question archive King's company is considering the following 5-year project to be conducted at the beginning of year 2021, the initial cost of the project is $20000, and the pre-tax cash flow from the project is 12000, 12000, 20000, 10000, 5000 for year one to year five
King's company is considering the following 5-year project to be conducted at the beginning of year 2021, the initial cost of the project is $20000, and the pre-tax cash flow from the project is 12000, 12000, 20000, 10000, 5000 for year one to year five
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King's company is considering the following 5-year project to be conducted at the beginning of year 2021, the initial cost of the project is $20000, and the pre-tax cash flow from the project is 12000, 12000, 20000, 10000, 5000 for year one to year five. The marginal tax rate for the company is 20% and the required rate of return is 8%. At the very beginning the company used the payback period technique to evaluate the project. However, the board subsequently asked the company to use the discounted payback period technique to evaluate the project. Discounted payback period gives the number of years it takes to break even from undertaking the initial expenditure, by discounting future cash flows and recognizing the time value of money. Basically, the discounted payback period is calculated following the same procedure as payback period but use discounted cash flows instead. What's the difference between the payback period and the discounted payback period of this opportunity? 0.197 0.186 0.561 0.177
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The cash flow data can be presented in the table as shown below
| Year | Pre tax cash flows |
After tax cash flows (1- marginal tax rate) x pre tax cash flows |
Discounted Cash flows (1/ (1 + required rate of return)^year) |
| 1 | 12000 | 9600 | 8888.8889 |
| 2 | 12000 | 9600 | 8230.4527 |
| 3 | 20000 | 16000 | 12701.316 |
| 4 | 10000 | 8000 | 5880.2388 |
| 5 | 5000 | 4000 | 2722.3328 |
Payback period is simply how long it takes for the after tax cash flows to breakeven the initial cost of project and discounted payback period is how long it takes for discounted cash flows to breakeven the initial project cost
Initial cost = $ 20000
We can see that in first 2 years company covers 19200 (9600 + 9600) of the total 20000 initial cost
And remaining 800 (20000 - 19200) will be covered in 3rd year and will take 0.05 years (800/16000)
Hence payback period = 2 + 0.05 = 2.05 years
For discounted payback period we can see that in first 2 years company covers 17119.33 (8888.88 + 8230.45) of the total initial cost of 20000
Remaining 2880.67 (20000 - 17119.33) will be covered in 3rd year and will take 0.2268 years (2880.67/12701.32)
Hence Discounted payback period = 2 + 0.2268 = 2.2268 years
Hence difference between payback and discounted payback period = 2.2268 - 2.05 = 0.1768
Hence option (4) is correct
