Question & Answer: 2.53 The business plan for Knowlt, LLC, a start-up company that manufactures portable multi-gas detectors, showed equiva…..

2.53 The business plan for Knowlt, LLC, a start-up company that manufactures portable multi-gas detectors, showed equivalent annual cash flows of $400,000 for the first 5 years. If the cash flow in year 1 was S320,000 and the constant increase thereafter was S50,000 per year, what interest rate was used in the calculation? (Solve using factors or a spreadsheet as requested by your instructor.)

2.53 The business plan for Knowlt, LLC, a start-up company that manufactures portable multi-gas detectors, showed equivalent annual cash flows of $400,000 for the first 5 years. If the cash flow in year 1 was S320,000 and the constant increase thereafter was S50,000 per year, what interest rate was used in the calculation? (Solve using factors or a spreadsheet as requested by your instructor.)

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We can solve this problem by using trial & error method.
We are using interest rate of 15% and 25% for trial and error method
Year Cash inflow PVIF @ 15% PV of Cash inflow Cash inflow PVIF @ 25% PV of Cash inflow
1 320000               0.8696           2,78,261 320000 0.8000              2,56,000
2 370000               0.7561           2,79,773 370000              0.6400              2,36,800
3 420000               0.6575           2,76,157 420000              0.5120              2,15,040
4 470000               0.5718           2,68,724 470000              0.4096              1,92,512
5 520000               0.4972           2,58,532 520000              0.3277              1,70,394
Total               3.3522         13,61,447              2.6893            10,70,746
Equivalent annual cashflow (1361447/3.3522)     4,06,140.75        3,98,153.26
Equivalent annual cashflow using interest rate of 15%     4,06,140.75
Equivalent annual cashflow using interest rate of 25%     3,98,153.26
Required Equivalent annual cashflow 400000
From the above we can understand that the required interest rate is between 15% and 25%
We use interpolation method to get the required interest rate
Interest rate = Lower rate + ((NPV at lower rate-required NPV)/(NPV at lower rate-NPV at higher rate))*(higher rate-lower rate)
= 15% + ((406140.75-400000) / (406140.75-398153.26))*(25-15)
= 15%+(6140.75/7987.49)*10
= 15%+0.7687*10
= 15%+7.687% = 22.687%

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