Chapter 13

Discounted Cash-Flow Analysis

Present Value

Present value is the value today of benefits that are expected to accrue in the future

When discounting is done at the minimum acceptable rate of return on equity: Present value in excess of the

required initial equity cash outlay implies that a project is worthy of further considerations

A present value totaling less than the required initial equity expenditure results in automatic rejection

Present Value

To use this approach, discount all anticipated future cash flows at the minimum acceptable rate of return. The result is the present value of expected cash flows.

PV=CF1/(1+i)+CF2(1+i)2+CF3/(1+i)3+….+(CFn/(1+i)n

Net Present Value

Subtracting the required initial equity expenditure from the present value yields net present value A positive net present value means a

project is expected to yield a rate of return in excess of the discount rate, and therefore merits further consideration

A net present value of less than zero means the project is expected to yield a rate of return less than the minimum acceptable rate, and therefore should be rejected

Internal Rate of Return

There is an inverse relationship between discount rates and present value

The rate that will exactly equate the present value of a projected stream of cash flows with any positive initial cash investment is the internal rate of return

Internal Rate of Return

n Cost = Σ CF1/(1+k)t

t=1

Where CF is the cash flow projected for year t, cost is defined as the initial cash outlay, and k is the discount rate that makes the present value of the expected future cash flows exactly equal to the initial cash outlay

Internal Rate of Return

Decision criteria using the IRR is:

If the internal rate of return is equal to or greater than an investor’s required rate of return, a project is considered further

If the internal rate of return is less than the minimum acceptable rate of return, the project is rejected

Problems with the Internal Rate of Return

Can result in conflicting decision signals

Might result in investment error

Reinvestment–Rate Problem

Interproject comparison using internal rate of return analysis involves an implicit assumption that funds are reinvested at the internal rate of return. The internal rate of return method reliably discriminates between alternatives only if there are available other acceptable opportunities expected to yield an equally high rate.

The Multiple-Solutions Problem

Generally, a project’s net present value is a decreasing function of the discount rate employed. Thus, with successively higher discount rates, a point is reached where the net present value is zero. This is the internal rate of return, and any greater discount rate will result in a negative net present value.

The Multiple-Solutions Problem

Not all cash-flow forecasts have one internal rate of return equating all cash inflows with all cash outflows.

Investment proposals may have any number of internal rates of return, depending on the cash-flow pattern.

Comparing Net Present Value and IRR

When using internal rate of return, reject all projects whose internal rate of return is less than the minimum required rate of return. Projects with an internal rate of return equal to or greater than the minimum acceptable rate are considered further.

Comparing Net Present Value and IRR

When using net present value, discount at the minimum acceptable rate of return and reject all projects with a net present value of less than zero. Projects with a net present value of zero or greater are considered further.

Comparing Net Present Value and IRR

Under most circumstances, the internal rate of return and net present value approaches will give the same decision signals

In some conditions, contradictory signals emerge

Given different decision signals, results of net present value are usually preferred

Modified Internal Rate of Return

Discounts all negative cash flows back to the time at which the investment is acquired, and compounds all positive cash flows forward to the end of the final year of the holding period.

Financial Management Rate of Return

Findley and Messner have developed a variation on the internal rate of return called financial management rate of return which incorporates two intermediate rates: Cost of capital rate employed

to discount negative cash flows back to year zero

Specified reinvestment rate for compounding positive cash flows to the end of the projection period