CAPITAL BUDGETING DECISON IN BUSINESS FINANCE

Topic: Capital Budgeting Decision

1.                  The Sikah Company is considering two mutually exclusive projects.  For each project the depreciable value is equal to net investment straight line, depreciation (no salvage value) over a five year life is used in each case.  The firm has 10 percent cost of capital.

                 Project A                              Project B

Net Investment                   (N60,000)                                (N80,000)

1.                                       16,000                                     22,400

2.                                       16,000                                     24,000

3.                                       16,000                                     26,000

4.                                       16,000                                     20,000

5.                                       16,000                                     15,000

Required:

a.                  Calculate the average rate of return for each project:

b.                  Calculate the average and the actual payback period for each project

c.                   Calculate the net present value of each project

d.                  Calculate the profit ratio for each project

e.                  Calculate the Internal Rate of Return (to the nearest 1 per cent for each project)

f.                    Indicates which project you would recommend, and why.

Solution:

Calculate the average rate of return for each project:

Average Profit Formula is :                 average Profit     X 100

                                                       Average Investment      1

Note:  Average Profit means the addition of the amount in year 1 to year 5 divide by the number of years, in this examples is 5 years, will give you average profit. While Average Investment is your initial investment divide by 2 then now multiply both the answers of average profit and average investment with 100  divide by1.  That is the formula explanation.

Practical 1:

            Project A                                            Project B

ARR =   16,000  x 100  = 53.3%                       21, 480 x 100   = 53.7%

           30,000        1                                    40,000       1

Solution:

Calculate the average and the actual payback period for each project

Pay Back Period (PBP)

In Pay Back Period (PBP) you will need to know how many year before you can get back your investment.  So, you will start calculating the amount from year 1 till you get to the year that will give you either exact figure of your investment of above it, then you stop.  If it is above, you will get the difference of it and also know the year before of the amount before the figure that gives you the amount that is about.  Because Pay Back Period is calculate in Years and Months.

Now, you will write down the years, then the amount that is the difference divide by the figure where you stop x 12 months will give you (PBP).

Practical 2:

                          Project A                                                        Project B 

   3years + 12,000 X 12  = 3 years 9 months         3years + 7600 x 12 = 3 years and 5 months

                16,000                                                       20,000

Calculate the Net Present Value of each Project

The formula for this is   DCF =   1

                                                (1+i)ⁿ

The above formula; the 1 on top is constant, while the 1 beside is also constant, the i., is the percentage while the n is the number of years. Note, you have to raise to power n, your answer in the 1 + i.

Now there is going to be a table for the with four columns; years cash flows DFC and NPV.

Now the years are the number of years you have, but you start with 0, then the cash flows are the amount you have for each year but you start with your initial capital, DFC is the working of the formula, the working of the formula will come under this column, but you start with 1.000 and the NPV is the cash flows multiply by the DCF will give you the NPC, but you have to start with the initial capital too. Because the initial capital in the cash flow multiply by 1.000 in DCF will give you the same amount in NPV.  Note that  DFC @10% can change to 12% depends on the question and the percentage given to you.

Practical 1.

Project A                                                                    

Year	Cash flows	DCF @10%	NPV
0	60,000	1.000	60,000
1	16,000	0.9091	14,546
2	16,000	0.8264	13,222
3	16,000	0.7513	12,021
4	16,000	0.6830	10,928
5	16,000	0.6209	9,934
		NPV	651

Project B Year	Cash flows	DCF @10%	NPV
0	80,000	1.000	80,000
1	22,400	0.9091	20,364
2	24,000	0.8264	19,834
3	26,000	0.7513	19,534
4	20,000	0.6830	13,660
5	15,000	0.6209	9,314
		NPV	2,976

Year 1. DCF =      1

                     (1+10%)ⁿ

Year 1. DCF =      1

                       (1+0.1)¹     = 0.9091

Year 2. DCF =      1

                         (1+10%)ⁿ

Year 2. DCF =      1

                     (1+0.1)²       = 0.8264            

Continue from year 3 to 5 to get other answer.   And do the same table for Project B.  The difference will be the Cash flows multiply be DCF  in project B that will make the figure in NPV greater than Project A.     

