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5yearsasfollows.
Years 0 1 2 3 4 5
Cash
flows(TZS
'000)
(50,000) 20,000 30,000 40,000 35,000 18,000
Thediscountingfactoris8%.Calculatepaybackanddiscountedpayback.?
Anonymous
Feb 1
5yearsasfollows. Years 0 1 2 3 4 5 Cash flows(TZS '000) (50,000) 20,000 30,000 40,000 35,000 18,000 Thediscountingfactoris8%.Calculatepaybackanddiscountedpayback.?
5yearsasfollows.
Years 0 1 2 3 4 5
Cash
flows(TZS
'000)
(50,000) 20,000 30,000 40,000 35,000 18,000
Thediscountingfactoris8%.Calculatepaybackanddiscountedpayback.
Years 0 1 2 3 4 5
Cash
flows(TZS
'000)
(50,000) 20,000 30,000 40,000 35,000 18,000
Thediscountingfactoris8%.Calculatepaybackanddiscountedpayback.
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Feb 1
To calculate the payback period, we need to determine how long it takes for the cumulative cash flows to equal or exceed the initial investment.
Year 0: (50,000)
Year 1: 20,000
Year 2: 30,000
Year 3: 40,000
Year 4: 35,000
Year 5: 18,000
Cumulative cash flows:
Year 0: (50,000)
Year 1: (50,000 + 20,000) = (30,000)
Year 2: (30,000 + 30,000) = 0
Year 3: (0 + 40,000) = 40,000
Year 4: (40,000 + 35,000) = 75,000
Year 5: (75,000 + 18,000) = 93,000
The payback period is between Year 2 and Year 3 because the cumulative cash flows become positive in Year 2. To calculate the exact payback period, we can use the formula:
Payback period = Year before positive cash flow + (Positive cash flow / Cash flow in the following year)
Payback period = 2 + (30,000 / 40,000) = 2.75 years
To calculate the discounted payback period, we need to discount the cash flows using the discounting factor of 8%.
Year 0: (50,000 / (1 + 0.08)^0) = (50,000 / 1) = (50,000)
Year 1: (20,000 / (1 + 0.08)^1) = (20,000 / 1.08) = 18,518.52
Year 2: (30,000 / (1 + 0.08)^2) = (30,000 / 1.1664) = 25,747.77
Year 3: (40,000 / (1 + 0.08)^3) = (40,000 / 1.2597) = 31,746.03
Year 4: (35,000 / (1 + 0.08)^4) = (35,000 / 1.3605) = 25,694.04
Year 5: (18,000 / (1 + 0.08)^5) = (18,000 / 1.4693) = 12,259.61
Cumulative discounted cash flows:
Year 0: (50,000)
Year 1: (50,000 + 18,518.52) = (31,481.48)
Year 2: (31,481.48 + 25,747.77) = (5,733.71)
Year 3: (5,733.71 + 31,746.03) = 26,012.32
Year 4: (26,012.32 + 25,694.04) = 51,706.36
Year 5: (51,706.36 + 12,259.61) = 63,965.97
The discounted payback period is between Year 4 and Year 5 because the cumulative discounted cash flows become positive in Year 4. To calculate the exact discounted payback period, we can use the formula:
Discounted payback period = Year before positive discounted cash flow + (Positive discounted cash flow / Discounted cash flow in the following year)
Discounted payback period = 4 + (12,259.61 / 25,694.04) = 4.48 years
Year 0: (50,000)
Year 1: 20,000
Year 2: 30,000
Year 3: 40,000
Year 4: 35,000
Year 5: 18,000
Cumulative cash flows:
Year 0: (50,000)
Year 1: (50,000 + 20,000) = (30,000)
Year 2: (30,000 + 30,000) = 0
Year 3: (0 + 40,000) = 40,000
Year 4: (40,000 + 35,000) = 75,000
Year 5: (75,000 + 18,000) = 93,000
The payback period is between Year 2 and Year 3 because the cumulative cash flows become positive in Year 2. To calculate the exact payback period, we can use the formula:
Payback period = Year before positive cash flow + (Positive cash flow / Cash flow in the following year)
Payback period = 2 + (30,000 / 40,000) = 2.75 years
To calculate the discounted payback period, we need to discount the cash flows using the discounting factor of 8%.
Year 0: (50,000 / (1 + 0.08)^0) = (50,000 / 1) = (50,000)
Year 1: (20,000 / (1 + 0.08)^1) = (20,000 / 1.08) = 18,518.52
Year 2: (30,000 / (1 + 0.08)^2) = (30,000 / 1.1664) = 25,747.77
Year 3: (40,000 / (1 + 0.08)^3) = (40,000 / 1.2597) = 31,746.03
Year 4: (35,000 / (1 + 0.08)^4) = (35,000 / 1.3605) = 25,694.04
Year 5: (18,000 / (1 + 0.08)^5) = (18,000 / 1.4693) = 12,259.61
Cumulative discounted cash flows:
Year 0: (50,000)
Year 1: (50,000 + 18,518.52) = (31,481.48)
Year 2: (31,481.48 + 25,747.77) = (5,733.71)
Year 3: (5,733.71 + 31,746.03) = 26,012.32
Year 4: (26,012.32 + 25,694.04) = 51,706.36
Year 5: (51,706.36 + 12,259.61) = 63,965.97
The discounted payback period is between Year 4 and Year 5 because the cumulative discounted cash flows become positive in Year 4. To calculate the exact discounted payback period, we can use the formula:
Discounted payback period = Year before positive discounted cash flow + (Positive discounted cash flow / Discounted cash flow in the following year)
Discounted payback period = 4 + (12,259.61 / 25,694.04) = 4.48 years
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