Question 1 · Short Answer and Calculation
10 marksVanguard Tech is considering investing in a new automated assembly line. The financial details of the project are as follows:
- Initial investment cost: $250,000
- Expected net cash flows:
- Year 1: $70,000
- Year 2: $90,000
- Year 3: $100,000
- Year 4: $80,000
- Discount factors at 6%:
- Year 1: 0.9434
- Year 2: 0.8900
- Year 3: 0.8396
- Year 4: 0.7921
(a) Define the term *net cash flow*. [2 marks]
(b) Calculate the payback period for Vanguard Tech's investment (show your working). [2 marks]
(c) Calculate the Net Present Value (NPV) of the investment using the 6% discount rate (show your working). [3 marks]
(d) Explain one reason why Vanguard Tech might use Net Present Value (NPV) rather than the payback period to evaluate this investment. [3 marks]
- Initial investment cost: $250,000
- Expected net cash flows:
- Year 1: $70,000
- Year 2: $90,000
- Year 3: $100,000
- Year 4: $80,000
- Discount factors at 6%:
- Year 1: 0.9434
- Year 2: 0.8900
- Year 3: 0.8396
- Year 4: 0.7921
(a) Define the term *net cash flow*. [2 marks]
(b) Calculate the payback period for Vanguard Tech's investment (show your working). [2 marks]
(c) Calculate the Net Present Value (NPV) of the investment using the 6% discount rate (show your working). [3 marks]
(d) Explain one reason why Vanguard Tech might use Net Present Value (NPV) rather than the payback period to evaluate this investment. [3 marks]
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Worked solution
**(a) Definition of Net Cash Flow:**
Net cash flow is the difference between cash inflows (money received) and cash outflows (money paid out) of a business over a given time period.
**(b) Payback Period Calculation:**
To calculate the payback period, we determine the cumulative cash flows:
- Year 0: -$250,000
- Year 1: -$250,000 + $70,000 = -$180,000
- Year 2: -$180,000 + $90,000 = -$90,000
- Year 3: -$90,000 + $100,000 = +$10,000
The payback occurs in Year 3.
Fractional year in Year 3 = \(\frac{90,000}{100,000} = 0.9\) years.
Thus, Payback Period = 2.9 years (or 2 years and 10.8 months).
**(c) Net Present Value (NPV) Calculation:**
Calculate the Present Value (PV) for each year:
- Year 1 PV: \(\$70,000 \times 0.9434 = \$66,038\)
- Year 2 PV: \(\$90,000 \times 0.8900 = \$80,100\)
- Year 3 PV: \(\$100,000 \times 0.8396 = \$83,960\)
- Year 4 PV: \(\$80,000 \times 0.7921 = \$63,368\)
Total Present Value of Cash Inflows = \(\$66,038 + \$80,100 + \$83,960 + \$63,368 = \$293,466\)
Net Present Value (NPV) = Total PV of Inflows - Initial Investment
NPV = \(\$293,466 - \$250,000 = \$43,466\)
**(d) NPV vs Payback Period:**
NPV takes into account the time value of money, which means it recognizes that money received in the future is worth less than money received today due to inflation, opportunity cost, and risk. In contrast, the payback period treats all cash flows as if they have equal value regardless of when they occur, and it completely ignores cash flows received after the payback point (such as the Year 4 cash flow of $80,000), making NPV a more comprehensive investment appraisal tool.
Net cash flow is the difference between cash inflows (money received) and cash outflows (money paid out) of a business over a given time period.
**(b) Payback Period Calculation:**
To calculate the payback period, we determine the cumulative cash flows:
- Year 0: -$250,000
- Year 1: -$250,000 + $70,000 = -$180,000
- Year 2: -$180,000 + $90,000 = -$90,000
- Year 3: -$90,000 + $100,000 = +$10,000
The payback occurs in Year 3.
Fractional year in Year 3 = \(\frac{90,000}{100,000} = 0.9\) years.
Thus, Payback Period = 2.9 years (or 2 years and 10.8 months).
**(c) Net Present Value (NPV) Calculation:**
Calculate the Present Value (PV) for each year:
- Year 1 PV: \(\$70,000 \times 0.9434 = \$66,038\)
- Year 2 PV: \(\$90,000 \times 0.8900 = \$80,100\)
- Year 3 PV: \(\$100,000 \times 0.8396 = \$83,960\)
- Year 4 PV: \(\$80,000 \times 0.7921 = \$63,368\)
Total Present Value of Cash Inflows = \(\$66,038 + \$80,100 + \$83,960 + \$63,368 = \$293,466\)
Net Present Value (NPV) = Total PV of Inflows - Initial Investment
NPV = \(\$293,466 - \$250,000 = \$43,466\)
**(d) NPV vs Payback Period:**
NPV takes into account the time value of money, which means it recognizes that money received in the future is worth less than money received today due to inflation, opportunity cost, and risk. In contrast, the payback period treats all cash flows as if they have equal value regardless of when they occur, and it completely ignores cash flows received after the payback point (such as the Year 4 cash flow of $80,000), making NPV a more comprehensive investment appraisal tool.
Marking scheme
**(a) Define net cash flow:**
- 2 marks: Clear definition that identifies both cash inflows and outflows and notes the difference between them.
- 1 mark: Partial understanding shown (e.g., "the money a business makes in cash").
**(b) Calculate payback period:**
- 2 marks: Correct answer of 2.9 years (or 2 years and 10.8 months) with working shown.
- 1 mark: Correct answer without working, or a minor mathematical error in cumulative calculations but with correct methodology.
**(c) Calculate Net Present Value (NPV):**
- 3 marks: Correct answer of $43,466 (allow rounding differences like $43,460 to $43,470 depending on decimal precision) with fully correct working shown.
- 2 marks: Process of calculation is correct, but there is a mathematical slip in summing up PVs or subtracting the initial investment.
- 1 mark: Attempt made to calculate present values (at least 2 correct years calculated), but formula not completed.
**(d) Explain NPV vs Payback:**
- 3 marks: Clear, detailed explanation that explicitly links the difference (time value of money or inclusion of subsequent cash flows) to Vanguard Tech's decision-making process.
- 2 marks: Explanation is given but lacks contextual depth or complete clarity.
- 1 mark: General statement about NPV or payback without proper explanation/context.
- 2 marks: Clear definition that identifies both cash inflows and outflows and notes the difference between them.
- 1 mark: Partial understanding shown (e.g., "the money a business makes in cash").
**(b) Calculate payback period:**
- 2 marks: Correct answer of 2.9 years (or 2 years and 10.8 months) with working shown.
- 1 mark: Correct answer without working, or a minor mathematical error in cumulative calculations but with correct methodology.
**(c) Calculate Net Present Value (NPV):**
- 3 marks: Correct answer of $43,466 (allow rounding differences like $43,460 to $43,470 depending on decimal precision) with fully correct working shown.
- 2 marks: Process of calculation is correct, but there is a mathematical slip in summing up PVs or subtracting the initial investment.
- 1 mark: Attempt made to calculate present values (at least 2 correct years calculated), but formula not completed.
**(d) Explain NPV vs Payback:**
- 3 marks: Clear, detailed explanation that explicitly links the difference (time value of money or inclusion of subsequent cash flows) to Vanguard Tech's decision-making process.
- 2 marks: Explanation is given but lacks contextual depth or complete clarity.
- 1 mark: General statement about NPV or payback without proper explanation/context.