Chapter 5

Question 1

Tools to measure the attractiveness of a project.

Answer 1

Profitability Index
Book rate of return
Payback
IRR
NPV

Question 2

Three Points to Remember about NPV

Answer 2

1. the NPV rule recognizes that a dollar today is worth
   more than a dollar tomorrow because the dollar today can be invested to start earning interest
   immediately.
   2.net present value depends solely on the forecasted cash flows from the project and the opportunity cost of capital.
2. because present values are all measured in today’s dollars, you can add them up. Therefore, if
   you have two projects A and B, the net present value of the combined investment is
   NPV(A + B) = NPV(A) + NPV(B)
   This adding-up property has important implications. Suppose project B has a negative NPV.
   If you tack it onto project A, the joint project (A + B) must have a lower NPV than A on its
   own. Therefore, you are unlikely to be misled into accepting a poor project (B) just because
   it is packaged with a good one (A). As we shall see, the alternative measures do not have this
   property. If you are not careful, you may be tricked into deciding that a package of a good and
   a bad project is better than a good project on its own.

Question 3

Book Returns

Answer 3

The accounting rate of return (ARR) is a formula that reflects the percentage rate of return expected on an investment or asset, compared to the initial investment’s cost. The ARR formula divides an asset’s average revenue by the company’s initial investment to derive the ratio or return that one may expect over the lifetime of an asset or project. ARR does not consider the time value of money or cash flows, which can be an integral part of maintaining a business.
Cash flows and book income are often very different. For example, the accountant labels
some cash outflows as capital investments and others as operating expenses. The operating
expenses are, of course, deducted immediately from each year’s income. The capital expenditures are put on the firm’s balance sheet and then depreciated. The annual depreciation charge
is deducted from each year’s income. Thus the book rate of return depends on which items the
accountant treats as capital investments and how rapidly they are depreciated

ARR=
InitialInvestment/
AverageAnnualProfit
or
Book rate of return = book income/
book assets
​
Pros
Determines a project’s annual rate of return

Simple comparison to minimum rate of return

Ease of use/Simple Calculation

Provides clear profitability

Cons
Does not consider the time value of money

Does not factor in long-term risk

Does not account for cash flow timing

Question 4

Understanding the Profitability Index (PI)

Answer 4

The profitability index (PI), alternatively referred to as value investment ratio (VIR) or profit investment ratio (PIR), describes an index that represents the relationship between the costs and benefits of a proposed project.

The profitability index is calculated as the ratio between the present value of future expected cash flows and the initial amount invested in the project. A higher PI means that a project will be considered more attractive.

PI= PV OF FUTURE CASH FLOWS/INITIAL INVESTMENT

Profitability Index Pros and Cons
Pros
Accounts for the time value of money

Allows comparisons across different projects

Cons
Does not consider ongoing future costs

Ignores project size

Bad forecasts or assumptions can make the analysis unreliable

Question 5

Payback rule

Answer 5

The term payback period refers to the amount of time it takes to recover the cost of an investment. Simply put, it is the length of time an investment reaches a breakeven point.

Payback Period=
Average Annual Cash Flow/
Cost of Investment
​
You can see why payback can give misleading answers:
1. The payback rule ignores all cash flows after the cutoff date
2.The payback rule gives equal weight to all cash flows before the cutoff date.
​

Question 6

Internal Rate of Return (IRR)

Answer 6

The internal rate of return (IRR) is a metric used in financial analysis to estimate the profitability of potential investments. IRR is a discount rate that makes the net present value (NPV) of all cash flows equal to zero in a discounted cash flow analysis.
Some people confuse the internal rate of return and the opportunity cost of capital because
both appear as discount rates in the NPV formula. The internal rate of return is a profitability
measure that depends solely on the amount and timing of the project cash flows. The opportunity cost of capital is a standard of profitability that we use to calculate how much the project
is worth. The opportunity cost of capital is established in capital markets. It is the expected
rate of return offered by other assets with the same risk as the project being evaluated.
Using IRR With WACC
Most IRR analyses will be done in conjunction with a view of a company’s weighted average cost of capital (WACC) and NPV calculations. IRR is typically a relatively high value, which allows it to arrive at an NPV of zero.

Most companies will require an IRR calculation to be above the WACC. WACC is a measure of a firm’s cost of capital in which each category of capital is proportionately weighted. All sources of capital, including common stock, preferred stock, bonds, and any other long-term debt, are included in a WACC calculation.