Question

1. Carson Trucking is considering whether to expand its regional service center in Maob, Utah. The expansion requires the expenditure of $10,000,000 on new service equipment and would generate annual net cash flows from reduced costs of operations equal to $2,500,000 per year for each of the next eight years. In Year 8 the firm will also get back a cash flow equal to the salvage value of the equipment, which is valued at $1 million. Thus in Year 8 the investment cash inflow totals $3,500,000. Calculate the project's NPV using each of the following discount rates: a. 9 percent b. 11 percent c. 13 percent d. 15 percent 2. East Coast Television is considering a project with an initial outlay of $X(you will have to determine the amount). It is expected that the project will produce a positive cash flow of $50,000 a year at the end of each year for the next 15 years. The appropriate discount rate for this project is 10 percent. If the project has a 14 percent internal rate of return, what is the project's net present value? 3. Your investment advisor has offered you an investment that will provide you with a single cash flow of $10,000 at the end of 20 years if you pay premiums of $200 per year in the interim period. Specifically, the annual premiums begin immediately and extend through the end of Year 19. You then receive the $10,000 at the end of Year 20. Find the internal rate of return on this investment.

Answer 1

1)NPV=Present Value of Discounted Cash Flows - Initial Investment

a)IRR=9
So NPV= 2500000/(1+.09)"1........2500000/(1+.09)"8+1000000"8 - 10000000

=1,38,37,048 + 501882 -10000000
  
=4338930.05

b)IRR=11

So NPV= 2500000/(1+.11)"1........2500000/(1+.11)"8+1000000"8 - 10000000

=1,28,65,307+433927.95-10000000

= 3299234

c)IRR=13

So NPV= 2500000/(1+.13)"1........2500000/(1+.13)"8+1000000"8 - 10000000

=1,28,65,307+433927.95-10000000

= 1996926+376222

=2373148.7

d)

c)IRR=15

So NPV= 2500000/(1+.15)"1........2500000/(1+.15)"8+1000000"8 - 10000000

=1,12,18,304+ 326904 -10000000

= 1996926+376222

=1545208.

2)IRR means the rate of return at which NPV is 0

So, 0=NPV=t=1∑T​(1+IRR)tCt​​−C0​

=50000/(1.14)"1..........50000/(1.14)"15

=307112.

so now

Initial Investment =307112

NPV= cash flow/(1+i)"n.....-Initial Invesmtnet

=50000/(1.1)"1....50000/(1.1)"15 - 307112

=69,982.

3)When 10000 discounted at a cretian rate equals premium for 19 year discounted at same rate then thats IRR

So 1000/(1+r)"20=200/(1+r)"1.......+200/(1+r)"19

So r=8.33%.