Management Accounting Math Solution (Capital Budgeting-1)
Posted by Ripon Abu Hasnat on Sunday, November 8, 2015 | 0 comments
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 – 4th year cumulative cash inflow)/5th 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.
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