I’m working on a practice math exam, and need explanations and answers for practice questions to help me study. The questions are look like following:
1. (20) Automobile dealerships often advertise promotions such as no payments for 90 days!” or similar deals
that sound too good to be true. The goal, of course, is to entice buyers with the ever-tantalizing prospect
of getting something now without having to worry about how to pay for it until later. Suppose that you are
looking to buy a car priced at $35,000 and are oered a loan with a down payment of $5,000 and an APR of
6% over 60 months.
(a) (5) Calculate the monthly payment for this loan.
(b) (5) Now suppose that the dealer oers you no money down, no interest, and no payments for 90 days!”
and you naively interpret this to imply that the remaining payments are unchanged. In present value
terms, what price do you think that you are paying for the car?
(c) (5) Somewhat coming to your senses, you realize that your monthly payment will go up to oset the
missing initial payments, but still believe that you will see some savings because of the time value of
avoiding interest for three months. What monthly payment do you calculate and what do price do you
think you are paying?
(d) (5) Finally, you realize that if the dealer had any intention of oering you a discount, he would have let
you know how much you’d be saving, and that no interest” simply means that any unpaid interest is
added to the principal. What is your actual monthly payment?
2. (20) One of the shortcomings of the dividend discount model is that it assumes that the rm can grow at the
same rate indenitely, and projecting a company’s future prospects based only on a brief snapshot of its current
status can lead to wildly unrealistic estimates of its growth opportunities. Suppose that shares of Fly By Night
Inc. are currently priced at P0 = 100, compared to a book value of B0 = 20 per share, with forecasted earnings
of E1 = 8 and a scheduled dividend payment of D1 = 3 per share.
(a) (5) Using the constant growth model, estimate Fly By Night’s growth rate g and market capitalization
rate r. Do these numbers seem plausible to you?
(b) (5) Upon closer inspection, you observe that all of Fly By Night’s growth opportunities consist only of a
single investment project this year. After this year it cannot repeat this or undertake any other positive
NPV project, and must pay out all subsequent earnings to shareholders. Suppose you believe that you
are the only one who is aware of this, while all other investors are convinced that the stock will continue
growing at the same rate forever. What should the stock be priced at?
(c) (10) You now realize that all investors are well aware of Fly By Night’s limited growth opportunities, and
that this is already re
ected in its price. What is the correct discount rate?
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