Math Problem Statement

PQR Ltd. is considering the purchase of a new machine. Two alternative machines have been suggested, each costing ₹4,00,000 and requiring ₹30,000 as additional working capital at the end of the 1st year. EAT (Earnings After Tax) are expected to be as follows: Machine A: Year 1 - ₹40,000, Year 2 - ₹1,20,000, Year 3 - ₹1,60,000, Year 4 - ₹2,40,000, Year 5 - ₹1,60,000, Total - ₹7,20,000 Machine B: Year 1 - ₹1,20,000, Year 2 - ₹1,60,000, Year 3 - ₹2,00,000, Year 4 - ₹1,20,000, Year 5 - ₹80,000, Total - ₹6,80,000 The company has a target return on capital of 10%. You are required to select the most profitable machine using the NPV method.

Solution

The problem provided is asking to determine the most profitable machine based on the Net Present Value (NPV) method. Let's break down the steps:

Step-by-Step Approach:

  1. Calculate NPV for both Machine A and Machine B.

    • The initial cost of the machines is ₹4,00,000 with an additional ₹30,000 of working capital needed at the end of the first year.
    • The target return (discount rate) is 10%.
  2. Formula for NPV: NPV=Cash Flowt(1+r)tInitial Investment\text{NPV} = \sum \frac{\text{Cash Flow}_t}{(1 + r)^t} - \text{Initial Investment} Where:

    • tt is the year,
    • rr is the discount rate (10% or 0.10),
    • Cash Flowt\text{Cash Flow}_t is the expected cash flow in year tt.
  3. Details to keep in mind:

    • The initial investment is ₹4,00,000 for both machines.
    • Additional working capital of ₹30,000 needs to be considered in year 1.

I will now calculate the NPVs for both Machine A and Machine B using the provided cash flows and the discount rate.

Let me perform the calculation.

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Math Problem Analysis

Mathematical Concepts

Net Present Value (NPV)
Discounting Cash Flows
Investment Decision Analysis

Formulas

NPV = Σ (Cash Flow_t / (1 + r)^t) - Initial Investment

Theorems

Time Value of Money

Suitable Grade Level

Undergraduate - Finance and Accounting