7. You decide to sell your car and a friend has offered you $1,000 now and four annual
payments of $1,800, with the annual payments starting at the end of the second year.
Your other option is to sell the car to a dealer today for $6,450. Assuming your friend
will not default on the payments and the market annual interest rate is 8%, should you
sell your car to your friend?
A) Yes; present value of the friend’s offer is $6,520
B) Yes; present value of the friend’s offer is $6,624
C) No; present value of the friend’s offer is $5,134
D) No; present value of the friend’s offer is $5,624
E) Both options offer the same value
Answer A
The PV of the annuity payment of $1,800 for 4 years is:
PV (at t=1): $1,800 x PVIFA(8%,4) = $5,962
PV (at t=0) = $5,962/ (1.08) = $5,520
Finally add the initial payment $1,000 today to the PV annuity at t=0
$(5,520 + 1,000) = $6,520
This is more than the $6,450 you would get today from the dealer. Therefore you
should sell your car to you friend.
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