Skip to main content

How to calculate Monthly payment and Present Value of Lease payment?

In previous post we had discussed about lease and its type and now we will discuss its methods.
Minimum payment: The guaranteed amount which lessee pays to lessor if he does not earn enough money from leased asset or not. It does not include executory cost that is insurance cost, taxes and maintenance cost.

Formula for present value of lease payment:
PV= C [(1-(1/ (1+i) n)) / i] + RV/ (1+i) n
Formula for monthly lease payment:
C= [PV - (RV/ (1+i) n)]/ (1-(1/ (1+i) n)/ i)
Formula for monthly lease payment with advance:
C= [PV - (RV/ (1+i) n)]/ [(1-(1/ (1+i) n - A)/ i) +A]
Formula for present value of minimum lease payment:
PV = (P / (1+i) n) + (RV / (1+i) n)

Where,
C = monthly payment
PV = present value of lease amount
RV = residual value of lease asset
i = interest rate on lease
n = number of years
A = number of advance payment
P = annual lease payment
  
Example: Suppose a company has taken a machine on lease for 6 years and pays Rs.20, 000 per month and the interest on it is 6% p.a. the residual value of lease is Rs.60, 000. Find out the present value of lease payment.

Solution: C = 20,000, i= 6/12 = 0.5, RV = 60, 000
PV= C [(1-(1/ (1+i) ^n)) / i] + RV/ (1+i) ^n
= 20, 000 [(1-(1/ (1+0.005^6)) / 0.005] + 60, 000/ (1+0.005) ^6
= 20, 000 [(1-(1/1.03) / 0.005] + 60, 000/ 1.03
= 20, 000[(1-0.97) / 0.005] + 60, 000 / 1.03
= 20, 000[0.03/0.005] + 60, 000 / 1.03
= 20, 000*6 + 58, 252.43
PV = 1, 78,252.43

Example: A company is willing to take a land on lease for 10 years and the lessor charge 7% interest on it and the residual value of that land is Rs. 10, 05,000. Find out the how much company will have to pay to lessor if the present value is Rs. 56, 00,000?

Solution: i= 7/12 = 0.58%,

C= [PV - (RV/ (1+i) ^n)]/ (1-(1/ (1+i) ^n)/ i)
= [56, 00,000 - (10, 05,000/ (1+0.0058) ^10)]/ (1-(1/ (1+0.0058) ^10)/ 0.0058)
= [56, 00,000 - (10, 05,000/ 1.06)]/ (1-(1/ 1.06)/ 0.0058)
= [56, 00,000 – 9, 48,116.21]/ ((1-0.94)/ 0.0058)
= 46, 51,883.79 / 0.06/0.0058
= 46, 51,883.79 / 10.34

C = Rs.4, 49,892.05

Example: Company has taken an asset on lease from lessor at 8% p.a. interest and the annual payment of lease is Rs.85, 000 for 5 years and the residual value of asset is Rs.98, 000. Find out the present value of minimum lease payment.

Solution: i= 8/12 = 0.67, P = 85,000, RV = 98, 000

PV = (P / (1+i) n) + (RV / (1+i) n)
= (85, 000 / (1+0.0067) 5) + (98, 000 / (1+0.0067) 5)
= (85, 000 / 1.03) + (98, 000 / 1.03)
= 82, 524.27 + 95, 145.63
PV= 1, 77,669.9

Example: Suppose a company has purchased a lease for 7 years by paying 2 months advance at the rate of 6% p.a. the present value of leased amount is Rs.50, 000 and the residual value is Rs.20, 000.  How much company will have to pay monthly to lessor?

Solution: i= 6/12 = 0.5, PV = 50,000, RV = 80, 000, A = 2

C= (PV - (RV/ (1+i) n))/ ((1-(1/ (1+i) n - 2)/ i) +A)
= (50,000 - (20,000/ (1+0.005) 7))/ ((1-(1/ (1+0.005) 7 -2)/ i) +2)
= (50,000 - (20,000/ 1.04))/ ((1-(1/ 1.03)/ 0.005) +2)
= [50,000 – 19, 230.77]/ ((1-0.97/ 0.005) + 2)
= 30, 769.23 / ((0.03/0.005) + 2)
= 30, 769.23 / (6 + 2)
 = 30, 769.23 / 8 
= 3, 846.15




Comments

Post a Comment

Popular posts from this blog

How to calculate Cost of Preference Share Capital?

Cost of Preference Share Capital:  An amount paid by company as dividend to preference shareholder is known as Cost of Preference Share Capital. Preference share is a small unit of a company’s capital which bears fixed rate of dividend and holder of it gets dividend when company earn profit. Dividend payable is not a tax deductible amount. So, there is no tax adjustments required for comparing with cost of debt. Formula for Cost of Preference Share: Irredeemable Preference Share Redeemable Preference Share K p  = Dp/NP K p  = D p +((RV-NP)/n )/ (RV+NP)/2 Where, K p  = Cost of Preference Share D p  = Dividend on preference share NP = Net proceeds from issue of preference share (Issue price – Flotation cost) RV = Redemption Value N = Period of preference share Example:  A company issues 20,000 irredeemable preference share at 8% whose face value is Rs.50 each at 4% discount. Find out the Cost of ...
89 comments
Read more

What is the difference between Cheque book and Pass book?

 Cheque book is issued by bank in customers / account holder request. With the help of this book account holder can withdraw cash from his/her account. Bank does not charge any fee to issued cheque book to its customer. But afterward bank charges some amount for using bank facility like cheque book, Debit card etc.So, Automatic some definite amount deducted from customer bank account. Pass book is  also issued by bank to its customer. It helps to record all the bank related activity according to date that is withdrawal and deposit. It is recorded by bank but the book is kept by customer to know the current balance of  his /her account.  Point of difference Pass book Cheque book What is the meaning of pass book and cheque book? Passbook is a book in which all withdrawal and deposit against customer account is recorded.   Cheque book is a book of cheques which are used to withdrawal the money to b...
Post a Comment
Read more

What is Working Capital Leverage (WCL)?

Working capital leverage: It shows the sensitivity of the return on investment with change in current assets. As we all know the working capital is difference between current assets and current liabilities. And the working capital is use for meeting day to day capital requirements in business operations. With the help of working capital leverage we will find out how productivity or profitability of a business is affected by change in current assets. Formula: Working Capital Leverage (WCL) = % ∆ ROE / % ∆ CA Or If % decreases in current assets: WCL= CA / TA - ∆ CA If % increases in current assets: WCL = CA / TA + ∆ CA Where, CA = current assets TA = total assets ROE = return of capital employed or return on investment ∆ CA = change in current assets Example: Company A total assets are Rs. 17, 60, 800 and the current assets are Rs. 6, 00,000. The fixed assets are Rs. 11, 60, 800. Find out the working capital leverage if the current asset increases by 15...
2 comments
Read more