Question

Your manager has tasked you with evaluating two alternative projects for the company’s expansion:

The first option costs $200,000 with the expected cash inflow to the firm estimated at $60,000 per year after depreciation and tax. The life of this project is 7 years.

The second option costs $350,000 and has a life span of 10 years. The cash inflow to the firm from this option is estimated to be $80,000 per annum, again after depreciation and tax.

This company has a cost of capital of 15%. Assume other similar projects will be implemented at the end of these two projects, whichever is chosen.

1. Calculate, for both projects, the:
   1. Internal Rate of Return (IRR)
   2. Net Present Value
   3. Profitability Index (PI) and;
   4. Payback period for project 1 and 2.
2. Can NPV be used to rank the projects? If not, what should you do? Explain fully which project should be chosen.
3. Identify, describe and discuss some of the limitations associated with the use of the NPV in analysing projects?

Insert your answer for Question 3 below.

QUESTION B-4 [18 marks]

Again, your manager has tasked you with providing a recommendation regarding two alternative projects. You have identified the following two projects with the following characteristics:

Project A Project B

CAPEX / Initial Outlay $500,000 $300,000

Project life 5 years 6 years

Revenue (per year) $350,000 $250,000

Variable costs $90,000 $80,000

Operating expense $60,000 $40,000

Investment in Net Working Capital (Year 0) $50,000 $30,000

The company’s tax rate is 30% and uses a straight-line depreciation method. There will be no ‘salvage’ value associated with these projects at the end of their project life. The company also anticipates it will recover all of the NWC at the end of the project. The company has a required rate of return of 13% per annum.

1. Determine the Free Cash Flows, for each year, to the firm for both projects.

2. Identify which project you recommend the company invest.

3. Using your own words, briefly describe how to use the techniques of sensitivity, scenario and simulation analyses to estimate project risk?

Answer 1

Q1.

a. IRR - The rate at which NPV = 0, or Initial Investment = PV of all future cash flows

0 (NPV) = CF1/(1+r)^1 + CF2/(1+r)^2 +......... CFn/(1+r)^t

where, CFt = Cash flow in year t

r = IRR (the rate at which the above equation balances)

t = period of the cash flow

Since cash flows are uniform, we will use excel function of PV to calculate the present value of all cash flows

Option 1

Lets try PV at 20%

For us to calculate PV in excel or financial calculator, we have given here

Initial Investment = $200,000

Rate = 20% (Our trial and error method rate)

Time = NPER = 7 years

Annual Cash flows = PMT = $60000

Future Value = 0

Type = 0 (Cash flows occur at end)

Thus PV = PV(20%,7,60000,0,0) = -216275.51 (The negative sign here is just a excel way of identifying cash inflow & outflow. This is the value of investment (cash outflow, therefore, negative sign) that will generate $60000 for 7 years at 20%)

Now this is generating higher cash flows than 200000

Lets try at 22%

PV = PV(22%,7,60000,0,0) = -$204930.09

Again a higher value,

Lets try at 23%

PV = PV(18%,7,60000,0,0) = -$199,622.17

IRR lies between 22% & 23%

We will use interpolation formula to calculate the IRR. The interpolation formula is

y- y1 = ((y2-y1) / (x2-x1))* (x-x1)

IRR

= 22% + ((23%-22%) /(199622.17-204930.09 ))*(200000-204930.09)

= 22% + 0.93%

IRR for Option 1 =22.93%

For Option 2

Lets try IRR = 20%

Here, Initial Investment = $350000 Rate = 20%, NPER = 10, PMT = $80000, FV = 0, Type =0

PV of all cash flows at 20% = PV(20%,10,80000,0,0) = - 335397.77

PV of all cash flows at 19% = PV(19%,10,80000,0,0) = - 347114.79 (we are still less than 350000)

PV of all cash flows at 18% = PV(18%,10,80000,0,0) = - 359526.90 (we are higher than 350000)

So IRR lies between 18% & 19%

Making use of Interpolation formula

y- y1 = ((y2-y1) / (x2-x1))* (x-x1)

IRR = 18% + ((19%-18%) / (347114.79 - 359526.90))*(350000 - 359526.90)

= 18% + 0.767%

IRR for option 2 = 18.77%

ii) NPV = Sum of PV of all future cash flows - Initial Investment

We will again use PV function here

For option 1,

Initial Investment = 200000, Rate = 15% (Cost of capital), NPER = 7 years, PMT = 60000 (Annual Cash flows), FV=0, Type = 0

NPV = PV(15,7,60000,0,0) - 200000

= 249625.18 - 200000 (Pls remember, in calculator, the PV will appear as a negative value)

NPV of Option 1 = 49625.18

For option 2,

Initial Investment = 350000, Rate = 15% (Cost of capital), NPER = 10 years, PMT = 80000 (Annual Cash flows), FV=0, Type = 0

NPV = PV(15,10,80000,0,0) - 350000

= 401501.59 - 350000 (Pls remember, in calculator, the PV will appear as a negative value)

NPV of Option 2 = 51501.49

iii) Profitability Index = PV of all future cash flows / Initial Investment

For Option 1, from above calculations

Profitability Index for Option 1

=  249625.18 / 200000

PI for option 1 = 1.25

Profitability Index for Option 2

=  401501.59 / 350000

PI for option 2 = 1.15

iv) Pay Back Period = The last period in which cumulative cash flow is negative + (Absolute Value of Cumulative cash flow in the last year in which it is negative / Cash flow in the year in which Cumulative Cash flow turn positive)

For Option 1

From the below table, we can see PBP lies between 3 &4 years

For Option 1, Pay Back Period = 3 + 20000/ 60000 = 3.33years

Year	Option 1 CF	Cumulative cash flows
0	-200000	-200000
1	60000	-140000
2	60000	-80000
3	60000	-20000
4	60000	40000
5	60000	100000
6	60000	160000
7	60000	220000

For Option 2

From the below table, we can see PBP lies between 4 &5 years

For Option 2, Pay Back Period = 4 + 30000/ 80000 = 4.375years

Year	Option 2 CF	Cumulative cash flows for option 2
0	-350000	-350000
1	80000	-270000
2	80000	-190000
3	80000	-110000
4	80000	-30000
5	80000	50000
6	80000	130000
7	80000	210000
8	80000	290000
9	80000	370000
10	80000	450000

B) NPV can be used here. Since both projects have NPV greater than 0, the one with higher NPV should be chosen

Thus Option 2 with NPV = $51501.49 should be chosen over Option 1 with NPV = $49625.18

However, since the NPV is very close to each other, it is to be observed that Option 1 has higher IRR & PI than Option 2

C) Some of the limitations of NPV

Discount Rate or Cost of Capital : It is difficult to assume a discount rate for a specific project. If the discount rate is higher, the NPV reduces. If the chosen discount rate is lower, the NPV increases. Choosing the discount rate or cost of capital for a project depends on overall cost of capital of company. The project may essentially not require the same cost.

Uncertain Cashflows : Projects may not generate same forecasted cash flow each other. The final NPV would change according to actual cash flows

Investment : The net present value (NPV) method uses the net present value but it does not take into account the amount of investment required for the project. Sometimes therefore, this method is not the best one for comparing or ranking competing projects that requires different amounts of initial investment. Profitability index and IRR along with NPV helps the finance managers to take more informed decision