Management Accounting Math Solution (Capital Budgeting-1)

Problem:

The Azad Int Ltd. is contemplating to invest in a new project that would require procurement of a machine costing Tk.25,50,000; and a working capital of Tk.1,00,000. The project is expected provide benefits for five years. The expected profit before depreciation and tax from the project is as below:

Year	Profit before Tax and Depreciation
1st year	8,50,000
2nd year	7,00,000
3rd year	6,50,000
4th year	6,00,000
5th year	4,50,000

 (The policy of the company is to depreciate fixed assets on straight line basis over the period of the asset. Salvage value of the machine is expected to be Tk.50,000. Assume a 40% tax rate and cost of capital of 10%)

Required: Determine the acceptability of the project on the basis of (i) Payback period; (ii) ARR; (iii) NPV; (iv) IRR; (v) Profitability Index.

(The present values of Tk1 for five years at 10% are 0.9091; 0.8264; 0.7513; 0.6830; 0.6209)

Solution:

Depreciation = Cost – Salvage value/No. of year in lifetime = 25,50,000 – (50,000/5) = 5,00,000.

Total Investment = 25,50,000 (Machine price) + 1,00,000 (Working capital) = 26,50,000.

Statement of cash inflow:

Particulars	1st year	2nd year	3rd year	4th year	5th year
Profit before Tax & Depreciation Less Depreciation	8,50,000 5,00,000	7,00,000 5,00,000	6,50,000 5,00,000	6,00,000 5,00,000	4,50,000 5,00,000
Profit before Tax Less Tax @40%	3,50,000 1,40,000	2,00,000 80,000	1,50,000 60,000	1,00,000 40,000	(50,000) -
Profit after Tax Add depreciation	2,10,000 5,00,000	1,20,000 5,00,000	90,000 5,00,000	60,000 5,00,000	(50,000) 5,00,000
Cash before Terminal cash inflow Add Salvage value at 5th year Add working Capital	7,10,000 - -	6,20,000 - -	5,90,000 - -	5,60,000 - -	4,50,000 50,000 1,00,000
	7,10,000	6,20,000	5,90,000	5,60,000	6,00,000

Required 1: (Pay Back Period (PBP)):

Year	Cash inflow	Cumulative cash inflow
1	7,10,000	7,10,000
2	6,20,000	13,30,000
3	5,90,000	19,20,000
4	5,60,000	24,80,000
5	6,00,000	30,80,000

PBP = 4 + (Total investment – 4^th year cumulative cash inflow)/5^th year cash inflow

        = 4 + (26,50,000 – 24,80,000)/6,00,000 = 4.28 years

Required 2: Average rate of return:

ARR= (Average annual profit / Average investment)*100

        =[{(2,10,000+1,20,000+90,000+60,000-50,000)/5}/(26,50,000+50,000)/2]*100=(86,000/13,50,000)*100

        = 6.37%

Required 3: Net Present Value (NPV) calculation:

Year	Cash flow	Discount factor@10%	Present value
1	7,10,000	0.9091	6,45,467
2	6,20,000	0.8264	5,12,368
3	5,90,000	0.7513	4,43,267
4	5,60,000	0.6830	3,82,480
5	6,00,000	0.6209	3,72,540
Present Value of cash Less, investment	=23,56,116 =(26,50,000)
Net Present Value (NPV)	(293884)

Required 4: Internal Rate of Return (IRR):

Since the NPV at 10% discounting rate is negative; Let us take lower discounting rate 5%

Therefore,

Present Value = {7,10,000/(1+0.05)+(620000)/(1+0.05) +5,90,000/(1+0.05)

+5,60,000/(1+0.05) +6,00,000/(1+0.05) } – 26,50,000 (total investment)

= (6,76,190.48 + 5,62,358.28 + 5,09,664.18 + 4,60,713.39 + 4,70,115.70) - 26,50,000 (total investment)

= 26,77,488 – 26,50,000 (total investment)

= 27,488.

IRR= A+C/C-D(B-A)

=5% +27,488/27,488-(-2,93,884)*(10%-5%) =5% + 27,488/321372 * 5% =5% +0.0855*5% =0.05+0.0042 = 0.0542 = 5.42%

Here, A= Lower discounting rate B= Higher discounting rate C=NPV of lower discounting rate D= NPV of higher discounting rate

Required 5: Calculation of Profitability Index (PI)

PI = PV of cash inflow/PV of investment cost

     = 23,56,116/26,50,000 = 0.889 = 0.89 (Approximated)

Ans:

i)                   Pay Back Period 4.28 years

ii)                ARR = 6.37%

iii)              NPV = (-2,93,884)

iv)              PI = 0.89

 

Comments: 

Out of 5 years project life, the investment will return within 4.28 years, ARR is 6.37% which is lower than cost of capital, PI is less than 1 and NPV value negative, So the project is not acceptable.