Time Value of Money & Investment Analysis: Solved Problem

Mr. Joshi is the Finance Manager at M/s Vriddhi Impex. The Company is looking at lateral growth and diversification into garment making from cloth making. For doing this, there needs to be put up a factory with all the latest machinery for cutting and stitching garments. The cost of acquisition of land, setting up the factory and buying the machinery works out to Rs. 100 lacs. It is estimated that the project will start generating revenue immediately from year 1. The Net revenue (after tax) for the next 5 years is Rs. 20 lacs, 30 lacs, 35 lacs, 45 lacs, 48 lacs. A new loan is available to Vridhi Impex at 9% p.a. interest rate (net of tax). Mr. Joshi has another proposal which gives him a return of 12% p.a. and hence he does not want to invest below this rate. Assist Mr. Joshi to evaluate the project proposal using NPV and IRR. (Show all calculations for comparing it with the alternative proposal also). Should he go ahead with the project proposal?

To evaluate the project proposal, we will calculate the Net Present Value (NPV) and Internal Rate of Return (IRR) using the given data and compare it with Mr. Joshi’s required rate of return of 12%.

Given Data:

Initial Investment = Rs. 100 lacs
Net Revenue (Cash Flows after tax):
- Year 1 = Rs. 20 lacs
- Year 2 = Rs. 30 lacs
- Year 3 = Rs. 35 lacs
- Year 4 = Rs. 45 lacs
- Year 5 = Rs. 48 lacs
Discount Rate (Required Rate of Return) = 12%
Loan Available at = 9% p.a. (But Joshi’s required return is 12%)

Step 1: Calculate NPV

The NPV of the project is Rs. 22.52 lacs. Since NPV is positive, the project adds value to the company and is financially viable.

Step 2: Calculate IRR

IRR is the discount rate (r) that makes NPV = 0. It satisfies the equation:

he IRR of the project is approximately 19.51%.

Step 3: Decision Making

Mr. Joshi’s required return is 12%, while the project’s IRR is 19.51%, which is higher.
The NPV is Rs. 22.52 lacs, which is positive, indicating profitability.
Since both NPV and IRR are favorable, Mr. Joshi should go ahead with the project.

Project Evaluation Report for M/s Vriddhi Impex

Prepared for: Mr. Joshi, Finance Manager
Project: Diversification into Garment Making

1. Introduction

M/s Vriddhi Impex is considering lateral growth by diversifying from cloth making to garment making. This requires setting up a factory with the latest machinery for cutting and stitching garments. The total project cost is estimated at Rs. 100 lacs.

2. Project Details

Initial Investment: Rs. 100 lacs
Projected Net Revenue (after tax):
- Year 1: Rs. 20 lacs
- Year 2: Rs. 30 lacs
- Year 3: Rs. 35 lacs
- Year 4: Rs. 45 lacs
- Year 5: Rs. 48 lacs
Available Loan Interest Rate: 9% p.a. (net of tax)
Required Rate of Return: 12% p.a.

3. Net Present Value (NPV) Calculation

Formula:

where:

Ct = Cash inflow in year t
r = Discount rate (12%)
C0= Initial investment (Rs. 100 lacs)

NPV Calculation:

Result: NPV = Rs. 22.52 lacs

Since NPV is positive, the project is financially viable.

4. Internal Rate of Return (IRR) Calculation

IRR is the discount rate that makes NPV = 0.

Using financial calculations, the IRR is found to be 19.51%.

5. Decision Making

The project’s IRR (19.51%) is higher than Mr. Joshi’s required return of 12%.
The NPV is positive (Rs. 22.52 lacs), indicating that the project will generate value.
As both indicators are favorable, the project should be accepted.

6. Conclusion

Based on the financial evaluation using NPV and IRR, the proposed investment in garment manufacturing is profitable. It is recommended that Mr. Joshi proceed with the project, as it offers a return significantly higher than the required rate of return.

Prepared by:
Finance Analysis Team
M/s Vriddhi Impex

Compute the effective yearly rate if the monthly rate is 1%.

The effective annual rate (EAR) is calculated using the formula:

Where:

r = Monthly interest rate = 1% = 0.01
n = Number of compounding periods per year = 12

The effective annual rate (EAR) for a monthly interest rate of 1% is approximately 12.68% per year.

Liphips Ltd has just paid a dividend per share of €1.20. Shares are valued only on the basis of expected dividends. An annual sustainable growth of dividends of 4% is assumed. The appropriate discount rate (i) is 10% per year. The planning horizon is limited to 20 years. Compute the share value.

To compute the share value, we use the Gordon Growth Model (Dividend Discount Model for a finite period):

Since dividends grow at a constant rate, we sum the present values of all expected dividends over 20 years:

The computed share value of Liphips Ltd, based on expected dividends over a 20-year planning horizon, is approximately €14.03 per share

Compute the share value of a company paying a dividend of €3.60 per year over infinite maturity, with expected zero growth. The discount rate (i) is assumed to be 12% yearly.

Since the dividend remains constant with zero growth, we use the Dividend Discount Model (Perpetuity Formula):

Where:

PV= Present value (share price)
D=3.60 (constant annual dividend)
i=12%=0.12 (discount rate)

Now, let’s compute the share value.

The computed share value of the company, based on a perpetual dividend of €3.60 per year with a 12% discount rate, is €30.00 per share.

Centuries ago, rich families in the province of Friesland established a fund to further welfare and education. From this fund, only the interest revenue was allowed to be spent, in order to keep the principal unattached. Assume the fund has amounted to €12 million and market interest rate (i) is 6% annually. What would be the perpetuity (or present value of the fund) endowed to the society?

Since only the interest revenue is spent while keeping the principal intact, this is a perpetuity scenario where the annual amount available for spending is given by:

Perpetuity Payment=Principal×i

Where: