Using CAPM's formula,
Return on equity = Risk-free rate + Beta*(Expected market return - risk-free rate)
With the given information,
Return on equity = 1% + 0.55*(8% - 1%) = 4.85%
Hence UCD's expected return on the projected investment is 4.85%. With this and the given information, the NPV of the investment can be determined as follows.
|
Year
|
0
|
1
|
2
|
3
|
4
|
5
|
|
Net cash flow
|
-$5,000,000.00
|
$200,000.00
|
$900,000.00
|
$1,500,000.00
|
$1,700,000.00
|
$2,000,000.00
|
|
PVIF @ 4.85%
|
1
|
0.9537
|
0.9096
|
0.8676
|
0.8274
|
0.7891
|
|
PV of cash flows
|
-$5,000,000.00
|
$190,748.69
|
$818,663.90
|
$1,301,325.54
|
$1,406,614.80
|
$1,578,293.70
|
|
NPV
|
$295,646.63
|
|
|
|
|
|
The NPV of the expansion project has been determined to be $295,646.63. Since this is positive and above zero, UCDV should undertake the project, according to the NPV criteria. If UCDV's beta were 1.5 instead of 0.55, the expected return on the investment would be higher and the NPV of the investment will be below zero. Hence the project should not be undertaken by UCDV. This is illustrated below.
Return on equity = 1% + 1.5*(8% - 1%) = 11. 5%
|
Year
|
0
|
1
|
2
|
3
|
4
|
5
|
|
Net cash flow
|
-$5,000,000.00
|
$200,000.00
|
$900,000.00
|
$1,500,000.00
|
$1,700,000.00
|
$2,000,000.00
|
|
PVIF @ 11.5%
|
1
|
0.8969
|
0.8044
|
0.7214
|
0.6470
|
0.5803
|
|
PV of cash flows
|
-$5,000,000.00
|
$179,372.20
|
$723,923.67
|
$1,082,098.16
|
$1,099,890.50
|
$1,160,528.10
|
|
NPV
|
-$754,187.38
|
|
|
|
|
|
Hence the expansion project should be rejected by UCDV if beta was 1.5.