Chapter 7 textbook problems Problem 1 counts 10 points and problem 11, 5 points SHOW YOUR WORK Problem 1 Answer the following questions assuming the interest rate is 8 percent Time Value of Money Problems a What is the present value of $1,000 to be received in four years b What is the present value of $1,000 in eight years Why does the present value fall as the number of years increases c What will be the value in seven years of $12,000 invested today d How much would you pay for the right to receive $5,000 at the end of year 1, $4,000 at the end of year 2, and $8,000 at the end of year 10 e How long will it take for a $2,000 investment to double in value f What will be the value in 20 years of $500 invested at the end of each year for the next 20 years g A couple wishes to save $250,000 over the next 18 years for their childs college education What uniform annual amount must they deposit at the end of each year to accomplish their objective h How long must a stream of $600 payments last to justify a purchase price of $7,500 00 Suppose the stream lasted only five years How large would the salvage value (liquidating payment) need to be to justify the investment of $7,500 00 Rate of Return Problems i An investment of $1,300 today returns $61,000 in 50 years What is the internal rate of return on this investment j An investment costs $750,000 today and promises a single payment of $11 2 million in 23 years What is the promised rate of return, IRR, on this investment k What return do you earn if you pay $22,470 for a stream of $5,000 payments lasting ten years What does it mean if you pay less than $22,470 for the stream More than $22,470 l An investment promises to double your money in five years What is the promised IRR on the investment m The projected cash flows for an investment appear below What is the investments IRR Year 0 1 2 3 4 5 Cash Flow $460 28 75 160 280 190 n In 1987, a Van Gogh painting, Sunflowers (not reputed to be one of his best), sold at auction, net of fees, for $36 million In 1889, 98 years earlier, the same paining sold for $125 Calculate the rate of return to the seller on this investment What does this suggest about the merits of fine art as an investment Bank Loan, Bond, and Stock Problems o How much would you pay for a 10 year bond with a par value of $1,000 and a 7 percent coupon rate Assume interest is paid annually p How much would you pay for a share of preferred stock paying a $5 per share annual dividend forever q A company is planning to set aside money to repay $150 million in bonds that will be coming due in eight years How much money would the company need to set aside at the end of each year for the next eight years to repay the bonds when they come due How would your answer change if the money was deposited at the beginning of each year r An individual wants to borrower $120,000 from a bank and repay it in six equal annual end of year payments, including interest What should the payments be for the bank to earn 8 percent on the loan Ignore taxes and default risk Problem 11 Whats wrong with this picture In the following discussion, see how many errors you can spot and explain briefly why each is an error You do not need to correct the error Loretta, I think weve got a winner here Take a look at these numbers ($000 omitted) Year 0 1 2 3 10 Initial cost 1 000 Units sold 100 100 100 100 Price unit 15 15 15 15 Total revenue 1,500 1,500 1,500 1,500 Cost of goods sold 800 800 800 800 Gross profit 700 700 700 700 Operating expenses Depreciation 100 100 100 100 Interest expense 100 100 100 100 Income before tax 500 500 500 500 Tax 40 200 200 200 200 Income after tax $300 $300 $300 $300 Now, Loretta, heres how I figure it The boss says our corporate goal should be to increase earnings by at least 15 percent every year, and this project certainly increases earnings It adds $300,000 to income after tax every year My trusty calculator tells me that the rate of return on this project is 30 percent ($300 $1,000), well above our minimum target return of 10 percent And if you want to use net present value, its NPV discounted at 10 percent is $843 50 So, what do you think, Loretta Well, Denny, it looks pretty good, but I do have a few questions Shoot, Loretta OK What about increases in accounts receivable and stuff like that Not relevant Well get that money back when the project terminates, so its equivalent to an interest free loan, which is more of a benefit than a cost But, Denny, what about extra selling and administrative costs Havent you left those out Thats the beauty of this, Loretta Given the recent recession, I figure we can handle the added business with existing personnel In fact, one of the virtues of the proposal is what we should be able to retain some people we would otherwise have to terminate Well, youve convinced me, Denny Now, I think it will be only fair if the boss puts you in charge of this exciting new project

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Chapter 7 textbook problems. Problem 1 counts 10 points and problem 11, 5 points. SHOW YOUR WORK!!! Problem 1: Answer the following questions assuming the

Chapter 7 textbook problems. Problem 1 counts 10 points and problem 11, 5 points.

