Problem 19 - Accounting

Question

Empire Healthcare Corp. is proposing to spend \(\$ 84,434\) on a 7 -year project whose estimated net cash flows are \(\$ 18,500\) for each of the seven years. a. Compute the net present value, using a rate of return of \(15 \%\). Use the table of present values of an annuity of \(\$ 1\) in the chapter. b. Based on the analysis prepared in (a), is the rate of return (1) more than \(15 \%\), (2) 15\%, or (3) less than 15\%? Explain. c. Determine the internal rate of return by computing a present value factor for an annuity of \(\$ 1\) and using the table of the present value of an annuity of \(\$ 1\) presented in the text.

Step-by-Step Solution

Answer

The NPV is -$7,470.6; the rate of return is less than 15%, approximately 12%.

Step 1: Understanding the Scenario

We need to calculate the Net Present Value (NPV) of a project proposal by Empire Healthcare Corp. The investment is $84,434, and the expected yearly net cash flow is $18,500 for 7 years. We're using a discount rate of 15%.

Step 2: Calculate the Present Value Factor

Find the Present Value Annuity Factor (PVAF) for 15% over 7 years. Use the present value annuity of $1 table to find this factor, which is approximately 4.1604.

Step 3: Calculate the Present Value of Cash Flows

Multiply the annual cash flow by the Present Value Annuity Factor: \[ PV = 18,500 \times 4.1604 = 76,963.4 \]

Step 4: Calculate the Net Present Value (NPV)

Subtract the initial investment from the present value of the cash flows:\[ NPV = 76,963.4 - 84,434 = -7,470.6 \]

Step 5: Analyze the Rate of Return

Since the NPV is negative, this means that the rate of return is less than 15%. The project is not yielding sufficient returns at this discount rate.

Step 6: Determine the Internal Rate of Return (IRR)

Calculate the IRR by determining the present value factor that makes the NPV zero. Rearrange the annuity formula to solve for the interest rate where the present value equals the initial investment:\[ 84,434 = 18,500 \times PVAF \]The factor (PVAF) is approximately 4.563. Check this against the annuity table to find that it corresponds to an IRR close to approximately 12%.

Key Concepts

Internal Rate of Return

The Internal Rate of Return (IRR) is a crucial financial metric used to evaluate the profitability of an investment. It represents the discount rate at which the net present value (NPV) of an investment is zero. In simpler terms, IRR is the percentage rate earned on each dollar invested for each period it is invested. This helps investors gauge whether a project is worthwhile.
To calculate IRR, we determine the rate at which the present value of cash inflows equals the initial investment. Mathematically, if IRR is the interest rate that brings the NPV to zero, it indicates that:

• The project breaks even, considering the time value of money.
• The cash flows over the investment period cover the initial cost.

In the original problem, Empire Healthcare needs to find the IRR to decide whether the project is financially viable. With an annuity factor from the table correlating to an IRR of approximately 12%, this suggests the project's returns don't meet the desired rate of 15%.

Present Value Annuity Factor

The Present Value Annuity Factor (PVAF) is integral for calculating the present value of a series of equal cash flows. This factor helps determine how much a series of regular payments is worth in today's dollars, given a particular discount rate.
For Empire Healthcare Corp., the PVAF is used to convert $18,500 received annually over seven years into present value terms, using a discount rate of 15%. To do so, we find the factor from a present value annuity table, which provides pre-calculated multipliers based on the period and interest rate.

• The calculated PVAF of 4.1604 means that the sum of the discounted cash flows, given an annuity of $18,500, has been adjusted to reflect its present value.
• This factor is crucial because it simplifies the process of calculating the NPV by providing a quick reference for discounting multiple periods of cash flows.

This ultimately aids in understanding the value of future cash flows today and assesses the project's potential profitability.

Discount Rate

The discount rate is the interest rate used to determine the present value of future cash flows. It reflects the time value of money, which acknowledges that a dollar today is worth more than a dollar in the future due to its potential earning capacity.
In financial decision-making, the selection of an appropriate discount rate is essential, as it impacts the evaluation of the project's financial feasibility. For Empire Healthcare's project, the chosen discount rate is 15%.

• A higher discount rate, like 15%, reduces the present value of future cash flows more significantly, highlighting the critical evaluation of risk and time preference in investment analysis.
• If the NPV results negative, as it does in this scenario, the return generated fails to meet or exceed the cost of capital or desired return rate.

Choosing a proper discount rate ensures accurately assessing whether an investment generates sufficient returns, thus guiding informed decisions on proceeding with projects.