Question

You are considering opening a new plant. The plant will cost $ 95.5 million up front and will take one year to build. After that it is expected to produce profits of $ 28.4 million at the end of every year of production. The cash flows are expected to last forever. Calculate the NPV of this investment opportunity if your cost of capital is 8.5 %. Should you make the? investment? Calculate the IRR and use it to determine the maximum deviation allowable in the cost of capital estimate to leave the decision unchanged.

1. The NPV of the project will be ?$ million.???(Round to one decimal? place.)

2. You should or should not make the investment.???

3. The IRR is ?%. (Round to two decimal? places.)

4. The maximum deviation allowable in the cost of capital estimate is ?% (Round to two decimal? places.)

Answer 1

1. Present Value of the annual cashflow of $28.4 million to perpetuity

= 28.4/8.5%

= 28.4/0.085

= $334.11 million

NPV          = $334.11 - $95.5

                        = $238.61 million

Since NPV is positive, the investment is recommended.

1. The IRR is calculated with trial and error method. Since NPV is positive at 8.5 percent discount rate, we use a higher discount rate of 30%

Present Value of the annual cashflow of $28.4 million to perpetuity

= 28.4/30%

= 28.4/0.3

= $94.67 million

IRR is where NPV is zero. At 30% NPV is negative (94.67 – 95.5) -$0.83 million

Hence IRR is less than 30%

Present Value of the annual cashflow of $28.4 million to perpetuity at 28% discount rate

= 28.4/29%

= 28.4/0.29

= $97.93 million

NPV = 97.93- 95.5 = $2.43 million

(2.43/3.26 ) +29%

0.74% + 29% So IRR is 29.74%

c) The maximum deviation allowed is

=          29.74- 8.5 = 21.24%

=          21.24%/8.5%

=          250%