Ross et al.: Fundamentals of Corporate Finance, Sixth Edition, Alternate Edition

III. Valuation of Future Cash Flows

6. Discounted Cash Flow Valuation

© The McGraw-Hill Companies, 2002

PART THREE Valuation of Future Cash Flows

The present value is the amount we finance. With a 10 percent down payment, we will be borrowing 90 percent of $21,000, or $18,900. So, to find the payment, we need to solve for C in the following:

$18,900 = C X Annuity present value factor = C X 47.2925

Rearranging things a bit, we have:

C = $18,900 X (1/47.2925) = $18,900 X .02115 = $399.64

Your payment is just under $400 per month.

The actual interest rate on this loan is 1.25 percent per month. Based on our work in the chapter, we can calculate the effective annual rate as:

The effective rate is about one point higher than the quoted rate.

To determine the loan balance in two years, we could amortize the loan to see what the balance is at that time. This would be fairly tedious to do by hand. Using the information already determined in this problem, we can instead simply calculate the present value of the remaining payments. After two years, we have made 24 payments, so there are 72 - 24 = 48 payments left. What is the present value of 48 monthly payments of $399.64 at 1.25 percent per month? The relevant annuity factor is:

Annuity present value factor = (1 - Present value factor)/r

= [1 - (1/1.012548)]/.0125 = [1 - (1/1.8154)]/.0125 = (1 - .5509)/.0125 = 35.9315

The present value is thus:

Present value = $399.64 X 35.9315 = $14,359.66 You will owe about $14,360 on the loan in two years.

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