An all-equity firm is considering the following projects:
Project Beta IRR
W .67 9.5 %
X .74 10.6
Y 1.37 14.1
Z 1.48 17.1
The T-bill rate is 5.1 percent, and the expected return on the market is 12.1 percent.
a. Compared with the firm's 12.1 percent cost of capital, Project W has a lower expected return, Project X has a lower expected return, Project Y has a higher expected return, and Project Z has a higher expected return.
b. Project W should be rejected , Project X should be accepted , Project Y should be rejected , and Project Z should be accepted .

Answer:

Projects W and X have lower expected returns

Projects Y and Z have higher expected returns

Explanation:

Given

[tex]\begin{array}{ccc}{Project} & {Beta} & {IRR} & {W} & {.67} & {9.5\%} & {X} & {.74} & {10.6\%} & {Y} & {1.37} & {14.1\%}& {Z} & {1.48} & {17.1\%} \ \end{array}[/tex]

[tex]T\ Bill\ Rate = 5.1\%[/tex]

[tex]Expected\ Return = 12.1\%[/tex]

Solving (a): Compare the expected return of each project to 12.1%

Expected Return of each project is calculated as:

[tex]Project = T\ Bill + (Beta * (Expected\ Return - T\ Bill))[/tex]

[tex]Project = 5.1\% + (Beta * (12.1\% - 5.1\%))[/tex]

[tex]Project = 5.1\% + (Beta * 7.0\%)[/tex]

For Project W:

[tex]W= 5.1\% + (0.67* 7.0\%)[/tex]

[tex]W= 5.1\% + 4.69\%[/tex]

[tex]W= 9.79\%[/tex]

Lower Expected return

For Project X:

[tex]X = 5.1\% + (0.74 * 7.0\%)[/tex]

[tex]X = 5.1\% + 5.18\%[/tex]

[tex]X = 10.28\%[/tex]

Lower Expected return

For Project Y:

[tex]Y = 5.1\% + (1.37 * 7.0\%)[/tex]

[tex]Y = 5.1\% + 9.59\%[/tex]

[tex]Y = 14.69\%[/tex]

Higher Expected return

For Project Z:

[tex]Z = 5.1\% + (1.48 * 7.0\%)[/tex]

[tex]Z = 5.1\% + 10.36\%[/tex]

[tex]Z = 15.46\%[/tex]

Higher Expected return

There is no question in (b)

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Difine the following
1 operetional cost
2 social cost and
3 complementary goods​

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