Example:

Directions: Page 110

Double your fun: Recalculate the interest rate using the back of the evelope calculation in your head and by using excel.

Rule of 72: DOUBLE YOUR FUN

You have been offered an investment that promises to double your money every 10 years. What is the approximate rate of return on the investment?From the Rule of 72, the rate of return is given approximately by 72/r% = 10, so the rate is approximately 72/10 = 7.2%. Verify that the exact answer is 7.177 percent.

Helpful Hints: >Formula, enter rate and number under the rate bar is the value of years so 10. > type and guess do not need to be filled out so do not worry about those

PVFVYEARSRATE

Directions: Page 110

Double your fun: Recalculate the interest rate using the back of the evelope calculation in your head and by using excel.

Rule of 72: DOUBLE YOUR FUN

You have been offered an investment that promises to double your money every 10 years. What is the approximate rate of return on the investment?From the Rule of 72, the rate of return is given approximately by 72/r% = 10, so the rate is approximately 72/10 = 7.2%. Verify that the exact answer is 7.177 percent.

100200

10??? Excel Rate

7.18%

Future Value: Multiple Cash Flows Example 5.1

You think you will be able to deposit $4,000 at the end of each of the next three years in a bank account paying 8 percent interest. You currently have $7,000 in the account.How much will you have in 3 years?How much in 4 years?

TIMELINE

200*(1.07) =

Total interest = $628.49-600=28.49 * (1.07)^2 = $719.56

$300.00

$214.00

4 5

-$300.00

$628.49

7%

-$100.00 -$200.00

100*(1.07)^2 = $114.49

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Future Value: Multiple Uneven Cash Flows Example 5.2 – Formulas & Time Line

TIMELINE

200*(1.07) =

Total interest = $628.49-600=28.49 * (1.07)^2 = $719.56

$300.00

$214.00

4 5

-$300.00

$628.49

7%

-$100.00 -$200.00

100*(1.07)^2 = $114.49

0 1 2 3

Future Value: Multiple Cash Flows Example 5.1

You think you will be able to deposit $4,000 at the end of each of the next three years in a bank account paying 8 percent interest. You currently have $7,000 in the account.How much will you have in 3 years?How much in 4 years?

TIMELINE

200*(1.07) =

Total interest = $628.49-600=28.49 * (1.07)^2 = $719.56

$300.00

$214.00

4 5

-$300.00

$628.49

7%

-$100.00 -$200.00

100*(1.07)^2 = $114.49

0 1 2 3

Future Value: Multiple Uneven Cash Flows Example 5.2 – Formulas & Time Line

TIMELINE

200*(1.07) =

Total interest = $628.49-600=28.49 * (1.07)^2 = $719.56

$300.00

$214.00

4 5

-$300.00

$628.49

7%

-$100.00 -$200.00

100*(1.07)^2 = $114.49

0 1 2 3

DEPOSITS AT END OF EACH OF YRS 1,2,3 $4,000.00RATE 8%CURRENT VALUE IN ACCOUNT $7,000.00EXCEL FV IN 3 YEARS $21,803.58EXCEL FV IN 4 YEARS $27,547.87

AMOUNT IN 3 YEARS W/O INVESTING $19,000AMOUNT IN 4 YEARS W/O INVESTING $23,000

End of Yr 1 Deposit $100End of Yr 2 Deposit $200.00End of Yr 3 Deposit $300.00Interest RateTotal Excel FV in 3 yearsTotal Excel FV in 5 years, if no additional amounts added5 yr check figure using formula version of calculations

Excel FV in 3 years Excel FV in 4 years

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Chapter 5 - Quick Quiz 1Rate 7%

Year Nper CF PV Formula1 1 100 $93.46 =-PV($C$2,A4,0,C4)2 2 200 $174.69 =-PV($C$2,A5,0,C5)3 3 200 $163.26 =-PV($C$2,A6,0,C6)4 4 300 $228.87 =-PV($C$2,A7,0,C7)5 5 300 $213.90 =-PV($C$2,A8,0,C8)

