Calculate Present Value of 10-Year Lease w/ OCC & Variable Rental

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SUMMARY

The discussion focuses on calculating the Present Value (PV) of a 10-year lease with annual rental payments that increase by 2% each year, starting at £20, with an Opportunity Cost of Capital (OCC) of 10%. The correct formula for PV of growing annuities is provided, leading to a confirmed answer of £132.51. A miscalculation was identified, where the user initially obtained -£23.88 due to incorrect data entry into their calculator.

PREREQUISITES
  • Understanding of Present Value calculations
  • Familiarity with annuity formulas
  • Knowledge of financial concepts such as Opportunity Cost of Capital (OCC)
  • Proficiency in using financial calculators or spreadsheet software
NEXT STEPS
  • Study the formula for Present Value of growing annuities
  • Learn how to use financial calculators for annuity calculations
  • Explore the impact of varying OCC rates on Present Value
  • Review examples of lease agreements and their financial implications
USEFUL FOR

Finance students, real estate investors, and anyone involved in lease agreements or financial analysis will benefit from this discussion.

logicandtruth
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Hi all

Trying to improve my level of maths and would like some help with the below question please.

A 10-year lease with annual rental payments to be made at the end of each year, with the rent increasing by 2% each year. If the first year rent is £20 and the OCC is 10% per year, what is the Present value of the lease?

The formula for present value of a level annuities is below (for a growing interest rate)

View attachment 8227

According to my book the answer should be £132.51, but I get -23.88.

View attachment 8228

Could anyone tell me where I am misinterpreting the formula?
 

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Book is correct. Are you using a calculator?
You're probably entering the data wrongly...we can't tell...
Try it this way:
u = (1.02/1.10)^10
v = .10 - .02

PV = 20*(1 - u) / v
 
Yes it works I must have been using the incorrect figure with my calculator.

Many thanks
 

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