Solution: The working of the problem is as under:-
Lease Option for use of Car | ||||||||||
CAR VALUE | $40,000.00 | Lease Value or Present Value | ||||||||
Term | 4 years | In months it will be 48 months | ||||||||
Nominal Annual Interest | 5% | In month the rate will be =5% / 12 = 0.42% | ||||||||
Payment per month will be calculated using Present Value Annuity Formula i.e. PVIA = A*[1-(1+r)^-n] / r | ||||||||||
N= Term i.e. 48 months; R= Monthly Rate i.e. 0.42% and PVIA = 40000, thus we have to calculate only for A i.e. monthly payment | ||||||||||
40000 | = A*[1 - (1+0.42%)^-48] / 0.42% | |||||||||
40000 | =A*43.389 | |||||||||
A= | =40000/43.389 | 921.893 | ||||||||
As this is a monthly payment it is an outflow | ||||||||||
Present Value of Annuity Leasing @ 3% annual compounded monthly i.e. @3% / 12 = 0.250% | ||||||||||
PVIA = | A*[1-(1+r)^-n] / r | |||||||||
=921.893*[1- (1+0.250%)^-48]/ 0.250% | ||||||||||
Present Value of Leasing = | 41649.9181 | |||||||||
Borrowing Option for use of Car | ||||||||||
CAR VALUE | $40,000.00 | Borrowed Value or Present Value | ||||||||
Term | 4 years | In months it will be 48 months | ||||||||
Nominal Annual Interest | 5% | In month the rate will be =5% / 12 = 0.42% | ||||||||
Payment per month will be calculated using Present Value Annuity Formula i.e. PVIA = A*[1-(1+r)^-n] / r | ||||||||||
N= Term i.e. 48 months; R= Monthly Rate i.e. 0.42% and PVIA = 40000, thus we have to calculate only for A i.e. monthly payment | ||||||||||
40000 | = A*[1 - (1+0.42%)^-48] / 0.42% | |||||||||
40000 | =A*43.389 | |||||||||
A= | =40000/43.389 | 921.893 | ||||||||
As this is a monthly payment it is an outflow | ||||||||||
Present Value of Borrowing @ 3% annual compounded monthly i.e. @3% / 12 = 0.250% | ||||||||||
PVIA = | A*[1-(1+r)^-n] / r | |||||||||
=921.893*[1- (1+0.250%)^-48]/ 0.250% | ||||||||||
41649.9181 | Cash Outflow | |||||||||
In the Last 48th month we have Car Worth $12000.00 whose Present Value if calculated will be | ||||||||||
Present Value of Car Residual Value = 12000*(1/(1+0.250%)^48 | =12000*0.887 | |||||||||
PV of Residual Car Value | 10644.000 | Cash Inflow | ||||||||
Thus Present Value of Borrowing Option is = PV of Cash Outflow = -41649.918 Adding Present Value of Residual Car Value = 10644 | ||||||||||
Net Present Value = | -31005.918 | |||||||||
We conclude our Answer by choosing the Borrowing Option |
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