1. Management 3 Quantitative Methods The Time Value of Money A Practical Conclusion

2. Five Fundamental Practical Problems 1.Do I make “this” Investment today, i.e. does it offer a good return? 2.“When” do I take my Pension? 3.“What” will my payments be on this Loan 4.“When and how much” do I need to save for something – a house, a car, or my retirement? 5.Should I Lease or Buy this equipment?

3. #5 Should I Lease or Buy the equipment? If you “buy” you pay the full purchase price now, i.e “PV” and you own the equipment including all the rights that go with that. If you “lease” you make a modest down- payment followed by regular lease payments for a few years, then you return the equipment (because you don’t own it).

4. The Decision Based on analysis. Analysis is a systematic comparison of two, or more, alternatives. For us this means “cost”, the least cost. Systematic means on the same basis. For us the basis is present value.

5. Lease versus Buy? The Lease Terms are $ 5,000 down and $ 400 per month for 36 months. Purchase: $35,000. Resale? Estimated to be $22,000 in 3 years.

6. The Present Value of Leasing Down-payment + PV(payments) $ 5,000 + PV($ 400, 36, 7% /12)

7. The Present Value of Leasing Down-payment + PV(payments) $ 5,000 + PV($ 400, 36, 7% /12) $ 5,000 + $ 400 x [[1-(1.005833) -36 ] /0.005833 ]

8. The Present Value of Leasing Down-payment + PV(payments) $ 5,000 + PV(A=$ 400, 36, 7% /12) $ 5,000 + $ 400 x [[1-(1.005833) -36 ] /0.005833 ] $ 5,000 + $ 400 x (1- 0.811079) / 0.005833

9. The Present Value of Leasing Down-payment + PV(payments) $ 5,000 + PV(=$ 400, 36, 7% /12) $ 5,000 + $ 400 x [[1-(1.005833) -36 ] /0.005833 ] $ 5,000 + $ 400 x (1- 0.811079) / 0.005833 $ 5,000 + $ 400 x (1 - 0.18921) / 0.005833

10. The Present Value of Leasing Down-payment + PV(payments) $ 5,000 + PV(A= $ 400, 36, 7% /12) $ 5,000 + $ 400 x [[1-(1.005833) -36 ] /0.005833 ] $ 5,000 + $ 400 x (1- 0.811079) / 0.005833 $ 5,000 + $ 400 x (1 - 0.18921) / 0.005833 $ 5,000 + $ 400 x 32.38 $ 5,000 + $ 12,955 $ 17,955

11. The Present Value of Purchasing Purchase price less PV(Resale value) $ 35,000 - PV($ 22,000, 36, 7% /12)

12. The Present Value of Purchasing Purchase price less PV(Resale value) $ 35,000 - PV($ 22,000, 36, 7% /12) $ 35,000 - $ 22,000 x (1.005833) -36

13. The Present Value of Purchasing Purchase price less PV(Resale value) $ 35,000 - PV($ 22,000, 36, 7% /12) $ 35,000 - $ 22,000 x (1.005833) -36 $ 35,000 - $ 22,000 x 0.811079

14. The Present Value of Purchasing Purchase price less PV(Resale value) $ 35,000 - PV($ 22,000, 36, 7% /12) $ 35,000 - $ 22,000 x (1.005833) -36 $ 35,000 - $ 22,000 x 0.811079 $ 35,000 - $ 17,844 $ 17,156

15. The Present Value of Purchasing is less than the Present Value of Leasing Is there a purely conceptual reason why this ought to be so?