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.)

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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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