Question

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 1

Projects W and X have lower expected returns

Projects Y and Z have higher expected returns

Explanation:

Given

`\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}`

`T\ Bill\ Rate = 5.1\%`

`Expected\ Return = 12.1\%`

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

Expected Return of each project is calculated as:

`Project = T\ Bill + (Beta * (Expected\ Return - T\ Bill))`

`Project = 5.1\% + (Beta * (12.1\% - 5.1\%))`

`Project = 5.1\% + (Beta * 7.0\%)`

For Project W:

`W= 5.1\% + (0.67* 7.0\%)`

`W= 5.1\% + 4.69\%`

`W= 9.79\%`

Lower Expected return

For Project X:

`X = 5.1\% + (0.74 * 7.0\%)`

`X = 5.1\% + 5.18\%`

`X = 10.28\%`

Lower Expected return

For Project Y:

`Y = 5.1\% + (1.37 * 7.0\%)`

`Y = 5.1\% + 9.59\%`

`Y = 14.69\%`

Higher Expected return

For Project Z:

`Z = 5.1\% + (1.48 * 7.0\%)`

`Z = 5.1\% + 10.36\%`

`Z = 15.46\%`

Higher Expected return

There is no question in (b)