| You are a consultant to a firm evaluating an expansion of its current business. The cash-flow forecasts (in millions of dollars) for the project are as follows: |
| Years | Cash Flow | ||
| 0 | – | 100 | |
| 1–10 | + | 19 | |
| On the basis of the behavior of the firm’s stock, you believe that the beta of the firm is 1.46. Assume that the rate of return available on risk-free investments is 4% and that the expected rate of return on the market portfolio is 13%. |
| What is the project IRR? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) |
| IRR | % |
| What is the cost of capital for the project? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) |
| Cost of capital | % |
| Does the accept-reject decision using IRR agree with the decision using NPV? | ||||
|
First of all we will calculate coast of capital as follow
Cost of Capital
= rate of return of risk-free investments + beta (market portfolit – risk-free rate)
= 4% + 1.46 ( 13%-4%)
=4% +13.14%
=17.14%
Now we will calculate NPV as follow
| Year | CF | PV Factor @16.4% |
PV |
| 0 | -100 | 1 | -100 |
| 1 | 19 | 0.85178876 | 16.18399 |
| 2 | 19 | 0.72554409 | 13.78534 |
| 3 | 19 | 0.61801029 | 11.7422 |
| 4 | 19 | 0.52641422 | 10.00187 |
| 5 | 19 | 0.44839371 | 8.519481 |
| 6 | 19 | 0.38193672 | 7.256798 |
| 7 | 19 | 0.32532941 | 6.181259 |
| 8 | 19 | 0.27711193 | 5.265127 |
| 9 | 19 | 0.23604083 | 4.484776 |
| 10 | 19 | 0.20105692 | 3.820082 |
| -12.7591 |
NPV of the project is -12.7591
NOw we will calculate IRR of the project as follow
IRR =(100) +19(1+r)+19(1+r)2+19(1+r)3+19(1+r)4+19(1+r)5+19(1+r)6+19(1+r)7+19(1+r)8+19(1+r)9+19(1+r)10
By solving above equation by trial and error method we have found IRR =
=13.77%
So IRR =13.77%
| Does the accept-reject decision using IRR agree with the decision using NPV? |
NO
Company should reject the project as IRR of the project is less then Required Return of the project
