Present Value and Capital Budgeting

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 |