Present Value and Capital Budgeting

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Part I
A.Present Value with Discount rate of 7% = 15000/(1+7%) = 15000/1.07 = $14,018.69 Present Value with Discount rate of 4% = 15000/(1+4%) = 15000/1.04 = $14,423.08 B.Account A - Present Value with Discount rate of 6% = 6500/(1+6%) = 6500/1.06 = $6,132.08 Account B - Present Value with Discount rate of 6% = 12600/(1+6%)^2 = 12600/1.1236 = $11,213.96 C.Present Value of Gold Mine 7% = 4900000/1.07 + 61,000,000/(1.07)^2 + 85,000,000/(1.07)^3 = 45,794,392.52 + 61,000,000/1.1449 + 85,000,000/1.2250

= 45,794,392.52 + 53,279,762.42 + 69,385,319.54
= $168,459,474.48
By using the same concept above we can determine the present value of Gold Mine. Present Value of Gold Mine @ 5% = 175,421,660.73
Present Value of Gold Mine @ 3% = 182,858,207.04
When the discount rate is 7%, the present value of gold mine is $168.46m. This value increase by approximately $6.96 when the discount rate is 2% less than 7%. When the discount rate is 3% value of gold mine is 182.86. Part II

A. Consider the project with the following expected cash flows: Year| Cash flow|
0| -$400,000|
1| $100,000|
2| $120,000|
3| $850,000|

If the discount rate is 0%, what is the project’s net present value? Year| Cash flow| Discount rate| Discount factor| Discounted cash flow| 0| -$400,000| 0%| 1.00| -$400,000|
1| $100,000| 0%| 1.00| $100,000|
2| $120,000| 0%| 1.00| $120,000|
3| $850,000| 0%| 1.00| $850,000|
| | | Net present value| $670,000|

If the discount rate is 2%, what is the project’s net present value? Year| Cash flow| Discount rate| Discount factor| Discounted cash flow| 0| -$400,000| 2%| 1.00| -$400,000|
1| $100,000| 2%| 1.02| $98,039|
2| $120,000| 2%| 1.04| $115,340|
3| $850,000| 2%| 1.06| $800,974|
| | | Net present value| $614,353|

If the discount rate is 6%, what is the project’s net present value? Year| Cash flow| Discount rate| Discount factor| Discounted cash flow| 0| -$400,000| 6%| 1.00| -$400,000|
1| $100,000| 6%| 1.06| $94,340|
2| $120,000| 6%| 1.12| $106,800|
3| $850,000| 6%| 1.19| $713,676|
| | | Net present value| $514,816|

If the discount rate is 11%, what is the project’s net present value? Year| Cash flow| Discount rate| Discount factor| Discounted cash flow| 0| -$400,000| 11%| 1.00| -$400,000|
1| $100,000| 11%| 1.11| $90,090|
2| $120,000| 11%| 1.23| $97,395|
3| $850,000| 11%| 1.37| $621,513|
| | | Net present value| $408,997|

With a capital cost of capital of 5%, what is the project’s modified internal rate of return? | | Discount rate| Discount factor| Discounted cash flow| Year| Cash flow| Lower rate| Higher rate| Lower rate| Higher rate| Lower rate| Higher rate| 0| -$400,000| 40%| 50%| 1.00| 1.00| | |

2| $100,000| 40%| 50%| 1.96| 2.25| $196,000| $225,000| 1| $120,000| 40%| 50%| 1.40| 1.50| $168,000| $180,000| 0| $850,000| 40%| 50%| 1.00| 1.0| $850,000| $850,000| | | | | | Future value| $1,214,000| $1,255,000|

| | | | | Present Value| $422,420| $371,852|
| | | | | | 44.78%| 46.40%|
| | | | | MIRR| 46.01%| |

The graph I drew shows the net present value profile of the cash flows. The graph shows that the net present value decreases as the discount rate increases. The net present value crosses the horizontal line at the point where the discount rate is equal to the internal rate of return (46%).

B. Consider a project with the expected cash flows:

Year| Cash flow|
0| -$815,000|
1| $141,000|
2| $320,000|
3| $440,000|

What is this project’s internal rate of return?
| | Discount rate| Discount factor| Discounted cash flow| Year| Cash flow| Lower rate| Higher rate| Lower rate| Higher rate| Lower rate| Higher rate| 0| -$815,000| 4%| 5%| 1.00| 1.00| -$815,000| -$815,000| 2| $141,000| 4%| 5%|...
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