E connect FINA 5320-Managerial Finance- Fall 2018 WO1 Fall 2018 WO1 Homework #3

Question

E connect FINA 5320-Managerial Finance- Fall 2018 WO1 Fall 2018 WO1 Homework #3 Question 2 (of 9) 2. An investment project has annual cash inflows of $4,800, $3,500, $4.700, and $3,900, and a discount rate of 15 percent What is the discounted payback period for these cash flows i# the initial cost is $5,300? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g.. 32.16 Discounted payback period What is the discounted payback period for these cash flows if the initial cost is $7.400? (Do not round Discounted payback periodml years What is the discounted payback period for these cash flows if the initial cost is $10.400? (Do not round years ions and round your answer to 2 decimal places, eg, 32.16.) intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Diacounted payback periodyears eBook & Resources O Type here to search

Explanation / Answer

Payback period is the period within which the intial cash outflow or initial investment is recovered by the cash inflows of the project. In case of discounted payback period, we need to compute the present value of cash inflows and see the point in time when they fully recover the initial cost.

Present value of a cash flow can be computed as -

PV = Amount / (1 + r)n

where, r = discount rate, n = no. of years

PV of Year 1 cash flow = $4800 / (1 + 0.15)1 = $4173.91304347

PV of Year 2 cash flow = $3500 / (1 + 0.15)2 = $2646.50283553

PV of Year 3 cash flow = $4700 / (1 + 0.15)3 = $3090.32629241

PV of Year 4 cash flow = $3900 / (1 + 0.15)4 = $2229.8376578

The above will remain the same irrespective of the initial cost.

Initial cost is $5300

The initial outflow of (-)$5300 is recovered or becomes positive in year 2. So, discounted payback period is beyond year 1 but before the end of year 2 since cumulative cash flow is not zero in year 2 but actually more than that as cash flow in year 2 is more than required for the payback. Therefore, we need to interpolate -

Payback period = 1 year + 1 year x (Cash flow required in Year 2 / Total cash flow in year 2)

or, Payback period = 1 year + 1 year x ($1126.08695653 / $2646.50283553) = 1.4255 years or 1.43 years

Initial cost is $7400

Payback period = 2 years + 1 year x (Cash flow required in Year 3 / Total cash flow in year 3)

Payback period = 2 years + 1 year x ($579.584121 / $3090.32629241) = 2.1875 years or 2.19 years

Initial cost is $10400

Payback period = 3 years + 1 year x (Cash flow required in Year 4 / Total cash flow in year 4)

Payback period = 3 years + 1 year x ($489.25782866 / $2229.8376578) = 3.2194 years or 3.22 years

Year Discounted Cash Flows Cumulative discounted cash flows 0 (-)$5300 (-)$5300 1 $4173.91304347 (-)$1126.08695653 2 $2646.50283553 $1520.415879 3 $3090.32629241 $4610.74217141 4 $2229.8376578 $6840.57982921

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