Financial manager has responsibility to perform various financial decisions of any business company. Suppose you are BBA graduates from Tribhuvan University with finance specialization. Kathmandu…

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a. Payback Period Calculation

The payback period is the time required to recover the initial investment from the project’s cash flows.

Project A

• Year 0: -Rs 1,000,000
• Year 1: Rs 700,000 (Cumulative: -1,000,000 + 700,000 = -Rs 300,000)
• Year 2: Rs 700,000 (Cumulative: -300,000 + 700,000 = Rs 400,000)

Since the investment is recovered between Year 1 and Year 2, we calculate the exact payback period: $$\text{Fractional Year}=\frac{\text{Remaining Amount at Year 1}}{\text{Cash Flow in Year 2}}=\frac{300,000}{700,000}=0.4286$$ $$\text{Payback Period (Project A)}=1+0.4286=\text{1.43 years}$$

Project B

• Year 0: -Rs 1,000,000
• Year 1: Rs 950,000 (Cumulative: -1,000,000 + 950,000 = -Rs 50,000)
• Year 2: Rs 750,000 (Cumulative: -50,000 + 750,000 = Rs 700,000)

The investment is recovered between Year 1 and Year 2: $$\text{Fractional Year}=\frac{50,000}{750,000}=0.0667$$ $$\text{Payback Period (Project B)}=1+0.0667=\text{1.07 years}$$

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b. Net Present Value (NPV) Calculation

NPV is calculated using the formula: $$NPV=\sum \frac{C{F}_t}{(1+r{)}^t}-\text{Initial Investment}$$ where $r=10\%$.

Project A

$$NP{V}_A=\frac{700,000}{(1.10{)}^1}+\frac{700,000}{(1.10{)}^2}+\frac{700,000}{(1.10{)}^3}-1,000,000$$ $$=636,364+578,704+526,094-1,000,000=\text{Rs 741,162}$$

Project B

$$NP{V}_B=\frac{950,000}{(1.10{)}^1}+\frac{750,000}{(1.10{)}^2}+\frac{300,000}{(1.10{)}^3}-1,000,000$$ $$=863,636+616,438+225,394-1,000,000=\text{Rs 705,568}$$

Decision Rule (Independent Projects): Since both projects have positive NPV, both should be accepted.

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c. Internal Rate of Return (IRR) Calculation

IRR is the discount rate that makes NPV = 0. We solve for $r$ in: $$0=\sum \frac{C{F}_t}{(1+r{)}^t}-\text{Initial Investment}$$

Project A

Using the IRR formula (or financial calculator): $${\text{IRR}}_A=\text{30.23\%}$$

Project B

$${\text{IRR}}_B=\text{22.15\%}$$

Decision Rule (Mutually Exclusive Projects): Since Project A has a higher IRR (30.23%), it should be selected.

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d. Merits and Demerits of Payback Period, NPV, and IRR

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Python Code for NPV and IRR Calculation

import numpy_financial as npf

# Cash Flows for Project A
CF_A = [-1000000, 700000, 700000, 700000]
NPV_A = npf.npv(0.10, CF_A[1:]) - abs(CF_A[0])
IRR_A = npf.irr(CF_A)

# Cash Flows for Project B
CF_B = [-1000000, 950000, 750000, 300000]
NPV_B = npf.npv(0.10, CF_B[1:]) - abs(CF_B[0])
IRR_B = npf.irr(CF_B)

print(f"NPV of Project A: Rs {NPV_A:.2f}")
print(f"IRR of Project A: {IRR_A:.2%}")
print(f"NPV of Project B: Rs {NPV_B:.2f}")
print(f"IRR of Project B: {IRR_B:.2%}")

How it works:

• Uses numpy_financial to compute NPV and IRR for given cash flows.
• Inputs are structured as a list of cash flows (including Year 0).
• Outputs NPV and IRR for both projects.