Present Value of an Annuity of $1 at Compound Interest Year 6% 10% 12% 15% 20% 1 2 3 4 5 6 7 8 D 0.943 1.833 2.673 3.465 4.212 4.917 5.582 6.210 6.802 0.909 1.736 2.487 3.170 3.791 4.355 4.868 5.335 5 750 0.893 1.690 2.402 3.037 3.605 4.111 4.564 4.968 5.328 0.870 1.626 2.283 2.855 3.353 3.785 4.160 4.487 4.772 0.833 1.528 2.106 2.589 2.991 3.326 3.605 3.837 4. 031

FINANCIAL ACCOUNTING
10th Edition
ISBN:9781259964947
Author:Libby
Publisher:Libby
Chapter1: Financial Statements And Business Decisions
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### Present Value of an Annuity of $1 at Compound Interest

| Year | 6%  | 10% | 12% | 15% | 20% |
|------|-----|-----|-----|-----|-----|
| 1    | 0.943 | 0.909 | 0.893 | 0.870 | 0.833 |
| 2    | 1.833 | 1.736 | 1.690 | 1.626 | 1.528 |
| 3    | 2.673 | 2.487 | 2.402 | 2.283 | 2.106 |
| 4    | 3.465 | 3.170 | 3.037 | 2.855 | 2.589 |
| 5    | 4.212 | 3.791 | 3.605 | 3.353 | 2.991 |
| 6    | 4.917 | 4.355 | 4.111 | 3.785 | 3.326 |
| 7    | 5.582 | 4.868 | 4.564 | 4.160 | 3.605 |
| 8    | 6.210 | 5.335 | 4.968 | 4.487 | 3.837 |
| 9    | 6.802 | 5.759 | 5.328 | 4.772 | 4.031 |
| 10   | 7.360 | 6.145 | 5.650 | 5.019 | 4.192 |

---

### Instructions:

1. **Compute Net Present Value (NPV) for Each Project**:
   - Use the above table to determine the present value of the unequal lives of the projects.
   - Ignore the unequal lives if not applicable.
   - Round the results to the nearest dollar, if required.

### Office Expansion vs. Servers Upgrade

|                         | Office Expansion | Servers Upgrade |
|-------------------------|------------------|-----------------|
| Present value of annual net cash flows | $513,875           | $501,105        |
| Amount to be invested   | $490,000           | $490,000        |
| **Net Present Value**   | **$23,875**        ✔️ | **
Transcribed Image Text:### Present Value of an Annuity of $1 at Compound Interest | Year | 6% | 10% | 12% | 15% | 20% | |------|-----|-----|-----|-----|-----| | 1 | 0.943 | 0.909 | 0.893 | 0.870 | 0.833 | | 2 | 1.833 | 1.736 | 1.690 | 1.626 | 1.528 | | 3 | 2.673 | 2.487 | 2.402 | 2.283 | 2.106 | | 4 | 3.465 | 3.170 | 3.037 | 2.855 | 2.589 | | 5 | 4.212 | 3.791 | 3.605 | 3.353 | 2.991 | | 6 | 4.917 | 4.355 | 4.111 | 3.785 | 3.326 | | 7 | 5.582 | 4.868 | 4.564 | 4.160 | 3.605 | | 8 | 6.210 | 5.335 | 4.968 | 4.487 | 3.837 | | 9 | 6.802 | 5.759 | 5.328 | 4.772 | 4.031 | | 10 | 7.360 | 6.145 | 5.650 | 5.019 | 4.192 | --- ### Instructions: 1. **Compute Net Present Value (NPV) for Each Project**: - Use the above table to determine the present value of the unequal lives of the projects. - Ignore the unequal lives if not applicable. - Round the results to the nearest dollar, if required. ### Office Expansion vs. Servers Upgrade | | Office Expansion | Servers Upgrade | |-------------------------|------------------|-----------------| | Present value of annual net cash flows | $513,875 | $501,105 | | Amount to be invested | $490,000 | $490,000 | | **Net Present Value** | **$23,875** ✔️ | **
### Sentry Insurance Co. Investment Analysis

The investment committee of Sentry Insurance Co. is assessing two projects: office expansion and server upgrades. Both projects necessitate an investment of $490,000 but yield varying net cash flows over different timeframes.

#### Estimated Net Cash Flows

The estimated annual net cash flows from each project are detailed below:

| Year | Office Expansion | Servers |
|------|------------------|---------|
| 1    | $125,000         | $165,000|
| 2    | $125,000         | $165,000|
| 3    | $125,000         | $165,000|
| 4    | $125,000         | $165,000|
| 5    | $125,000         |         |
| 6    | $125,000         |         |

To facilitate the net present value (NPV) analysis, the committee has chosen a discount rate of 12%. Additionally, while the residual value at the end of each project's useful life is considered to be $0, the office expansion's residual value at the end of the fourth year is projected to be $180,000.

#### Present Value of $1 at Compound Interest

The table below shows the present value of $1 at various compound interest rates over a range of years:

| Year | 6%   | 10%  | 12%  | 15%  | 20%  |
|------|------|------|------|------|------|
| 1    | 0.943| 0.909| 0.893| 0.870| 0.833|
| 2    | 0.890| 0.826| 0.797| 0.756| 0.694|
| 3    | 0.840| 0.751| 0.712| 0.658| 0.579|
| 4    | 0.792| 0.683| 0.636| 0.572| 0.482|
| 5    | 0.747| 0.621| 0.567| 0.497| 0.402|
| 6    | 0.705| 0.564| 0.507| 0.432| 0.335|
| 7    |
Transcribed Image Text:### Sentry Insurance Co. Investment Analysis The investment committee of Sentry Insurance Co. is assessing two projects: office expansion and server upgrades. Both projects necessitate an investment of $490,000 but yield varying net cash flows over different timeframes. #### Estimated Net Cash Flows The estimated annual net cash flows from each project are detailed below: | Year | Office Expansion | Servers | |------|------------------|---------| | 1 | $125,000 | $165,000| | 2 | $125,000 | $165,000| | 3 | $125,000 | $165,000| | 4 | $125,000 | $165,000| | 5 | $125,000 | | | 6 | $125,000 | | To facilitate the net present value (NPV) analysis, the committee has chosen a discount rate of 12%. Additionally, while the residual value at the end of each project's useful life is considered to be $0, the office expansion's residual value at the end of the fourth year is projected to be $180,000. #### Present Value of $1 at Compound Interest The table below shows the present value of $1 at various compound interest rates over a range of years: | Year | 6% | 10% | 12% | 15% | 20% | |------|------|------|------|------|------| | 1 | 0.943| 0.909| 0.893| 0.870| 0.833| | 2 | 0.890| 0.826| 0.797| 0.756| 0.694| | 3 | 0.840| 0.751| 0.712| 0.658| 0.579| | 4 | 0.792| 0.683| 0.636| 0.572| 0.482| | 5 | 0.747| 0.621| 0.567| 0.497| 0.402| | 6 | 0.705| 0.564| 0.507| 0.432| 0.335| | 7 |
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