Management Accounting Math Solution (Capital Budgeting-2)
Posted by Ripon Abu Hasnat on Sunday, November 8, 2015 | 0 comments
Problem:
A large size company is considering to invest in a new project that costs Tk.4,00,000.
The estimated salvage value is zero; tax rate is 35%.
The company uses straight line depreciation and the proposed project has cash flows before tax (CBFT) as below:
| Year | Profit before Tax and Depreciation |
| 1st year | 1,00,000 |
| 2nd year | 1,00,000 |
| 3rd year | 1,50,000 |
| 4th year | 1,50,000 |
| 5th year | 2,50,000 |
Required: Determine the following: (i) Payback period; (ii) ARR; (iii) NPV at 15%; (iv) Profitability Index.
(The PV at 15% are 0.870; 0.756; 0.658; 0.572; 0.497)
Solution:
Depreciation = Cost – Salvage value/No. of year in lifetime = 4,00,000-0/5 = 80,000.
Statement of cash inflow:
| Particulars | 1st year | 2nd year | 3rd year | 4th year | 5th year |
| Profit before Tax & Depreciation Less Depreciation | 1,00,000 80,000 | 1,00,000 80,000 | 1,50,000 80,000 | 1,50,000 80,000 | 2,50,000 80,000 |
| Profit before Tax Less Tax @35% | 20,000 7,000 | 20,000 7,000 | 70,000 24,500 | 70,000 24,500 | 1,70,000 59,500 |
| Profit after Tax Add depreciation | 13,000 80,000 | 13,000 80,000 | 45,500 80,000 | 45,500 80,000 | 1,10,500 80,000 |
| Cash inflow | 93,000 | 93,000 | 1,25,500 | 1,25,500 | 1,90,500 |
Required 1: (Pay Back Period (PBP)):
| Year | Cash inflow | Cumulative cash inflow |
| 1 | 93,000 | 93,000 |
| 2 | 93,000 | 1,86,000 |
| 3 | 1,25,500 | 3,11,500 |
| 4 | 1,25,500 | 4,37,000 |
| 5 | 1,90,500 | 6,27,500 |
PBP = 3 + (Total investment – 3rd year cumulative cash inflow)/4th year cash inflow
= 4 + (4,00,000 – 3,11,500)/1,25,500 = 3.71 years
Required 2: Average rate of return:
ARR= (Average annual profit / Average investment)*100
=[{(13,000+13,000+45,500+45,500+1,10,500)/5}/(4,00,000)/2]*100=(45,500/2,00,000)*100
= 22.75%
Required 3: Net Present Value (NPV) calculation:
| Year | Cash flow | Discount factor@10% | Present value |
| 1 | 93,000 | 0.870 | 80,910 |
| 2 | 93,000 | 0.756 | 70,308 |
| 3 | 1,25,500 | 0.658 | 82,579 |
| 4 | 1,25,500 | 0.572 | 71,786 |
| 5 | 1,90,500 | 0.497 | 94,679 |
| Present Value of cash Less, investment | =4,00,262 =(4,00,000) | ||
| Net Present Value (NPV) | 262 | ||
Required 4: Calculation of Profitability Index (PI)
PI = PV of cash inflow/PV of investment cost
= 4,00,262/4,00,000 = 1.000655
Ans:
i) Pay Back Period 3.71 years
ii) ARR = 22.75%
iii) NPV = 262
iv) PI = 1.000655
Comments: Out of 5 years project life, the investment will return within 3.71 years, ARR is 22.75% which is higher than cost of capital, PI is greater than 1 and NPV value negative, So the project is viable.
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