Capital Budgeting Decisions UAA – ACCT 202 Principles of Managerial Accounting Dr. Fred Barbee

Time Value of Money UAA – ACCT 202 Principles of Managerial Accounting Dr. Fred Barbee

Future Value Today...Future... Add interest at interest rate “i” for “n” periods.

Principal Interest Rate Time Simple Interest

 Suppose you invest $100 at an interest rate of 10%. At the end of one year you would have $110.

Future Value of $1

FV of Single Cash Flow

Present Value

The Concept of Present Value Today...Future... Deduct interest at interest rate “i” for “n” periods.

The Formulas

Present Value Formula

Using the PV Formula  What is the present value of $1,000 received five years from now if your required rate of return is 12%.

Using the PV Formula

Present Value Factors

Compounding Illustrated Future Value Future Value $ for 5 12% compounded annually

Compounding Illustrated x $ $ $ $ $ $ $ $ $ Add interest for “5” periods at 12%.

Reverse Compounding Illustrated Present Value Present Value $1,000 for 5 12% compounded annually

Reverse Compounding Illustrated $ $ $ $ $ $ $ $ $1, $ Deduct interest for “5” periods at 12%.

Practice Exercise 1 Using Present Value Tables

Practice Exercise 1  What is the present value of $100 received at the end of five years if the required return is 10%? Exhibit 14C-3 Present Value of $1 $100 ? Years

Practice Exercise 2 Using Present Value Tables

Practice Exercise 2  What is the present value of $100 per year for five years if the required return is 10%? Exhibit 14C-4 Present Value of an Annuity of $1 in Arrears $100 ? Years $100 ?

Practice Exercise 3 Using Present Value Tables

Practice Exercise 3  Examine the table “Present Value of $1”  Explain why the numbers decrease as you move from left to right in a given row.

The numbers decrease from left to right in a given row because cash received in the future is worth less the higher your required rate of return. Remember the formula:

Practice Exercise 4  Examine the table “Present Value of $1”  Explain why the numbers decrease as you move from left to right in a given row.  Explain why the numbers decrease as you move from top to bottom in a given column.

The numbers decrease from top to bottom in a given column because cash received further in the future is less valuable today. Remember the formula:

Practice Exercise 5 Calculate Present Value

 Suppose you face the prospect of receiving $200 per year for the next 5 years plus an extra $500 payment at the end of 5 years.  Determine how much this prospect is worth today if the required rate of return is 10%. Practice Exercise 5

Cash FlowPV FactorAmount $ $ Total$1, N=5, i=10

Practice Exercise 6 Calculate Present Value

 Juanita Martinez is ready to retire and has a choice of three pension plans.  Plan A provides for an immediate cash payment of $100,000  Plan B provides for the payment of $10,000 per year for 10 years and $100,000 at the end of year 10.  Plan C will pay $20,000 per year for 8 years. Practice Exercise 6 8% Required Rate of Return

 Plan A:  Plan B:  Plan C: Cash FlowPV FactorTotal $10, $67, , ,300 $113,400 Cash FlowPV FactorTotal $20, $114,940 Cash FlowPV FactorTotal $100, $100,000