# BBA3301 Columbia Southern University Financial Management Questions 1. What is the future value of $500 a year for 9 years compounded annually at 10%? What

BBA3301 Columbia Southern University Financial Management Questions 1. What is the future value of $500 a year for 9 years compounded annually at 10%? What is the future value of $900 for nine years compounded annually at 10%?

2. You have just introduced “must have” headphones for the iPod. Sales of the product are expected to be 20,000 units this year and are expected to increase by 16% annually in the future. What are the expected sales in each of the next three years? If the 20,000 units were expected to increase by 18% a year, what are the expected sales next year for this product?

3. What is the present value of a perpetual stream of cash flow that pays $80,000 at the end of one year and grows at a rate of 5% indefinitely? The rate of interest used to discount the cash flows is 10%. What is the present value of the growing perpetuity?

4. What is the present value of a $650 perpetuity discounted back to the present at 10%? What is the present value of the perpetuity?

5. How much do you have to deposit today so that, beginning 11 years from now, you can withdraw $9,000 a year for the next 8 years (periods 11 through 18) plus an additional amount of $18,000 in the last year (period 18)? Assume an interest rate of 6%. UNIT III STUDY GUIDE

Time Value of Money

Course Learning Outcomes for Unit III

Upon completion of this unit, students should be able to:

3. Apply time value of money techniques to various pricing (valuation) and budgeting problems.

3.1 Explain compounding and discounting to calculate future and present values.

3.2 Determine annuities from a single sum.

3.3 Demonstrate how to apply time value of money concepts to complex cash streams.

Reading Assignment

Chapter 5:

Time Value of Money – The Basics, pp. 126-150

Chapter 6:

The Time Value of Money – Annuities and Other Topics, pp. 156-179

Unit Lesson

Creating value hinges on timing of cash flows. In finance, understanding time value of money is critical to

value creation because cash flows resolve when an organization can create value. Discounting and

compounding are key ingredients for looking at how time affects value creation. Take the case of Brite

Phuteur, who has started a career and needs a new car.

Phuteur has looked at different cars and has a good idea what he wants to buy. After looking at several

dealerships, Phuteur noted pricing did not necessarily line up with his ideas about paying a fair price for the

value he thought he would receive. Phuteur found dealerships varied their pricing on identical cars.

Despite not understanding price variances between dealers, Phuteur set aside money from his pay each pay

period for a good down payment. Interest rates on savings at his local bank amounted to roughly 2%. If

Phuteur set aside $100 a month at the end of the year, he wanted to know how much he would have after

earning interest. This scenario is Phuteur’s first experience where he needed to understand compounding.

Phuteur asked his banker, Cash Kownter, for help. Kownter explained that compound interest adds interest

earned to principal used when calculating future interest. For example, Phuteur started by putting $1,000 in

savings in his bank, which pays 2% interest a year compounded monthly. Since Phuteur’s local bank figures

interest monthly, his monthly interest rate is just .16667% but compounds each of the 12 months during the

year. Kownter showed Phuteur a formula to calculate the amount he would have by year’s end. A general

future value formula solves this calculation as follows (Titman, Keown, & Martin, 2014, p. 130):

FV = PV(1 + i)n, where FV equals future value, PV equals present value, i equals an interest rate, and n is the

number of periods. Applying this equation, Phuteur can substitute his numbers into the formula as follows:

FV = $1,000(1 + .16667%)12

Thus,

FV = $1,000(1.0016667)12

FV = $1,020.18

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Phuteur observed he has more than simple interest, which simply adds 2% to UNIT

$1,000,

which only

accounts for

x STUDY

GUIDE

$1,020.00 of the $1,020.18 earned. Kownter showed Phuteur how to solve this

problem in Excel as follows:

Title

Despite compound interest exceeding simple interest, Phuteur noted the amount earned is not much more

than he put in his savings to start. Phuteur asked Kownter what he would earn if he left the money in the bank

for five years. Kownter changed his calculation as follows:

FV = $1,000(1 + .16667%)12

Thus,

FV = $1,000(1.0016667)12*5

FV = $1,105.08

Again Kownter made the calculation in Excel as follows:

This time, Phuteur noted more interest earned by comparing $1,105.08 with $1,020.00 principal plus simple

interest. Phuteur earned $85.08 in interest compared with just $.18 for just a year. Phuteur inferred the more

periods the greater the interest earned. Kownter explained compounding calculates interest on interest each

period. Instead of simply computing interest on $1,000.00, compounding recalculates interest each period (in

this case 60 periods), which grows interest earned.

