# CH7 - Chapter 7 Investment Decision Rules Note All problems in this chapter are available in MyFinanceLab An asterisk indicates problems with a

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Chapter 7 Investment Decision Rules Note: All problems in this chapter are available in MyFinanceLab. An asterisk (*) indicates problems with a higher level of difficulty. 1. Plan: We can compute the NPV of the project using Eq. (7.2). The cash flows are an immediate \$8 million outflow followed by an annuity inflow of \$5 million per year for 3 years and a discount rate of 8%. Execute: a. NPV 3 51 8 1 \$4.885 million. 0.08 (1.08) ⎛⎞ =− + = ⎜⎟ ⎝⎠ The NPV rule dictates that you should accept this contract. b. The value of the firm will increase by \$4.885 million. Evaluate: The NPV rule indicates that by making the investment, your factory will increase the value of the firm today by \$4.885 million, so you should undertake the project. 2. Plan: We can compute the NPV of the project using Eq. (7.2). The cash flows are an immediate \$100 million outflow followed by an annuity inflow of \$30 million and a discount rate of 8%. We can compute the IRR using a financial calculator or spreadsheet or by setting the NPV equal to zero and solving for r. After we find the IRR we can compute the maximum deviation allowable in the cost of capital estimate to leave the decision unchanged by subtracting the cost of capital from the IRR. Execute: Timeline: 0 1 2 3 4 –100 30 30 30 13 0 NPV 100 1.08 0.08 \$247.22 million =− =

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70 Berk/DeMarzo/Harford • Fundamentals of Corporate Finance The IRR solves 13 0 100 0 24.16%. 1 r rr ⎛⎞ −=⇒ = ⎜⎟ + ⎝⎠ So, the cost of capital can be underestimated by 16.16% without changing the decision. Evaluate: The NPV rule indicates that by making the investment, your factory will increase the value of the firm today by \$4.885 million, so you should undertake the project. The IRR is the discount rate that sets the net present value of the cash flows equal to zero. The difference between the cost of capital and the IRR tells us the amount of estimation error in the cost of capital estimate that can exist without altering the original decision. 3. Plan: We can compute the NPV of agreeing to write the book ignoring any royalty payments using Eq. (7.2). The cash flows are an immediate \$10 million outflow followed by an annuity inflow of 8 million per year for 3 years and a discount rate of 10%. We can compute the NPV of the book with the royalty payments by first computing the present value of the royalties at year three. Once we compute the royalties at year 3 we can compute the present value of the royalties today and add that number to the NPV of agreeing to write the book ignoring any royalty payments. Execute: a. Timeline: 0 1 2 3 10 –8 –8 –8 3 81 NPV 10 1 0.1 (1.1) \$9.895 million =− b. Timeline: 0 1 2 3 4 5 6 10 –8 –8 –8 5 5(1 – 0.3) 5(1 – 03) 2 First calculate the PV of the royalties at year 3. The royalties are a declining perpetuity: = −− = = 5 5 PV 0.1 ( 0.3) 5 0.4 12.5 million
Chapter 7 Investment Decision Rules 71 so the value today is = = royalties 3 12.5 PV (1.1) 9.391.

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## This note was uploaded on 02/09/2010 for the course FINA 3001 taught by Professor Molly during the Spring '10 term at University of Minnesota Duluth.

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CH7 - Chapter 7 Investment Decision Rules Note All problems in this chapter are available in MyFinanceLab An asterisk indicates problems with a

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