Pohgf
6/27/2010
Choosing Between Mutually Exclusive Projects
Two Sticky Situations:
1. Choice between long- and short-lived projects: Should the firm save money today by investing in shorter-lived projects (such as less durable machinery)? ⇒ This is a job for Equivalent Annual Annuities 2. Investment timing and replacement decisions: ⇒ Should you invest in a new computer system today or invest in a new computer system next year? ⇒ When should existing machinery be replaced?
Equivalent Annual Annuities
Example: • You own a hotel in Bend. The location is killer but the place is run down. • Remodeling will cost you $100,000 but generate cash flows of $50,000 per year for the next five years. • Rebuilding will cost you $300,000 but generate cash flows of $66,000 per year for the next ten years. • Your opportunity cost of capital is 10% Cash Flows:
Time Remodel Rebuilding
0 1 2 3 4 5 6 7 8 9 10 -100 +50 +50 +50 +50 +50 -300 +66 +66 +66 +66 +66 +66 +66 +66 +66 +66
Equivalent Annual Annuities (cont.)
What is the NPV of remodeling your hotel?
Equivalent Annual Annuities (cont.)
What is the NPV of rebuilding your hotel?
50,000 50,000 50,000 50,000 50,000 NPV= −100,000 + + + + + 1.10 1.102 1.103 1.10 4 1.105 = 89,550
What is the IRR of remodeling your hotel?
NPV= −300,000 + = 105,570
66,000 66,000 66,000 66,000 + + + ...+ 1.10 1.10 2 1.103 1.1010
What is the IRR of rebuilding your hotel?
100,000 =
50,000 50,000 50,000 50,000 50,000 + + + + (1+ IRR) (1+ IRR) 2 (1+ IRR) 3 (1+ IRR) 4 (1+ IRR) 5 IRR = 40%
300,000 =
66,000 66,000 66,000 66,000 + + + ...+ (1+ IRR) (1+ IRR) 2 (1+ IRR) 3 (1+ IRR)10 IRR = 17%
Note: you could use Excel or a financial calculator to find IRR but I will not ask you to solve for it.
Equivalent Annual Annuities (cont.)
Summary: • Remodeling has an NPV of $89,550 and an IRR of 40% • Rebuilding has an NPV of $105,570 and an IRR of 17% • Therefore, IRR says remodel while NPV says rebuild. (Normally we would use
Choosing Between Mutually Exclusive Projects
Two Sticky Situations:
1. Choice between long- and short-lived projects: Should the firm save money today by investing in shorter-lived projects (such as less durable machinery)? ⇒ This is a job for Equivalent Annual Annuities 2. Investment timing and replacement decisions: ⇒ Should you invest in a new computer system today or invest in a new computer system next year? ⇒ When should existing machinery be replaced?
Equivalent Annual Annuities
Example: • You own a hotel in Bend. The location is killer but the place is run down. • Remodeling will cost you $100,000 but generate cash flows of $50,000 per year for the next five years. • Rebuilding will cost you $300,000 but generate cash flows of $66,000 per year for the next ten years. • Your opportunity cost of capital is 10% Cash Flows:
Time Remodel Rebuilding
0 1 2 3 4 5 6 7 8 9 10 -100 +50 +50 +50 +50 +50 -300 +66 +66 +66 +66 +66 +66 +66 +66 +66 +66
Equivalent Annual Annuities (cont.)
What is the NPV of remodeling your hotel?
Equivalent Annual Annuities (cont.)
What is the NPV of rebuilding your hotel?
50,000 50,000 50,000 50,000 50,000 NPV= −100,000 + + + + + 1.10 1.102 1.103 1.10 4 1.105 = 89,550
What is the IRR of remodeling your hotel?
NPV= −300,000 + = 105,570
66,000 66,000 66,000 66,000 + + + ...+ 1.10 1.10 2 1.103 1.1010
What is the IRR of rebuilding your hotel?
100,000 =
50,000 50,000 50,000 50,000 50,000 + + + + (1+ IRR) (1+ IRR) 2 (1+ IRR) 3 (1+ IRR) 4 (1+ IRR) 5 IRR = 40%
300,000 =
66,000 66,000 66,000 66,000 + + + ...+ (1+ IRR) (1+ IRR) 2 (1+ IRR) 3 (1+ IRR)10 IRR = 17%
Note: you could use Excel or a financial calculator to find IRR but I will not ask you to solve for it.
Equivalent Annual Annuities (cont.)
Summary: • Remodeling has an NPV of $89,550 and an IRR of 40% • Rebuilding has an NPV of $105,570 and an IRR of 17% • Therefore, IRR says remodel while NPV says rebuild. (Normally we would use