A 3-year project requires an initial investment of $100 million (CF0=-100), and will return cash infows...

A 3-year project requires an initial investment of $100 million (CF0=-100), and will return
cash infows of $70 million, $50 million, and $20 million at the end of the years 1, 2, and
3, respectively. Assuming a weighted average cost of capital of 10%, what is the discounted
payback period for this project?

(Please show work and explain on paper)

Solutions

Expert Solution

Discounted Payback period is the time it takes for the initial cost of a project to equal to discounted value of cash inflows.

Calculation of Discounted Payback Period

Firstly will calculate Present Value of Cash Flows and then each such cash flows are added together i.e.cumulative cash flows.

Year	Cash Flows	Present Value Factor @10%	Present Value of Cash Flows	Present Value Cumulative Cash Flows
0	$(100)MM	1	$(100)MM	$(100)M
1	$70MM	0.9091	$63.637MM	$(36.363)MM (100 - 63.637)
2	$50MM	0.8264	$41.32MM	$4.957MM (-36.363+41.32)
3	$20MM	0.7513	$15.026MM	$19.983MM

From the above table, it can be seen that initial investment is recovered between Year 1 and Year 2

Payback Period = P + PVCCF / PVCF

where,
P = last Time Period where the Present Value Cumulative Cash flows was negative
PVCCF = Present Value Cumulative Cash flows of period P
PVCF = Present Value of Cash Flows of period following the period P

Payback Period = P + PVCCF / PVC
= Year 1 + $36.363MM / $41.32MM
= 1 + 0.8800
= 1.88 years

Ans : Discounted Payback period for this project is 1.88 years.

jeff jeffy answered 1 year ago

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