chapter04 xlssol updated (1)

8/3/2019 Chapter04 XlsSol Updated (1)

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Problems

Problem 4-12

bl 4 13


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Problem 4-12

Interest Rate: 3.50%

0 1

Cash flow: $10,000.00 $20,000

Present Value

Using formulas 55,390.33Using Excel functions 55,390.33

You have just receiveda windfall from an investmentyou made in a friend

be paying you $10,000 at the end of this year, $20,000 at the end of the f

$30,000 at the end of the year after that (three years fromtoday). The intereyear.

Year

a. What is the present value of your windfall?


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Problem 4-13

Interest Rate: 5.00%

0 1

Cash flow: $1,000.00 $1,000.0

Future value

You have a loan outstanding. It requires making three annual payments at

next three years of $1000 each. Your bank has offered to allow you to skip m

two payments in lieu of making one large payment at the end of the loan

years. If the interest rate on the loan is 5%, what final payment will the bank

make so that it is indifferent between the two forms of payment?

Year


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Problem 4-14

Interest rate 6.00%

NPV (2,609.36)

0 1 2 3 4 5 6 7

Cash flow: ($10,000.00) $500.00 $1,500.00 $0.00 $0.00 $0.00 $0.00 $0.00

Discounted value (10,000.00) 471.70 1,334.99 0.00 0.00 0.00 0.00 0.00

NPV (2,609.36)

At an interest rate of 6.00% the NPV is (2,609.36) so reject the project.

At an interest rate of 2.00% the NPV is 135.43 so accept the project.

The relationship is illustrated by the chart below:

Year

You have been offered a unique investment opportunity. If you invest $10,000 today, you will receive $500 one year from no

$10,000 ten years from now.

a. What is the NPV of the opportunity if the interest rate is 6% per year? Should you take the opportunity?

b. What is the NPV of the opportunity if the interest rate is 2% per year? Should you take it now?

2 000 00

3,000.00

NPV


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Problem 4-15

Interest rate 2.00%

NPV using Excel function 5,729.69

0 1

Cash flow: ($1,000.00) $4,000.00 ($1,000.00

Discounted cash flow (1,000.00) 3,921.57 (961.17

NPV the "long" way 5,729.69

Marian Plunket owns her own business and is considering an inv

undertakes the investment, it will pay $4000 at the end of each of the n

The opportunity requires an initial investment of $1000 plus an additiat the end of the second year of $5000. What is the NPV of this op

interest rate is 2% per year? Should Marian take it?

Year


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Problem 4-23

PMT $1,000.00Rate 3.00%

Years 18

FV $23,414.44

Your grandmother has been putting $1000 into a saving

every birthday since your first (that is, when you turaccount pays an interest rate of 3%. How much money w

account on your 18th birthday immediately after your g

makes the deposit on that birthday?


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Problem 4-24

a. What is todays value of the bequest?

First Payment $1,000.00

Growth Rate 8.00%

Interest Rate 12.00%

Value $25,000.00

A rich relative has bequeathed you a growing perpetuity. The fir

occur in a year and will be $1000. Each year after that, you will re

on the anniversary of the last payment that is 8% larger than the las

pattern of payments will go on forever. If the interest rate is 12% pe

b. What is the value of the bequest immediately after the first paym


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Problem 4-27

Payment $10,000.00

Years 13

Value $130,000.00

Your oldest daughter is about to start kindergarten at a private school. T

per year, payable at the beginning of the school year. You expect to kee

private school through high school. You expect tuition to increase at a raover the 13 years of her schooling. What is the present value of the tuiti

interest rate is 5% per year?

Look at 4-28 for an explanation. In this problem, the difference is that

occurs today. (If you want to look at this like 4-28, change that sheet ju

can see the balance go to zero.)

This is true only because the growth rate equals the interest rate.


