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Obviously, the package is not worth \$25 million because the payments are spread out over three years. The bonus is paid today, so it's worth \$2 million. The present values for the three subsequent salary payments are:

The package is worth a total of \$18.9721 million.

We will calculate the future values for each of the cash flows separately and then add them up. Notice that we treat the withdrawals as negative cash flows:

\$1,000 X 1.078 = \$2,000 X 1.076 = -\$1,500 X 1.075 = \$2,000 X 1.073 = -\$1,000 X 1.071 =

Total future value

\$1,000 X 1.7812 \$2,000 X 1.5007 \$1,500 X 1.4026 \$2,000 X 1.2250 \$1,000 X 1.0700

This value includes a small rounding error.

To calculate the present value, we could discount each cash flow back to the present or we could discount back a single year at a time. However, because we already know that the future value in eight years is \$3,995.91, the easy way to get the PV is just to discount this amount back eight years:

Present value = \$3,995.91/1.078 = \$3,995.91/1.7182 = \$2.325.64

Ross et al.: Fundamentals I III. Valuation of Future I 6. Discounted Cash Flow I I © The McGraw-Hill of Corporate Finance, Sixth Cash Flows Valuation Companies, 2002

Edition, Alternate Edition

CHAPTER 6 Discounted Cash Flow Valuation

We again ignore a small rounding error. For practice, you can verify that this is what you get if you discount each cash flow back separately.

6.3 The most you would be willing to pay is the present value of \$12,000 per year for 10 years at a 15 percent discount rate. The cash flows here are in ordinary annuity form, so the relevant present value factor is:

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

The present value of the 10 cash flows is thus:

This is the most you would pay.

6.4 A rate of 8 percent APR with monthly payments is actually 8%/12 = .67% per month. The EAR is thus:

6.5 We first need to calculate the annual payment. With a present value of \$10,000, an interest rate of 14 percent, and a term of five years, the payment can be determined from:

\$10,000 = Payment X {[1 - (1/1.145)]/.14} = Payment X 3.4331

Therefore, the payment is \$10,000/3.4331 = \$2,912.84 (actually, it's \$2,912.8355; this will create some small rounding errors in the following schedule). We can now prepare the amortization schedule as follows:

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