Question

Problem 5-4 Calculating Discounted Payback An investment project costs $10,000 and has annual cash flows of $2,830 for six years. a. What is the discounted payback period if the discount rate is 0 percent? (Enter 0 if the project never pays back on a discounted payback basis. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. What is the discounted payback period if the discount rate is 4 percent? (Enter 0 if the project never pays back on a discounted payback basis. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) c. What is the discounted payback period if the discount rate is 21 percent? (Enter 0 if the project never pays back on a discounted payback basis. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) This is the last question in the assignment. To submit, use Alt + S. To access other questions, proceed to the question map button.

Answer 1

Here initial investment is $ 10,000. Now if the discounted rate is 0% then your future cash flows will be same for present or you can say that the future value and present value of the cash flows will be the same. For 4% and 21% we have to use present value factor

NOW, we can see the below table to find the exact period.

Year	cash flows@0%	pvf@4%	cash flows@4%	pvf@21%	cash flows@21%
1	2830	0.962	2722.46	0.826	2337.58
2	2830	0.925	2617.75	0.683	1932.89
3	2830	0.889	2515.87	0.564	1596.12
4	2830	0.855	2419.65	0.467	1321.61
5	2830	0.822	2326.26	0.386	1092.38
6	2830	0.790	2235.7	0.319	902.77

A) for 0% as we can see that in 3 years the total cash flow will be $8490 and 4 years total cash flow will be $11320. The rest of the cash that is to be received is $1510($10000-$8490) which will be received in part of the 4th year. we can calculate it by following way

($1510/$11320-$8490)*(4-3) = 0.533years

So total discounted payback period for 0% will be = 3.533 years

B) Similarly, for 4% discount rate the total cash flow for 3 years cumulative will be $7856.08 and for 4 years will be $10275.73. The rest outflow amount of $2143.92($10000-$7856.08) will be received in part of the 4th year. which can be calculated as follows:

($2143.92/$10275.73-$7856.08)*(4-3)= 0.89

so total discounted payback period for the 4% will be = 3.89 years

C) now for 21% discounted rate the total cash flow of all the 6 years after discount will be $9183.35 which is less than the total outflow that is $10,000. So at this rate the project will never pay back. so the answer will be 0.

This is simplest form to understand a question of discounted payback. Discounted payback simply means that in how much years our present outflow will be recovered keeping the profits as low as possible and taking the adequate required rate of return or discount rate.

Thanku