Your neighbor is buying a new Tesla electric car. He has the following options t

ID: 2815421 • Letter: Y

Question

Your neighbor is buying a new Tesla electric car. He has the following options to finance the purchase:

I. Pays $90,000 today (in time 0)

II. Buy under a "no payments for three years" program by agreeing to pay $110,000 three years from today (in time 3)

III. Make 60 monthly payments over 5 years of $1,750 payable at the end of each month

(a) If the interest rate is 6% annually, calculate the present value of each option.

(b) At what interest rate do Option II and Option III have the same present value?

(Not in excel function, but the regular present value equation that can be plugged into a calculator)

presnt value of annuity = P * (1 - (1+r/12)^(-12*n))/r/12

Ans a) PV of option I = $90000

PV of option II = $110000/(1+r)^3 = $110000/(1.06)^3 = $92358.12

PV of option III = $1750 * (1 - (1.005)^(-60))/.005 = $90519.73

Ans b) we will equate the both equation and find the value of

110000/(1+r)^3 = $1750 * (1 - (1 + r/12)^(-60))/r/12

we will try to solve by trail and error r = 10.8% (approx)

value will be equal to 80860 (approx)

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