Hello, Pls help me in solveing the problem mentioned below:

Ram & Co is considering investment costing rs 450 lacs. This is financed by loan of Rs. 300 lacs on which interest @ 15 % is payable. The estimated useful life is 5 years. The project involves plant costiing Rs 200 lacs & working capital is Rs 250 lacs. The plant is subjected to be depreciated @ 15 % p a fixed installment method. At the end of project life, plant will realise 25% of cost & Working capital will realise 90% of cost. The loan will be repaid. The PBD& T is estimated & PV factor @ 10 % & 16% are as follows:

year PBDIT PV Factor

10% 16%

1 125 0.909 0.862

2 150 0.826 0.743

3 175 0.751 0.641

4 195 0.683 0.552

5 160 0.621 0.476

Income tax applicable @ 35 % You are required to calculate

1 Payback period

2 ARR on total investment

3 NPV @ 10 % & 16%

4 IRR

To tackle the investment analysis for Ram & Co, we need to break down the problem into manageable parts. We will calculate the Payback Period, Average Rate of Return (ARR), Net Present Value (NPV) at both 10% and 16%, and the Internal Rate of Return (IRR). Let's go through each of these calculations step by step.

1. Payback Period Calculation

The Payback Period is the time it takes for the initial investment to be recovered from the cash inflows generated by the project. Here’s how we can calculate it:

• Initial Investment: Rs. 450 lacs
• Annual Cash Inflows: We need to calculate the cash inflows after considering depreciation and tax.

Calculating Annual Cash Inflows

First, we need to determine the annual cash inflows (PBDIT) after tax:

• Depreciation: The plant cost is Rs. 200 lacs, and with a depreciation rate of 15%, the annual depreciation is:

Depreciation = 200 lacs * 15% = Rs. 30 lacs

• Taxable Income: We will calculate the taxable income for each year:

Taxable Income = PBDIT - Depreciation

Tax = Taxable Income * 35%

Net Income = Taxable Income - Tax

Cash Inflow = Net Income + Depreciation

Calculating for Each Year

• Year 1: PBDIT = 125 lacs
• Year 2: PBDIT = 150 lacs
• Year 3: PBDIT = 175 lacs
• Year 4: PBDIT = 195 lacs
• Year 5: PBDIT = 160 lacs

Now, let's calculate the cash inflows for each year:

• Year 1: Cash Inflow = (125 - 30) * (1 - 0.35) + 30 = 125 - 30 - 33.25 + 30 = Rs. 91.75 lacs
• Year 2: Cash Inflow = (150 - 30) * (1 - 0.35) + 30 = 150 - 30 - 42 = Rs. 108 lacs
• Year 3: Cash Inflow = (175 - 30) * (1 - 0.35) + 30 = 175 - 30 - 51.75 + 30 = Rs. 123.25 lacs
• Year 4: Cash Inflow = (195 - 30) * (1 - 0.35) + 30 = 195 - 30 - 57.75 + 30 = Rs. 137.25 lacs
• Year 5: Cash Inflow = (160 - 30) * (1 - 0.35) + 30 = 160 - 30 - 45.5 + 30 = Rs. 114.5 lacs

Cumulative Cash Inflows

Now, we can calculate the cumulative cash inflows:

• Year 1: 91.75 lacs
• Year 2: 199.75 lacs (91.75 + 108)
• Year 3: 323 lacs (199.75 + 123.25)
• Year 4: 460.25 lacs (323 + 137.25)
• Year 5: 574.75 lacs (460.25 + 114.5)

The Payback Period occurs between Year 4 and Year 5, as the cumulative cash inflow exceeds the initial investment of Rs. 450 lacs. To find the exact time, we can calculate:

Payback Period = 4 + (450 - 460.25) / 114.5 = 4 + 0.87 = 4.87 years

2. Average Rate of Return (ARR)

ARR is calculated as the average annual profit from the investment divided by the initial investment. First, we need to find the average annual profit:

• Total Profit: Total cash inflows over 5 years - Total investment
• Total Cash Inflows = 574.75 lacs
• Total Profit = 574.75 - 450 = 124.75 lacs
• Average Annual Profit = Total Profit / 5 = 124.75 / 5 = Rs. 24.95 lacs

Now, we can calculate ARR:

ARR = (Average Annual Profit / Initial Investment) * 100 = (24.95 / 450) * 100 = 5.55%

3. Net Present Value (NPV) Calculation

NPV is calculated by discounting the cash inflows to their present value and subtracting the initial investment. We will calculate NPV at both 10% and 16% discount rates.

NPV at 10%

• NPV = Σ (Cash Inflow / (1 + r)^t) - Initial Investment
• Where r = discount rate and t = year

Calculating NPV at 10%:

• Year 1: 91.75 / (1 + 0.10)^1 = 83.41
• Year 2: 108 / (1 + 0.10)^2 = 89.25
• Year 3: 123.25 / (1 + 0.10)^3 = 92.67
• Year 4: 137.25 / (1 + 0.10)^4 = 94.43
• Year 5: 114.5 / (1 + 0.10)^5 = 71.12

Summing these values gives:

NPV = (