Problem $1$:

There are many possible adoption criteria that a firm can use to decide whether or not to adopt a

particular project. One such criterion is to adopt all non$-$mutually$-$exclusive projects that generate a

positive Net Present Value $($NPV$),$ where NPV is defined as the present value of all the positive and

negative cash flows associated with the project; a positive cash flow at a particular time period represents

an in$-$flow of cash net of any expenses during that period; a negative cash flow at a particular time period

represents an outflow of cash $($expenses exceeding revenues$).$ The discount rate used should be the

required rate of return $($RRR$),$ also called the opportunity cost of capital $($both are the return the firm could

get if$,$ rather than investing in the project being considered, it invested in other assets or securities with

the same risk as the project$).$ The NPV of a project is the additional wealth to the owners of the firm that

that project generates. Thus, if the NPV is positive, if adopted, the owners of the firm will get wealthier;

management should adopt all positive NPV projects $$ since they work for the owners of the firm.

Another criterion is based on the internal rate of return $($IRR$)$ of the project. The IRR is defined the single

discount rate that, when applied to all of the cash flows of the project, makes the present value of the

cash flows equal to zero. $($It is like a YTM on the project.$)$ The adoption rule is to take all projects that

have an IRR greater than the opportunity cost of capital or RRR$.$ In some cases, the IRR rule is misleading

$($see the cases below$).$ Sometimes the IRR can exceed the cost of capital, but the NPV is negative at the

cost of capital. The examples below have you explore this.

Consider the following five projects and their projected cash flows.

Project A Project B Project C Project D Project E

Required rate of return $($RRR$)\mathrm{.}14\mathrm{.}10\mathrm{.}20\mathrm{.}15\mathrm{.}18$

Cash Flows per Period

$($years$,$ t $=0$ is now$)$

$0-1000-800200070002200$

$14003003000-30003000$

$2200200-12000-3000-12000$

$31001004000-30004000$

$4400400100010001000$

$55002002500-30002500$

a$.$ For each project, calculate the following variables $($you will need to use goal seek or solver to calculate

IRR$)$:

Project A Project B Project C Project D Project E

IRR

NPV

Do the two adoption criteria agree with each other? That is$,$ when one implies you should adopt $($reject$)$

the project, does the other also imply you should adopt $($reject$)?$

b$.$ If the projects are not mutually exclusive, which of these projects should you adopt? Why?

c$.$ If the projects are mutually exclusive $($i$.$e$.,$ you can only adopt one$),$ which should you adopt? Why?