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Although compound interest showed a nice improvement in interest earned, Phuteur

what he could

UNIT x wondered

STUDY GUIDE

earn if he also saved $100 a month. Kownter told Phuteur, “Now you are talking

about an annuity.” Kownter

Title

explained an annuity is a series of equal payments for a specific time. Again, Kownter showed Phuteur how

to calculate compound interest as follows:

FVn = PMT(1 + i)n-1 + PMT(1 + i)n-2…+ PMT(1 + i)1 + PMT(1 + i)0

Alternatively, one can apply a future value annuity factor (FVA) to an annuity payment (PMT) using the

formula as follows:

(1+ ) −1

FVA = = [

]

Applying this factor to the payment results in the following formula:

(1+ ) −1

FVn = PMT = [

]

Using $100 a month savings deposit Kownter filled in this formula as follows:

FVA = [(1.001667)60/.001667]

FVA = 63.04734

FV60 = 100(63.04734)

FV60 = 6304.74

Alternatively, Kownter again substitutes in Excel as follows:

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With both an initial deposit of $1,000 in savings and an added $100 a month, the

result

is as follows:

UNIT

x STUDY

GUIDE

Title

Phuteur felt better about saving for a down payment after calculating what he would have. Interest earned

over five years is $409.82 ($105.08 plus $304.74) plus principal of $7,000 ($1,000 plus $6,000 or 60

payments times $100). Compound interest allowed Phuteur to grow his money by adding interest on interest

earned.

Besides resolving he could have a large down payment, Phuteur still needed to know what he would have to

pay monthly on a car. Phuteur looked at several cars on the Internet and settled on a car that sells for

$25,000. Phuteur figured he would have a balance of $17,509.81 ($25,000 minus $7,409.81) he would need

to finance. Phuteur asked at the bank what rate he would have to pay on a car loan. The bank gave Phuteur a

rate of 4.5%. Phuteur asked Kownter how he could calculate his payments. Kownter responded by saying it

might benefit Phuteur to prepare an amortization table to break down his payments between principal and

interest.

Kownter explained first Phuteur would need to calculate his payment. Kownter showed Phuteur how to

calculate his payment in Excel as follows:

BBA 3301, Financial Management

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Kownter assumed a normal five year loan and interest would compound monthly.

a variant

of the

UNITUsing

x STUDY

GUIDE

formula used to calculate the future value (FV) Kownter calculated Phuteur’s payment

Title as follows:

PVn = PMT = [

(1+

1

×

)

/

]

Substituting the above information Kownter solved the equation for the payment.

$17,509.81 = PMT[

1

045 5×12

(1+.

)

12

.045/12

]

$17,509.81 = PMT(53.63938)

PMT = $17,590.81/$53.64197

PMT = 327.93

Kownter prepared the following amortization table in Excel:

Payments

Original balance

Payment

Payment

Payment

Payment

Payment

1

2

3

4

5

Payment

Payment

Payment

Payment

Payment

Payment

55

56

57

58

59

60

327.93

327.93

327.93

327.93

327.93

Principal

Interest Reduction

65.96

64.98

63.99

63.00

62.01

261.97

262.95

263.94

264.93

265.92

327.93

7.28

320.65

327.93

6.08

321.85

327.93

4.87

323.06

327.93

3.66

324.27

327.93

2.45

325.49

327.93

1.23

326.71

19,676.06 2,085.87 17,590.19

Principal

$17,590.19

17,328.22

17,065.27

16,801.33

16,536.40

16,270.47

1,621.39

1,299.53

976.47

652.20

326.71

0.00

With Kownter’s table, Phuteur had an idea what interest and principal he would have to pay each month.

