Question

Divine plc is a pure-honey producing plant. The firm wants to replace its aging processing machine. One option is to purchase a similar machine for $250,000. However, the output may not be able to meet the growing demand, therefore the revenue will be relatively stable. A second option is to invest in a more efficient equipment that cost $350,000. The revenue from this option is expected to be greater than the first option due to increased demand but the revenue varies. Both equipment have useful lives of 10 years and the cost of capital in investing in these equipment is 10%. The cash flows from the investments are contained in the table below
Project A Project B
investment 250000 350000
Year Cash inflow
1 45100 72500
2 45100 65500
3 45100 73800
4 45100 71500
5 45100 69800
6 45100 75500
7 45100 31000
8 45100 47500
9 45100 55500
10 45100 29200
NPV
IRR

a. Determine the net present value (NPV) and Internal rate of return (IRR) of both investments and identify the more preferred project under each of the project evaluation methods. Note: There is a conflict between NPV and IRR in the project decision
b. Now that the NPV and IRR do not reach a consensus on a particular project, explain the likely cause of the conflict.

Answer 1

Answer:

Project A

Years      Cashflows     Discount factor     Present values

0            250,000                    1                           -250,000

1-10            45,100                   6.144                     277,094.40

Sum of all present value=NPV=27,094.40

IRR (by using trial and error method) = 12.4696%

Note: Discount factor for the year 1-10 is calculated by using annuity formula i.e [1-(1+10%)]/10% = 6.144

Project B

Years Cashflows Discount factor  Present values

0        (350,000)           1                              (350,000)

1           72,500               0.91                   65,975  

2           65,500               0.83                    54,365  

3           73,800                  0.75                    55,350  

4            71,500                  0.68                    48,620  

5           69,800                  0.62                   43,276  

6           75,500             0.56                   42,280  

7           31,000                  0.51                            15,810  

8           47,500                  0.47                           22,325  

9           55,500                  0.42                   23,310  

10           29,200                  0.38                    11,096

Sum of all present values=NPV=32,407

IRR(by using trial and error method=12.4186%

On the basis of NPV project B is better because it gives higher NPV than project A. Whereas, Project A is better than project B on the basis of IRR because project A has slightly higher IRR than project B.

b)The conflict between both the investment appraisal technique is likely due to different cash flow patterns of both the project. In such situation decision should be based on NPV because this is an absolute measure

Answer 2

Answer:

a. For $250000 machine option the IRR= 6.08% and NPV =$0

For $350000 machine option the IRR =5.39% and NPV= $0, option for $250000 is the more preferred option.

b. Option For $250000 is the better option as it is closest to the cost of capital and costs the company less to take it. the IRR is directly proportional to the future cash flows

Explanation:

a.For $250000 machine we will start by calculating the future value of investing in the equipment to see how much the total amount the company will get in over 10 years if it were to buy this machinery so we will find the sum of all cash flows over the 10 year period therefore it will be $45100x10 years=$451000  as the company gets a stable cash flow over the ten year period of the equipment's useful life, we know that the net present value of the equipment will be $0 as the equipment will be used up in 10 years time . Now we will use the future value formula to calculate the IRR which is :      $Fv = Pv(1+IRR) ^n$

Fv is the sum of the future cash flows of the equipment $451000

Pv is the cost of the equipment $250000

IRR is the internal rate of return of the equipment during the course of its 10 year useful life. which is what we are looking for.

n is the useful life of the equipment which is 10 years.

now we substitute on the above mentioned formula and solve for IRR:

$451000 = $250000(1+IRR)^10  ,divide both sides by $250000

$451000/$250000 = (1+IRR)^10    ,find the tenth root of both sides

1.060775922 = 1+IRR             subtract by 1 both sides

0.060775922 = IRR        multiply by 100

6.08 % = IRR     rounded off to two decimal places.

For $350000 the net present value is $0 as after 10 years the equipment will be used up so now we calculate the IRR as above to see what the rate of return on this equipment is firstly we get the sum of cash flows for 10 years for this equipment (Fv) = $72500+$65500+$73800+$71500+$69800+$75500+$31000+$47500+$55500+$29200= $591800

Now we use the formula Fv= Pv (1+IRR)^n

where Pv is the equipment cost $350000

IRR is the internal rate of return we will calculate

n is the useful life of the equipment 10 years

now we substitute and solve for IRR :

$591800 = $350000(1+IRR)^10

$591800/$350000 = (1+IRR)^10 then we get the tenth root of both sides

1.053927391 = 1+IRR

0.053927391 = IRR

5.39% = IRR

the more preferred project is the one for $250000 as it has a greater IRR which is also closer to the cost of capital of 10%.

b. When the Internal rate of return is big then the cash flows also increase in value but when the IRR is small then it gives a smaller overall cash flows even when the equipment costs much more in this case.