Total PV $874.17 =SUM(C4:C8)

Year Nper CF FV Year1 4 100 $131.08 =-FV($C$2,B12,0,C12)2 3 200 $245.01 =-FV($C$2,B13,0,C13)3 2 200 $228.98 =-FV($C$2,B14,0,C14)4 1 300 $321.00 =-FV($C$2,B15,0,C15)5 0 300 $300.00 =-FV($C$2,B16,0,C16)

Total FV $1,226.07 =SUM(C12:C16)

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Chapter 5 - Quick Quiz 1Rate 7%

Year Nper CF PV Formula1 1 100 $93.46 =-PV($C$2,A4,0,C4)2 2 200 $174.69 =-PV($C$2,A5,0,C5)3 3 200 $163.26 =-PV($C$2,A6,0,C6)4 4 300 $228.87 =-PV($C$2,A7,0,C7)5 5 300 $213.90 =-PV($C$2,A8,0,C8)

Total PV $874.17 =SUM(C4:C8)

Year Nper CF FV Year1 4 100 $131.08 =-FV($C$2,B12,0,C12)2 3 200 $245.01 =-FV($C$2,B13,0,C13)3 2 200 $228.98 =-FV($C$2,B14,0,C14)4 1 300 $321.00 =-FV($C$2,B15,0,C15)5 0 300 $300.00 =-FV($C$2,B16,0,C16)

Total FV $1,226.07 =SUM(C12:C16)

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A B C D E

Chapter 5 - Quick Quiz 1Rate 7%

Year Nper CF PV Formula1 1 100 $93.46 =-PV($C$2,A4,0,C4)2 2 200 $174.69 =-PV($C$2,A5,0,C5)3 3 200 $163.26 =-PV($C$2,A6,0,C6)4 4 300 $228.87 =-PV($C$2,A7,0,C7)5 5 300 $213.90 =-PV($C$2,A8,0,C8)

Total PV $874.17 =SUM(C4:C8)

Year Nper CF FV Year1 4 100 $131.08 =-FV($C$2,B12,0,C12)2 3 200 $245.01 =-FV($C$2,B13,0,C13)3 2 200 $228.98 =-FV($C$2,B14,0,C14)4 1 300 $321.00 =-FV($C$2,B15,0,C15)5 0 300 $300.00 =-FV($C$2,B16,0,C16)

Total FV $1,226.07 =SUM(C12:C16)

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Chapter 5 - Quick Quiz 1Rate 7%

Year Nper CF PV Formula1 1 100 $93.46 =-PV($C$2,A4,0,C4)2 2 200 $174.69 =-PV($C$2,A5,0,C5)3 3 200 $163.26 =-PV($C$2,A6,0,C6)4 4 300 $228.87 =-PV($C$2,A7,0,C7)5 5 300 $213.90 =-PV($C$2,A8,0,C8)

Total PV $874.17 =SUM(C4:C8)

Year Nper CF FV Year1 4 100 $131.08 =-FV($C$2,B12,0,C12)2 3 200 $245.01 =-FV($C$2,B13,0,C13)3 2 200 $228.98 =-FV($C$2,B14,0,C14)4 1 300 $321.00 =-FV($C$2,B15,0,C15)5 0 300 $300.00 =-FV($C$2,B16,0,C16)

Total FV $1,226.07 =SUM(C12:C16)

Treasury bills are excellent examples of pure discount loans. Principal amount is repaid at some future dateNo periodic interest paymentsIf a T-bill promises to repay $10,000 in 12 months and the market interest rate is 7 percent, how much will the bill sell for in the market?1 N; 10,000 FV; 7 I/Y; CPT PV = -9345.79=PV(.07,1,0,10000)

N 1FV 10,000R 7

-$1,250.00

Treasury bills are excellent examples of pure discount loans. Principal amount is repaid at some future dateNo periodic interest paymentsIf a T-bill promises to repay $10,000 in 12 months and the market interest rate is 7 percent, how much will the bill sell for in the market?1 N; 10,000 FV; 7 I/Y; CPT PV = -9345.79=PV(.07,1,0,10000)

Valuing a "Discount" BondPar or face value $1,000/00Coupon Rate 10%Annual Coupons $100.00Maturity in years 5YTM 11%What is the current market value of the bond? (pv)

A technique for determining the fair value of a particular bond. Bond valuation includes calculating the present value of the bond's future interest payments, also known as its cash flow, and the bond's value upon maturity, also known as its face value or par value.