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Discount rate 5.00%

Number of payments 20

Payment amount $5,000.00

PV = 95,238.10

Growth Rate= 5.00%

Here's why:

- amount paid

which is equal to the payment amo

number of periods discounted for o

In order to have enough to make all her payments

would have to deposit that much now. Here's how

depleted:

A rich aunt has promised you $5000 one year from today. In addition, each year

promised you a payment (on the anniversary of the last payment) that is 5% larg

payment. She will continue to show this generosity for 20 years, giving a total of

the interest rate is 5%, what is her promise worth today?

Problem 4-28


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Starting growth rate 30.00%

Number of years of high growth 5

Later growth rate 2.00%

Discount rate 8.00%

0 1 2 3 4

Cash flow $1,000,000.00 $1,300,000.00 $1,690,000.00 $2,197,000.00 $2,856,100.00

PV(cash flow) $1,203,703.70 $1,448,902.61 $1,744,049.43 $2,099,318.76

PV(infinite cash flows)

Value of company 51,981,214.36

Year

Problem 4-29

You are running a hot Internet company. Analysts predict that its earnings will grow at 30% per year for the next five years. After th

growth is expected to slow to 2% per year and continue at that level forever. Your company has just announced earnings of $1,000,0

future earnings if the interest rate is 8%? (Assume all cash flows occur at the end of the year.)


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$100

3%20

6.00%

a. How much money will you need to deposit into the account today?

PV of

growing

annuity 1,456.15$

Beginning balance +interest

- amount paid out

end of year ending balance

moun

princip

that pa

1 100.00 1,456.15 87.37 100.00 1,443.52

2 103.00 1,443.52 86.61 103.00 1,427.13

3 106.09 1,427.13 85.63 106.09 1,406.67

4 109.27 1,406.67 84.40 109.27 1,381.80

5 112.55 1,381.80 82.91 112.55 1,352.16

Discount rate

b. Using an Excel spreadsheet, show explicitly that you can deposit this amount of money into the accwithdraw what your brother has promised, leaving the account with nothing after the last withdrawal.

Problem 4-30

Your brother has offered to give you $100, starting next year, and after that growing at 3% for the next 20 ye

calculate the value of this offer by calculating how much money you would need to deposit in the local bank

generate the same cash flows as he is offering you. Your local bank will guarantee a 6% annual interest rate

in the account.

Initial payment

Annual growth rateNumber of periods


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Problem 4-32

Cost of House $350,000.00

Down Payment $50,000.00

Number of Years 30

Interest Rate 7.00%

Annual Payment

Amount (24,175.92)

You are thinking of purchasing a house. The house costs $350,

$50,000 in cash that you can use as a down payment on the hous

to borrow the rest of the purchase price. The bank is offering a 30that requires annual payments and has an interest rate of 7% per

your annual payment be if you sign up for this mortgage?


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Problem 4-34

Payment $23,500.00

Cost $300,000.00

Term 30

Rate 7.00%

Balloon 63,848.03

- OR -

You would like to buy the house and take the mortgage described

You can afford to pay only $23,500 per year. The bank agrees to a

this amount each year, yet still borrow $300,000. At the end of the

years), you must make a balloon payment; that is, you must repa

balance on the mortgage. How much will this balloon payment be?


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Your age Payment

Cumulative

value of account

(end of year)

30 (20,868.91) (21,912.36)

31 (20,868.91) (44,920.34) Interest rate

32 (20,868.91) (69,078.71) Future value33 (20,868.91) (94,445.01)

34 (20,868.91) (121,079.62) Payment amount

Number of payments

You are saving for retirement. To live comfortably, you decide you will nee

million by the time you are 65. Today is your 30th birthday, and you decide

and continuing on every birthday up to and including your 65th birthday, thsame amount into a savings account. If the interest rate is 5%, how much m

each year to make sure that you will have $2 million in the account on your

Problem 4-35


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Problem 4-36

Your age Payment

Cumulative

value of account

(end of year)