SHOW YOUR WORK!!!

Problem 1:

Answer the following questions assuming the interest rate is 8 percent.

Time Value of Money Problems

a. What is the present value of $1,000 to be received in four years?
b. What is the present value of $1,000 in eight years? Why does the present value fall as the number of years increases?
c. What will be the value in seven years of $12,000 invested today?
d. How much would you pay for the right to receive $5,000 at the end of year 1, $4,000 at the end of year 2, and $8,000 at the end of year 10?
e. How long will it take for a $2,000 investment to double in value?
f. What will be the value in 20 years of $500 invested at the end of each year for the next 20 years?
g. A couple wishes to save $250,000 over the next 18 years for their childs college education. What uniform annual amount must they deposit at the end of each year to accomplish their objective?
h. How long must a stream of $600 payments last to justify a purchase price of $7,500.00? Suppose the stream lasted only five years. How large would the salvage value (liquidating payment) need to be to justify the investment of $7,500.00?

Rate of Return Problems

i. An investment of $1,300 today returns $61,000 in 50 years. What is the internal rate of return on this investment?
j. An investment costs $750,000 today and promises a single payment of $11.2 million in 23 years. What is the promised rate of return, IRR, on this investment?
k. What return do you earn if you pay $22,470 for a stream of $5,000 payments lasting ten years? What does it mean if you pay less than $22,470 for the stream? More than $22,470?
l. An investment promises to double your money in five years. What is the promised IRR on the investment?
m. The projected cash flows for an investment appear below. What is the investments IRR?

Year	0	1	2	3	4	5
Cash Flow	-$460	-28	75	160	280	190

n. In 1987, a Van Gogh painting, Sunflowers (not reputed to be one of his best), sold at auction, net of fees, for $36 million. In 1889, 98 years earlier, the same paining sold for $125. Calculate the rate of return to the seller on this investment. What does this suggest about the merits of fine art as an investment?

Bank Loan, Bond, and Stock Problems

o. How much would you pay for a 10-year bond with a par value of $1,000 and a 7 percent coupon rate? Assume interest is paid annually.
p. How much would you pay for a share of preferred stock paying a $5-per-share annual dividend forever?
q. A company is planning to set aside money to repay $150 million in bonds that will be coming due in eight years. How much money would the company need to set aside at the end of each year for the next eight years to repay the bonds when they come due? How would your answer change if the money was deposited at the beginning of each year?
r. An individual wants to borrower $120,000 from a bank and repay it in six equal annual end-of-year payments, including interest. What should the payments be for the bank to earn 8 percent on the loan? Ignore taxes and default risk.

Problem 11: Whats wrong with this picture?

In the following discussion, see how many errors you can spot and explain briefly why each is an error. You do not need to correct the error.

Loretta, I think weve got a winner here. Take a look at these numbers!

($000 omitted)

Year	0	1	2	3	10
Initial cost	-1.000
Units sold		100	100	100	100
Price/unit		15	15	15	15
Total revenue		1,500	1,500	1,500	1,500
Cost of goods sold		800	800	800	800
Gross profit		700	700	700	700
Operating expenses
Depreciation		100	100	100	100
Interest expense		100	100	100	100
Income before tax		500	500	500	500
Tax @ 40%		200	200	200	200
Income after tax		$300	$300	$300	$300

Now, Loretta, heres how I figure it: The boss says our corporate goal should be to increase earnings by at least 15 percent every year, and this project certainly increases earnings. It adds $300,000 to income after tax every year.

My trusty calculator tells me that the rate of return on this project is 30 percent ($300/$1,000), well above our minimum target return of 10 percent. And if you want to use net present value, its NPV discounted at 10 percent is $843.50.

So, what do you think, Loretta?

Well, Denny, it looks pretty good, but I do have a few questions.

Shoot, Loretta

OK. What about increases in accounts receivable and stuff like that? Not relevant! Well get that money back when the project terminates, so its equivalent to an interest-free loan, which is more of a benefit than a cost.

But, Denny, what about extra selling and administrative costs? Havent you left those out?

Thats the beauty of this, Loretta. Given the recent recession, I figure we can handle the added business with existing personnel. In fact, one of the virtues of the proposal is what we should be able to retain some people we would otherwise have to terminate.

Well, youve convinced me, Denny. Now, I think it will be only fair if the boss puts you in charge of this exciting new project.