A technique for determining the fair value of a particular bond. Bond valuation includes calculating the present value of the bond's future interest payments, also known as its cash flow, and the bond's value upon maturity, also known as its face value or par value.

PREFERRED STOCKPreferred stock (or preference stock) is an important example of a perpetuity. When a corporation sells preferred stock, the buyer is promised a fixed cash dividend every period (usually every quarter) forever. This dividend must be paid before any dividend can be paid to regular stockholders, hence the term preferred.Suppose the Fellini Co. wants to sell preferred stock at $100 per share. A very similar issue of preferred stock already outstanding has a price of $40 per share and offers a dividend of $1 every quarter. What dividend will Fellini have to offer if the preferred stock is going to sell?The issue that is already out has a present value of $40 and a cash flow of $1 every quarter forever. Since this is a perpetuity:

To be competitive, the new Fellini issue will also have to offer 2.5 percent per quarter; so, if the present value is to be $100, the dividend must be such that:

PREFERRED STOCKPreferred stock (or preference stock) is an important example of a perpetuity. When a corporation sells preferred stock, the buyer is promised a fixed cash dividend every period (usually every quarter) forever. This dividend must be paid before any dividend can be paid to regular stockholders, hence the term preferred.Suppose the Fellini Co. wants to sell preferred stock at $100 per share. A very similar issue of preferred stock already outstanding has a price of $40 per share and offers a dividend of $1 every quarter. What dividend will Fellini have to offer if the preferred stock is going to sell?The issue that is already out has a present value of $40 and a cash flow of $1 every quarter forever. Since this is a perpetuity:

To be competitive, the new Fellini issue will also have to offer 2.5 percent per quarter; so, if the present value is to be $100, the dividend must be such that:

Chapter 7: Problems 231 #1-7

Question 4

Input Area:

Divident Paid $ 3.65Dividend Growth Rate 5.10%Required Return 12%

Output Area Price $ 52.9

Problem 4: pg 232 Stock Values. Nofal Corporation will pay a $3.65 per share dividend next year. The company pledges to increase its dividend by 5.1 percent per year, indefinitely. If you require a return of 12 percent on your investment, how much will you pay for the company's stock today?

Problem 4: pg 232 Stock Values. Nofal Corporation will pay a $3.65 per share dividend next year. The company pledges to increase its dividend by 5.1 percent per year, indefinitely. If you require a return of 12 percent on your investment, how much will you pay for the company's stock today?

Slide 8-2

Capital Budgeting Project Formula BasedNPV

Year CF Required 12%Return Disc CF's

01 62,120.00 56,441.332 70,800.00 66,828.943 91,000.00 12,627.4`

Slide 8-6

Present Vale

OPEN: Estimating NPV- copy and paste page 240 section on estimating NPV including figure 8.1

OPEN: Estimating NPV- copy and paste page 240 section on estimating NPV including figure 8.1

Estimating Net Present ValueImagine we are thinking of starting a business to produce and sell a new product, say, organic fertilizer. We can estimate the start-up costs with reasonable accuracy because we know what we will need to buy to begin production. Would this be a good investment? Based on our discussion, you know that the answer depends on whether or not the value of the new business exceeds the cost of starting it. In other words, does this investment have a positive NPV?

