Fundamentals of Financial Management (MGT215)

Nepal Mine Company (NMC) – Investment Analysis

Given Data

• Initial Investment (Cost of Truck): Rs. 6,000,000
• Annual Net Cash Flows:
  • Year 1: Rs. 2,500,000
  • Year 2: Rs. 2,500,000
  • Year 3: Rs. 1,500,000
  • Year 4: Rs. 2,000,000
  • Year 5: Rs. 2,000,000
• Required Rate of Return (Discount Rate): 10%
• Maximum Cost Recovery Period (Payback Period Threshold): 3 years

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(a) Payback Period (PBP) and Decision

Step 1: Calculate Cumulative Cash Flows

The Payback Period is the time required to recover the initial investment from the project’s cash inflows.

Step 2: Determine Exact Payback Period

The investment is fully recovered between Year 2 and Year 3.

• Remaining Balance at End of Year 2: Rs. 1,000,000
• Cash Flow in Year 3: Rs. 1,500,000

$$\text{Fractional Year}=\frac{1,000,000}{1,500,000}=\frac{2}{3}\text{ year}\approx 0.67\text{ year}$$

$$\text{Payback Period}=2+0.67=2.67\text{ years}$$

Step 3: Decision Based on Maximum Cost Recovery Period

• Company’s Threshold: 3 years
• Calculated PBP: 2.67 years

Conclusion: Since 2.67 < 3, the project should be accepted based on the payback period criterion.

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(b) Net Present Value (NPV) and Decision

Step 1: Calculate Present Value (PV) of Each Cash Flow

The NPV is calculated using the formula:

$$NPV=-C_0+\sum _{t=1}^n\frac{C{F}_t}{(1+r{)}^t}$$

Where:

• $C_0=6,000,000$
• $C{F}_t=\text{Cash Flow in Year }t$
• $r=10\%$

Step 2: Sum Up Present Values

$$NPV=-6,000,000+2,272,750+2,066,000+1,126,950+1,366,000+1,241,800$$

$$NPV=-6,000,000+8,073,500=\text{2,073,500}$$

Step 3: Decision Based on NPV

• NPV = Rs. 2,073,500 > 0
• Interpretation: The project is profitable and should be accepted.

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(c) Internal Rate of Return (IRR) and Decision

Step 1: Find IRR Using Trial and Error

The IRR is the discount rate that makes NPV = 0.

We test different discount rates to find the IRR.

Trial 1: 15%

$$NPV=-6,000,000+\frac{2,500,000}{1.15}+\frac{2,500,000}{1.15^2}+\frac{1,500,000}{1.15^3}+\frac{2,000,000}{1.15^4}+\frac{2,000,000}{1.15^5}$$

$$NPV\approx -6,000,000+2,173,913+1,889,446+972,196+873,418+759,400=-1,407,127(\text{Negative})$$

Trial 2: 12%

$$NPV=-6,000,000+\frac{2,500,000}{1.12}+\frac{2,500,000}{1.12^2}+\frac{1,500,000}{1.12^3}+\frac{2,000,000}{1.12^4}+\frac{2,000,000}{1.12^5}$$

$$NPV\approx -6,000,000+2,232,143+2,002,846+1,044,409+1,036,762+935,134=341,294(\text{Positive})$$

Trial 3: 13%

$$NPV\approx -6,000,000+2,232,143+1,956,522+1,003,020+989,239+880,956=-1,797,019(\text{Negative})$$

Interpolation to Find Exact IRR

Since NPV changes from positive (12%) to negative (13%), the IRR lies between 12% and 13%.

Using linear interpolation:

$$IRR=12\%+\left(\frac{341,294}{341,294+1,797,019}\right)\times (13\%-12\%)$$

$$IRR\approx 12\%+0.16\%=\text{12.16\%}$$

Step 2: Decision Based on IRR

• Company’s Required Rate of Return: 10%
• Calculated IRR: 12.16%

Since 12.16% > 10%, the project should be accepted.

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(d) Comparison: NPV vs. IRR

Conclusion: NPV is the better method because it provides a clear measure of value addition and avoids the ambiguity that can arise with IRR in certain scenarios (e.g., multiple IRRs or conflicting rankings).

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# Python Code to Calculate NPV and IRR
import numpy as np

# Cash Flows
initial_investment = -6000000
cash_flows = [2500000, 2500000, 1500000, 2000000, 2000000]

# NPV Calculation
discount_rate = 0.10
npv = -initial_investment + np.npv(discount_rate, cash_flows)
print(f"NPV: {npv:.2f}")

# IRR Calculation
irr = np.irr([initial_investment] + cash_flows)
print(f"IRR: {irr*100:.2f}%")

How it works:

• The np.npv() function calculates the Net Present Value using the given discount rate.
• The np.irr() function computes the Internal Rate of Return by finding the discount rate that makes NPV zero.
• The cash flows are structured as a list, with the initial investment as the first element (negative) followed by positive cash inflows.

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