Mathematics of FinancePYQ May 25Question 4323 of 507
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A project is expected to provide cash inflows as follows for 3 years: Year 1: ₹ 40,000, Year 2: ₹ 50,000, Year 3: ₹ 30,000. The company's cost of capital or required rate of return is 15%. What is the present value of cash inflows of the company?

Options

A₹ 99,240
B₹ 1,02,840
C₹ 1,12,640
D₹ 92,315
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Correct Answer

Option d₹ 92,315

All Options:

  • A₹ 99,240
  • B₹ 1,02,840
  • C₹ 1,12,640
  • D₹ 92,315

Detailed Solution & Explanation

To find the present value of the cash inflows, we need to discount each annual cash inflow to its present value using the cost of capital (15%\displaystyle 15\%) and sum them up.
Formula for the present value of cash inflows is:
PV=C11+r+C2(1+r)2+C3(1+r)3PV = \frac{C_1}{1 + r} + \frac{C_2}{(1 + r)^2} + \frac{C_3}{(1 + r)^3}
Where:
- Cost of capital (r\displaystyle r) = 15%=0.15\displaystyle 15\% = 0.15
- Cash inflow at end of Year 1 (C1\displaystyle C_1) = 40,000\displaystyle ₹ 40,000
- Cash inflow at end of Year 2 (C2\displaystyle C_2) = 50,000\displaystyle ₹ 50,000
- Cash inflow at end of Year 3 (C3\displaystyle C_3) = 30,000\displaystyle ₹ 30,000

Now, discount each inflow:
1. Present Value of C1\displaystyle C_1:
PV1=400001.1534782.61PV_1 = \frac{40000}{1.15} \approx 34782.61
2. Present Value of C2\displaystyle C_2:
PV2=50000(1.15)2=500001.322537807.18PV_2 = \frac{50000}{(1.15)^2} = \frac{50000}{1.3225} \approx 37807.18
3. Present Value of C3\displaystyle C_3:
PV3=30000(1.15)3=300001.52087519725.49PV_3 = \frac{30000}{(1.15)^3} = \frac{30000}{1.520875} \approx 19725.49

Total Present Value (PV\displaystyle PV):
PV=PV1+PV2+PV3PV = PV_1 + PV_2 + PV_3
PV=34782.61+37807.18+19725.49=92315.28PV = 34782.61 + 37807.18 + 19725.49 = 92315.28
So the present value of the cash inflows is approximately 92,315\displaystyle ₹ 92,315.
Hence, **Option D** is the correct answer.

About This Chapter: Mathematics of Finance

Paper

Paper 3: Quantitative Aptitude

Weightage

12-16 Marks

Key Topics

Simple & Compound Interest, Annuity, Perpetuity

The most important mathematical chapter in the entire syllabus. It covers Simple Interest (SI), Compound Interest (CI), Nominal vs Effective rates, Present and Future Value, Annuities (Ordinary and Due), Sinking Funds, and Perpetuities. The concepts learned here are applied heavily in CA Intermediate and Final.

View Official ICAI Syllabus

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