Assume an $82,000 investment and the following cash flows for two alternatives:
Year | Investment X | Investment Y
---|---|---
1 | $24,000 | $35,000
2 | $16,000 | $35,000
3 | $24,000 | $22,000
4 | $24,000 | -
5 | $25,000 | -
a. Calculate the payback for investment X and Y.
Note: Do not round intermediate calculations. Round your answers to 2 decimal places.
Investment X: ____ years
Investment Y: ____ years
b. Which alternative would you select under the payback method?
Investment X
Investment Y
Answer (2)
Calculate the cumulative cash flow for each year for Investment X and Investment Y.
Determine the payback period for Investment X: The initial investment is recovered between Year 3 and Year 4, so the payback period is 3 + 24000 18000 = 3.75 years.
Determine the payback period for Investment Y: The initial investment is recovered between Year 2 and Year 3, so the payback period is 2 + 22000 12000 = 2.55 years.
Select the investment with the shorter payback period: Investment Y has a shorter payback period (2.55 years) compared to Investment X (3.75 years), so the answer is Investment Y and the payback periods are 3.75 years for Investment X and 2.55 years for Investment Y.
Explanation
Understanding the Problem We are given an initial investment of $82,000 and the cash flows for two investment alternatives, X and Y. Our goal is to calculate the payback period for each investment and determine which investment has a shorter payback period. The payback period is the amount of time it takes for an investment to generate cash flows equal to the initial investment.
Investment X - Cash Flows To calculate the payback period for Investment X, we need to determine when the cumulative cash flows equal or exceed the initial investment of $82,000. The cash flows for Investment X are as follows:
Year 1: $24,000 Year 2: $16,000 Year 3: $24,000 Year 4: $24,000 Year 5: $25,000
Investment X - Payback Period Calculation We calculate the cumulative cash flows for Investment X:
Year 1: $24,000 Year 2: $24,000 + $16,000 = $40,000 Year 3: $40,000 + $24,000 = $64,000 Year 4: $64,000 + $24,000 = $88,000
The initial investment of $82,000 is recovered between Year 3 and Year 4. To find the exact payback period, we calculate the fraction of Year 4 needed:
Amount remaining after Year 3: $82,000 - $64,000 = $18,000 Fraction of Year 4 needed: $\frac{18,000}{24,000} = 0.75
Therefore, the payback period for Investment X is 3 + 0.75 = 3.75 years.
Investment Y - Cash Flows To calculate the payback period for Investment Y, we need to determine when the cumulative cash flows equal or exceed the initial investment of $82,000. The cash flows for Investment Y are as follows:
Year 1: $35,000 Year 2: $35,000 Year 3: $22,000
Investment Y - Payback Period Calculation We calculate the cumulative cash flows for Investment Y:
Year 1: $35,000 Year 2: $35,000 + $35,000 = $70,000 Year 3: $70,000 + $22,000 = $92,000
The initial investment of $82,000 is recovered between Year 2 and Year 3. To find the exact payback period, we calculate the fraction of Year 3 needed:
Amount remaining after Year 2: $82,000 - $70,000 = $12,000 Fraction of Year 3 needed: $\frac{12,000}{22,000} \approx 0.55
Therefore, the payback period for Investment Y is 2 + 0.55 = 2.55 years.
Comparison and Selection Comparing the payback periods, Investment X has a payback period of 3.75 years, and Investment Y has a payback period of 2.55 years. Since Investment Y has a shorter payback period, it would be the preferred alternative under the payback method.
Final Answer Investment X payback period is 3.75 years. Investment Y payback period is 2.55 years. Under the payback method, Investment Y would be selected because it has a shorter payback period.
Examples
The payback period is a crucial concept in business and finance. Imagine you're deciding between two coffee shop franchises. Franchise A requires an initial investment of $100,000 and generates $25,000 in annual profit, while Franchise B needs an initial investment of $80,000 but generates $20,000 annually. Using the payback period, you can quickly determine how long it will take for each franchise to recover the initial investment. Franchise A's payback period is 4 years ($\frac{100,000}{25,000} ) , an d F r an c hi se B ′ s p a y ba c k p er i o d i s a l so 4 ye a rs ( $ 20 , 000 80 , 000 ). This simple calculation helps in making informed decisions about which investment recovers costs faster, aiding in financial planning and risk assessment.
The payback period for Investment X is 3.75 years, while for Investment Y it is 2.55 years. Therefore, Investment Y is preferred because it has a shorter payback period. Investment Y would be selected under the payback method.
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