PV

0

-400000

06%

1/((1+0.06)0)

-400000 x 1/((1+0.06)0)

-400000

1

100000

06%

1/((1+0.06)1)

100000 x 1/((1+0.06)1)

94339.62

2

120000

06%

1/((1+0.06)2)

120000 x 1/((1+0.06)2)

106799.6

3

850000

06%

1/((1+0.06)3)

850000 x 1/((1+0.06)3)

713676.4

NPV

514815.6

The NPV at 6% is $514,815.6/-

Net Present Value when Discount rate is 11%

Year

Cash flow

Discount rate

PVIF

PV

PV

0

-400000

11%

1/((1+0.11)0)

-400000 x 1/((1+0.11)0)

-400000

1

100000

11%

1/((1+0.11)1)

100000 x 1/((1+0.11)1)

90090.09

2

120000

11%

1/((1+0.11)2)

120000 x 1/((1+0.11)2)

97394.69

3

850000

11%

1/((1+0.11)3)

850000 x 1/((1+0.11)3)

621512.7

NPV

408997.5

The NPV at 11% is $408,997.5/-

Modified Internal Rate of when Cost of Capital is 5%

Yr

Cash flow

Cost of Capital

Discounted PV

Discounted PV

PV @ 38.758%

PV

0

-400000

5%

-400000 1/((1+0.05)0)

-400000

-400000 x 1/(1.38758)0

-400000

1

100000

5%

100000 x 1/((1+0.05)1)

95238.1

95,238.1x 1/(1.38758)1

68636.11

2

120000

5%

120000 x 1/((1+0.05)2)

108843.5

108843.5x 1/(1.38758)2

56530.99

3

850000

5%

850000 x 1/((1+0.05)3)

734262

734,262x 1/(1.38758)3

274838.1

NPV

5.198

The Modified IRR when cost of capital is 5% is 38.758%.

The point on horizontal axis where the NPV line cuts the axis is the IRR where NPV is equal to zero. It represents the point after which the project does not remains feasible to pursue.

Answer B.

Internal Rate of Return

Yr

Cash flow

PV @ ...