30 (13,823.91) (14,515.10) Number of payments

31 (14,791.58) (30,772.02) Interest rate

32 (15,826.99) (48,928.96) Present value

33 (16,934.88) (69,157.04) Growth rate

34 (18,120.32) (91,641.23) PV interest factor (formul

35 (19,388.75) (116,581.47)

36 (20,745.96) (144,193.80) Payment

37 (22,198.18) (174,711.57)

38 (23,752.05) (208,386.80)

39 (25,414.69) (245,491.57)

You realize that the plan in Problem 35 has a flaw. Because your income will increa

be more realistic to save less now and more later. Instead of putting the same amount

let the amount that you set aside grow by 3% per year. Under this plan, how much

today? (Recall that you are planning to make the first contribution to the account tod


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Problem 4-44

The question is, how long will it take

for $50,000.00 to equal $1,000,000.00 if it grows at

1000000 = 50000 * 1.05 ^

divide both sides by $ 50,000.00

1.05 ^(n-1) = $20.00

(n-1)* ln(1.05) = ln(20)

(n-1)* 0.048790164 = 2.995732274

You can solve this using logarithms, by solving the following equation for n:

You are thinking of making an investment in a new plant. The plant will generate revenues of $1 millio

long as you maintain it. You expect that the maintenance cost will start at $50,000 per year and will in

thereafter. Assume that all revenue and maintenance costs occur at the end of the year. You intend to r

as it continues to make a positive cash flow (as long as the cash generated by the plant exceeds the main

The plant can be built and become operational immediately. If the plant costs $10 million to build, and

6% per year, should you invest in the plant?


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Interest rate assumption 7.00%

You will need $100,000.00 per year for

PV as of age 65 = (1,294,767.23)

You can accumulate this amount in 35 years by paying 9,366

You have just turned 30 years old, have just received your MBA, and have accepted your

must decide how much money to put into your retirement plan. The plan works as follow

plan earns 7% per year. You cannot make withdrawals until you retire on your sixty-fifth

point, you can make withdrawals as you see fit. You decide that you will plan to live to 1turn 65. You estimate that to live comfortably in retirement, you will need $100,000 per

of the first year of retirement and ending on your one hundredth birthday. You will contr

to the plan at the end of every year that you work. How much do you need to contribute e

retirement?

Problem 4-45


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Problem 4-46

Interest rate assumption 7.00%

You will need $100,000.00 per year for

PV as of age 65= (1,294,767.23)

PV as of age 30= (121,271.70)

2.00%

Starting salary $75,000.00

PV interest factor 16.253689

You can accumulate this amount in 35 years by paying 7,461.

Problem 45 is not very realistic because most retirement plans do not allow you to spe

contribute every year. Instead, you are required to specify a fixed percentage of your s

contribute. Assume that your starting salary is $75,000 per year and it will grow 2% pe

Assuming everything else stays the same as in Problem 45, what percentage of your i

contribute to the plan every year to fund the same retirement income?

Your contributions will grow at an annual

rate of

45 $9,844.87 $210,877.30


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, ,

46 $10,041.77 $235,680.48

47 $10,242.60 $262,420.72

48 $10,447.45 $291,237.62

49 $10,656.40 $322,280.66

50 $10,869.53 $355,709.83

51 $11,086.92 $391,696.44

52 $11,308.66 $430,423.8553 $11,534.83 $472,088.36

54 $11,765.53 $516,900.07

55 $12,000.84 $565,083.92

56 $12,240.86 $616,880.65

57 $12,485.67 $672,547.97

58 $12,735.39 $732,361.71

59 $12,990.10 $796,617.13

60 $13,249.90 $865,630.22

61 $13,514.90 $939,739.23

62 $13,785.19 $1,019,306.17

63 $14,060.90 $1,104,718.50

64 $14,342.11 $1,196,390.91

65 $14,628.96 $1,294,767.23

chapter04 xlssol updated (1)

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