Management 3Quantitative Methods

The Time Value of MoneyA Practical Conclusion

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?

#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).

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.

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.

The Present Value of Leasing

Down-payment + PV(payments)

$ 5,000 + PV($ 400, 36, 7% /12)

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 ]

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

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

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

The Present Value of Purchasing

Purchase price less PV(Resale value)

$ 35,000 - PV($ 22,000, 36, 7% /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

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

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

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?