FNAN 301
Solutions to test bank problems – time value of money part 2
2. You just bought a new car today.
What is the present value of your cash flows if the discount rate is
12.3 percent, you will receive a rebate of $2,000 from the dealer in 2 years, and you will pay $40,000 to
the dealer in 4 years?
Note: the correct answer is less than zero.
(http://www.youtube.com/watch?v=fS4_fkwv584
file:auto sale with rebate.wmv)
(Fall 2009, quiz 1, question 6)
(Fall 2009, final, question 2)
(Spring 2010, quiz 1, question 2)
(Spring 2010, final, question 1)
PV = C
0
+ [C
1
/(1+r)
1
] + [C
2
/(1+r)
2
] + [C
3
/(1+r)
3
] + [C
4
/(1+r)
4
]
C
0
= 0
C
1
= 0
C
2
= 2,000
C
3
= 0
C
4
= -40,000
r = .123
PV = 0 +[0/(1.123)] + [2,000/(1.123)
2
] + [0/(1.123)
3
] + [-40,000/(1.123)
4
]
= 0 + 0 + 1,585.88 + 0 + (-25,150.17) = -$23,564.29
Solution – financial calculator
Year 0 CF: present value = 0
Year 1 CF: present value = 0
Year 2 CF: N = 2; FV = 2,000; I% = 12.3; PMT = 0; solve for PV = -1,585.88
so the present value of the cash flow = $1,585.88
Year 3 CF: present value = 0
Year 4 CF: N = 4; FV = -40000; I% = 12.3; PMT = 0; solve for PV = 25,150.17
so the present value of the cash flow = -25,150.17
Total present value of the cash flows = 0 + 0 + 1,585.88 + 0 + (-25,150.17) = -$23,564.29
Note that answers may differ slightly due to rounding
2