Capital Budgeting Decisions UAA – ACCT 202 Principles of Managerial

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

Simple Interest Interest Rate Principal 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 f (1 i ) n f n P(1 i ) n

FV of Single Cash Flow f n P (1 i ) n f n 100(1.10) 2 100(1.210) 121.00

Present Value

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

The Formulas f (1 i ) P (1 i ) n n

Present Value Formula P (1 i ) n 1 n (1 i )

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 F 1,000 P n 5 (1 i ) (1.12) 1,000 P 567.43 1.7623417

Present Value Factors 1 1 P n 5 (1 i ) (1.12) 1 .5674 1.7623417

1 1 P n 5 (1 i ) (1.12) 1 .5674 1.7623417

Compounding Illustrated Future Value 567.43 for 5 years @ 12% compounded annually

Compounding Illustrated 1 2 3 4 5 567.43 x 1.12 ----------- 635.52 635.52 x 1.12 ----------- 711.78 711.78 x 1.12 ----------- 797.19 797.19 x 1.12 ----------- 893.65 893.65 x 1.12 ----------- 1000.88 Add interest for “5” periods at 12%.

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

Reverse Compounding Illustrated 1 2 3 4 5 635.53 -----------1.12 567.44 711.79 -----------1.12 635.53 797.20 -----------1.12 711.79 892.86 -----------1.12 797.20 1,000.00 -----------1.12 892.86 Deduct interest for “5” periods at 12%.

Practice Exercise 1 Using Present Tables Value

Practice Exercise 1 What is the present value of 100 received at the end of five years if the required return is 10%? 1 ? 2 3 Years Exhibit 14C-3 4 5 100

Practice Exercise 2 Using Present Tables Value

Practice Exercise 2 What is the present value of 100 per year for five years if the required return is 10%? 1 ? 100 2 100 3 4 Years 100 100 5 100 100 Exhibit 14C-4 Present Value of an Annuity of 1 in Arrears

Practice Exercise 3 Using Present Tables Value

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: 1 P n (1 i )

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: 1 P n (1 i )

Practice Exercise 5 Calculate Present Value

Practice Exercise 5 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%.

N 5, i 10 Cash Flow 200 500 Total PV Factor 3.791 .621 Amount 758.20 310.50 1,068.70 N 5, i 10

Practice Exercise 6 Calculate Present Value

Practice Exercise 6 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. 8% Required Rate of Return

Plan A: Cash Flow PV Factor Total 100,000 1.000 100,000 Cash Flow PV Factor Total 10,000 100,000 6.710 .463 67,100 46,300 Plan B: 113,400 Plan C: Cash Flow PV Factor Total 20,000 5.747 114,940