## using the payback method

Describe the use of internal rate of return (IRR), net present value (NPV), and the payback method in evaluating project cash flows.

According to “Net Present Value And Internal Rate Of Return” (2017),  “NPV and IRR are two methods for choosing between alternate projects and investments when the goal is to maximize shareholder wealth” (para 6). To explain the NPV Method is easy: the present value of cash inflows minus the present value of cash outflows, which arrives at a dollar amount that is the net benefit to the organization (“Net Present Value And Internal Rate Of Return”, 2017).

The Internal Rate of Return
The IRR, is defined as the discount rate that makes NPV = 0. Like the NPV process, it starts by identifying all cash inflows and outflows. But instead of relying on external data the IRR is purely a function of the inflows and outflows of that project (“Net Present Value And Internal Rate Of Return”, 2017).  “The IRR rule states that projects or investments are accepted when the project’s IRR exceeds a hurdle rate. Depending on the application, the hurdle rate may be defined as the weighted average cost of capital” (“Net Present Value And Internal Rate Of Return”, 2017).

“Each of the two rules used for making capital-budgeting decisions has its strengths and weaknesses. The NPV rule chooses a project in terms of net dollars or net financial impact on the company, so it can be easier to use when allocating capital” (“Net Present Value And Internal Rate Of Return”, 2017).

It requires an assumed discount rate, and also assumes that this percentage rate will be stable over the life of the project, and that cash inflows can be reinvested at the same discount rate. In the real world, those assumptions can break down, particularly in periods when interest rates are fluctuating (“Net Present Value And Internal Rate Of Return”, 2017).  “The appeal of the IRR rule is that a discount rate need not be assumed, as the worthiness of the investment is purely a function of the internal inflows and outflows of that particular investment. However, IRR does not assess the financial impact on a firm; it only requires meeting a minimum return rate” (“Net Present Value And Internal Rate Of Return”, 2017).

Calculate the following time value of money problems:

If you want to accumulate \$500,000 in 20 years, how much do you need to deposit today that pays an interest rate of 15%?

PV of a single sum = \$500 000/ [ 1.15]^20

=\$30 550.14

FV of a single sum = \$200000* [1.05]^5

• What is the future value if you plan to invest \$200,000 for 5 years and the interest rate is 5%?

=\$255 256.31

r= [FV/ PV] *(1/n) -1

• What is the interest rate for an initial investment of \$100,000 to grow to \$300,000 in 10 years?

r= [300 000/ 100 000] ^( 1/10) -1

=11.61%

PV of an ordinary annuity =PMT*[1-(1+r]^-n]/r

• If your company purchases an annuity that will pay \$50,000/year for 10 years at a 11% discount rate, what is the value of the annuity on the purchase date if the first annuity payment is made on the date of purchase?

\$50 000*[1-[1.11]^-10]/ 0.11

=\$294 461.60 *1.11 [annuity due]

=\$326 852.38

What is the rate of return required to accumulate \$400,000 if you invest \$10,000 per year for 20 years. Assume all payments are made at the end of the period.

r=[Fv/PV]^(1/n) -1

= [\$400 000/10000]^(1/20) -1

=20.25%

Calculate the project cash flow generated for Project A and Project B

Referances:

Net Present Value and Internal Rate of Return. (2017). Retrieved from http://www.investopedia.com/exam-guide/cfa-level-1/quantitative-methods/discounted-cash-flow-npv-irr.asp

To view and download a complete answer, scroll down to the bottom to pay 