This problem is much more difficult than our “fixer-upper” house example, because entire fertilizer companies are not routinely bought and sold in the marketplace; so it is essentially impossible to observe the market value of a similar investment. As a result, we must somehow estimate this value by other means.Based on our work in Chapters 4 and 5, you may be able to guess how we will go about estimating the value of our fertilizer business. We will first try to estimate the future cash flows we expect the new business to produce. We will then apply our basic discounted cash flow procedure to estimate the present value of those cash flows. Once we have this estimate, we then estimate NPV as the difference between the present value of the future cash flows and the cost of the investment. As we mentioned in Chapter 5, this procedure is often called discounted cash flow, or DCF, valuation.

To see how we might go about estimating NPV, suppose we believe the cash revenues from our fertilizer business will be $20,000 per year, assuming everything goes as expected. Cash costs (including taxes) will be $14,000 per year. We will wind down the business in eight years. The plant, property, and equipment will be worth $2,000 as salvage at that time. The project costs $30,000 to launch. We use a 15 percent discount rate on new projects such as this one. Is this a good investment? If there are 1,000 shares of stock outstanding, what will be the effect on the price per share from taking the investment?

From a purely mechanical perspective, we need to calculate the present value of the future cash flows at 15 percent. The net cash inflow will be $20,000 cash income less $14,000 in costs per year for eight years. These cash flows are illustrated in Figure 8.1. As Figure 8.1 suggests, we effectively have an eight-year annuity of $20,000 − 14,000 = $6,000 per year along with a single lump-sum inflow of $2,000 in eight years. Calculating the present value of the future cash flows thus comes down to the same type of problem we considered in Chapter 5. The total present value is:

Estimating Net Present ValueImagine we are thinking of starting a business to produce and sell a new product, say, organic fertilizer. We can estimate the start-up costs with reasonable accuracy because we know what we will need to buy to begin production. Would this be a good investment? Based on our discussion, you know that the answer depends on whether or not the value of the new business exceeds the cost of starting it. In other words, does this investment have a positive NPV?

This problem is much more difficult than our “fixer-upper” house example, because entire fertilizer companies are not routinely bought and sold in the marketplace; so it is essentially impossible to observe the market value of a similar investment. As a result, we must somehow estimate this value by other means.Based on our work in Chapters 4 and 5, you may be able to guess how we will go about estimating the value of our fertilizer business. We will first try to estimate the future cash flows we expect the new business to produce. We will then apply our basic discounted cash flow procedure to estimate the present value of those cash flows. Once we have this estimate, we then estimate NPV as the difference between the present value of the future cash flows and the cost of the investment. As we mentioned in Chapter 5, this procedure is often called discounted cash flow, or DCF, valuation.

To see how we might go about estimating NPV, suppose we believe the cash revenues from our fertilizer business will be $20,000 per year, assuming everything goes as expected. Cash costs (including taxes) will be $14,000 per year. We will wind down the business in eight years. The plant, property, and equipment will be worth $2,000 as salvage at that time. The project costs $30,000 to launch. We use a 15 percent discount rate on new projects such as this one. Is this a good investment? If there are 1,000 shares of stock outstanding, what will be the effect on the price per share from taking the investment?

From a purely mechanical perspective, we need to calculate the present value of the future cash flows at 15 percent. The net cash inflow will be $20,000 cash income less $14,000 in costs per year for eight years. These cash flows are illustrated in Figure 8.1. As Figure 8.1 suggests, we effectively have an eight-year annuity of $20,000 − 14,000 = $6,000 per year along with a single lump-sum inflow of $2,000 in eight years. Calculating the present value of the future cash flows thus comes down to the same type of problem we considered in Chapter 5. The total present value is:

Years Outflow Inflow r= 9%012345

1) Payback period =4 years because the cum CF at year 4=0 so we have recovered all that we have put in2)NPVCalculated NPV in ExcelAdd: Inniral cash outflowNPV

3)Excel calculated IPR4) Reject- we should reject this project because the NPV is negative and the IRR is negative5) The priary decsion rules should be NPV

6)The IRR

1) Payback period =4 years because the cum CF at year 4=0 so we have recovered all that we have put in