Calculate the profit Ratio for each project

 

E.   Calculate the Internal Rate of Return (to the nearest 1 per cent for each project)

Internal Rate of Return (IRR)

This is just like the Net Present Value table which you have calculated, but you need to assume a percentage to work with that will give you a negative figure.  In this example, we are going to use, 12%.  With 12% in DCF column, just calculate every thing afresh and you will get a negative figure as below.  Then you use this negative figure with you first NPV value  in project A and another formula to calculate IRR.  See below:

Project A                                                         

Year	Cash flows	DCF @12%	NPV
0	60,000	1.000	60,000
1	16,000	0.8929	14,286
2	16,000	0.7972	12,755
3	16,000	0.7118	11,389
4	16,000	0.6355	10,168
5	16,000	0.5674	9,078
		NPV	(2324)

Year	Cash flows	DCF @12%	NPV
0	80,000	1.000	80,000
1	22,400	0.9091	20,364
2	24,000	0.8264	19,834
3	26,000	0.7513	19,534
4	20,000	0.6830	13,660
5	15,000	0.6209	9,314
		NPV	2,976

Year 1. DCF =      1

                         (1+12%)ⁿ

Year 1. DCF =      1

                      (1+1.2)¹     = 0.8929

Calculate for year 2 to 5.

IRR = rate +     NPV 1                          x (R2 – R1)

                     NPV1 + NPV2

10%  +         651           x (12-10)

            651 + 2324

10% +        651     X 2

                  2775 

IRR = 10% + 0.4376

IRR= 10.4376%

You can now do the same for Project B and recommend.

Regular Past Question

2a.  Consider the following information relating to the purchase of a new asset: Cost of the asset=N250,000, straight line depression over a 10 years life, increase in revenues = N150,000 per year, increase in operating expenses = N90,000 per year, increase in accounts payable = N30,000; no salvage value.

Required:

1. What is the initial cash flow at time period 0?
2. What is the operating cash flow?
3. What is the NPV if the required rate of return is 12%
4. What is the profitability index?
5. What is the accounting rate of return?

Solution

1. The initial cash flow at time period 0 is N250,000 which is the initial investment.

2. The operating cash flow is =               income =               N150,000

Less: Expenses             (N90,000)

Less account payable    (30,000)

Operating cash flow=     30,000

3. The NPV is :

The Working of the DFC column is  1

                                                (1+r)¹

                                                      1

                                           (1+12%)¹

You continue from year 1 to 10.

Year	Cash flows	DCF @ 12%	NPV
0	(250,000)	1.000	(250,000)
1	30,000	0.8929	26,787
2	30, 000	0.7972	23,916
3	30, 000	0.7118	21,354
4	30, 000	0.6355	19,065
5	30, 000	0.5674	17,022
6	30, 000	0.5066	15,198
7	30, 000	0.4523	13,569
8	30, 000	0.4039	12,117
9	30, 000	0.3606	10,818
10	30, 000	0.3220	9,660
			NPV=(80,494)

Note: that the NPV is the 250,000 – the total will give you 80,494.

4. Profitability Index (P.I) =           NPV

       Initial outlay

      Note that you have to pick the NPV without the minus

       i.e                                                              80,494

                                                            250,000

            Profitability Index (P.I)            = 0.32 

                                                            =32%  

5. ARR =                                         Average Profits

Average Investment

Before we continue, we have to depreciate as the question required. ARR calls for depreciation.

Annual Dep.                =          Cost – Scrap Value

                                                Number of years

                                    =          250,000 - 0

                                                       10

                                    =          250,000

                                                     10

                                    =          N25,000

Year	Cash flows	Depreciation	Net Profit
1	30,000	(25,000)	5,000
2	30, 000	(25, 000)	5,000
3	30, 000	(25, 000)	5,000
4	30, 000	(25, 000)	5,000
5	30, 000	(25, 000)	5,000
6	30, 000	(25, 000)	5,000
7	30, 000	(25, 000)	5,000
8	30, 000	(25, 000)	5,000
9	30, 000	(25, 000)	5,000
10	30, 000	(25, 000)	5,000

Ar Profit =                     Total Profits

                                    Number of year

                                    50,000

                                       10

                        =          5,000

ARR     =          Average Profit

                        Average Investment

ARR=                  5,000       X 100

                        125,000          1

                        = 0.04 x 100

                        4%

Note: Where you don’t feel like going through the long process of computing Depreciation and Subsequently deducting from your cash flows on annual basis, you can just add all the cash flows to arrive at total cash flows and subtract the initial investment from it.

Also, were there is scrap value given in the question, subtract the scrap value first from the initial investment and the balance is what you subtract from the total cash flows.