Payments for 60 months is an annuity because they are equal for a set time. Phuteur noticed early payments

had higher interest as part of payments, but later payments included more principal.

Because Kownter based payments on suggested retail price as suggested by the manufacturer, Phuteur

wondered if he could buy his car for less. Phuteur began looking at current prices to see what different

dealers offer. In today’s prices, a similar car sold for $21,500. Kownter helped Phuteur explained to Kownter

how discounting the payments based on inflation rate of 2% might give him a better idea of the value today.

Kownter first discounted the $7,409.19 down payment to express it in today’s dollars as follows:

BBA 3301, Financial Management

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UNIT x STUDY GUIDE

Title

Kownter also solves for present value using the following formula:

PV = FVx1/(1 + i)n or PV(1+i)-n

In Phuteur’s case substituting the values looks like the following:

PV = $7,409.19 x 1/(1 + .00166667)60

PV = $7,409.19 x 1/(1.01004)

PV = $7,409.19 x .90491

PV = $6,704.67

Next, Kownter calculated the present value of the payments Phuteur would have to make as follows:

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Combining the down payment and interest payments Kownter found the valueUNIT

todayx is

as follows:

STUDY

GUIDE

Title

Comparing the $25,413.85 with what Phuteur projected five years from now it appears $25,000 is a fair price.

Remember, however, Phuteur found one dealer selling the car he wanted for $21,500 at today’s prices. This

price suggests the $25,000 price in five years is too high, and Phuteur might well do better than the price

Kownter used to calculate future payments. Assuming $25,000 is more than Phuteur would have to pay in five

years, he likely will have lower payments based on dealer price variation. This revelation excited Phuteur

about saving for his new car.

In summary, compounding cash flows results in future values, while discounting cash flows, brings future

cash flows back to today’s dollars for the sake of comparison. Some cash streams are complex and have

both—a single sum plus an annuity, or series of equal payments for a set time. Phuteur benefited from doing

his homework and reaching out to his friend at the bank. Phuteur did a good job with his homework and is

now ready to buy a car when the time comes.

Reference

Titman, S., Keown, A. J., & Martin J. D. (2014). Financial management: Principles and applications (12th ed.).

Upper Saddle River, NJ: Pearson.

Suggested Reading

In order to access the resource below, you must first log into the myCSU Student Portal and access the

ABI/Inform database within the CSU Online Library.

This article further explores the concept of time value of money.

Benshoof, M. (2005). The time value of money. Professional Builder, 70(3), 74.

Learning Activities (Non-Graded)

The following video tutorials will help you with the concepts covered in the textbook. You are strongly

encouraged to watch these videos prior to starting the unit assessment.

Click here for CheckPoint 5.2 Calculating Future Value

Click here for CheckPoint 5.3 Calculating Future Values Using Non-Annual Compounding Periods

Click here for CheckPoint 5.4 Calculating Present Value

Click here for CheckPoint 5.5 Solving for n

Click here for CheckPoint 5.6 Solving for i

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Click here for CheckPoint 5.7 Calculating EAR

UNIT x STUDY GUIDE

Click here for Checkpoint 6.1 Solving for an Ordinary Annuity Payment

Title

Click here for Checkpoint 6.2 Present Value an Ordinary Annuity

Click here for Checkpoint 6.3 Determining the Outstanding Balance on a Loan

Click here for Checkpoint 6.4 Calculation of a Level Perpetuity

Click here for Checkpoint 6.5 Calculation of a Growing Perpetuity

Click here for Checkpoint 6.6 Calculation of a Complex Cash Flow Stream

Non-graded Learning Activities are provided to aid students in their course of study. You do not have to

submit them. If you have questions, contact your instructor for further guidance and information.

BBA 3301, Financial Management

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