Essentials of Corporate Finance

Stephen Ross, Randolph Westerfield, Bradford Jordan

Chapter 4 Introduction to Valuation: The Time Value of Money - all with Video Answers

Educators

Chapter Questions

Problem 1

First City Bank pays 7 percent simple interest on its savings account balances, whereas Second City Bank pays 8 percent interest compounded annually. If you made an $$\$ 8,000$$ deposit in each bank, how much more money would you earn from your Second City Bank account at the end of 10 years?

Anna Jones

Numerade Educator

Problem 2

For each of the following, compute the future value:
$$
\begin{array}{cccc}
\hline \text { Present Value } & \text { Years } & \text { Interest Rate } & \text { Future Value } \\
\hline \$ 3,150 & 6 & 18 \% & \\
8,453 & 19 & 6 & \\
89,305 & 13 & 11 & \\
227,382 & 29 & 5 & \\
\hline
\end{array}
$$

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Problem 3

For each of the following, compute the present value:
$$
\begin{array}{cccc}
\hline \text { Present Value } & \text { Years } & \text { Interest Rate } & \text { Future Value } \\
\hline 12 & 4 \% & \$ 17,328 \\
4 & 9 & 41,517 \\
16 & 12 & 790,382 \\
21 & 11 & 647,816 \\
\hline
\end{array}
$$

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Problem 4

Solve for the unknown interest rate in each of the following:
$$
\begin{array}{cccc}
\hline \text { Present Value } & \text { Years } & \text { Interest Rate } & \text { Future Value } \\
\hline \$ 115 & 6 & & 1,381 \\
905 & 7 & & 1,718 \\
15,000 & 18 & 141,832 \\
70,300 & 21 & 312,815 \\
\hline
\end{array}
$$

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Problem 5

Solve for the unknown number of years in each of the following:
$$
\begin{array}{cccc}
\hline \text { Present Value } & \text { Years } & \text { Interest Rate } & \text { Future Value } \\
\hline \$ 250 & & 9 \% & \$ 1,105 \\
1,941 & 7 & 3,700 \\
32,805 & 12 & 387,120 \\
32,500 & 19 & 198,212 \\
\hline
\end{array}
$$

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01:20

Problem 6

Assume the total cost of a college education will be $$\$ 320,000$$ when your child enters college in 18 years. You presently have $$\$ 50,000$$ to invest. What annual rate of interest must you earn on your investment to cover the cost of your child's college education?

Amit Srivastava

Numerade Educator

Problem 7

At 7 percent interest, how long does it take to double your money? To quadruple it?

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01:25

Problem 8

In 2009, an 1893 Morgan silver dollar sold for $$\$ 6,450$$. What was the rate of return on this investment?

James Kiss

Numerade Educator

Problem 9

You're trying to save to buy a new $$\$ 160,000$$ Ferrari. You have $$\$ 25,000$$ today that can be invested at your bank. The bank pays 3.2 percent annual interest on its accounts. How long will it be before you have enough to buy the car?

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Problem 10

Imprudential, Inc., has an unfunded pension liability of $$\$ 750$$ million that must be paid in 25 years. To assess the value of the firm's stock, financial analysts want to discount this liability back to the present. If the relevant discount rate is 8 percent, what is the present value of this liability?

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Problem 11

You have just received notification that you have won the $$\$2$$ million first prize in the Centennial Lottery. However, the prize will be awarded on your 100th birthday (assuming you're around to collect), 80 years from now. What is the present value of your windfall if the appropriate discount rate is 9 percent?

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02:02

Problem 12

Your coin collection contains 501952 silver dollars. If your grandparents purchased them for their face value when they were new, how much will your collection be worth when you retire in 2062 , assuming they appreciate at a 5.7 percent annual rate?

Sanchit Jain

Numerade Educator

01:32

Problem 13

In 1895, the first U.S. Open Golf Championship was held. The winner's prize money was $$\$ 150$$. In 2009 , the winner's check was $$\$ 1,350,000$$. What was the annual percentage increase in the winner's check over this period? If the winner's prize increases at the same rate, what will it be in 2045 ?

Cory Kuzinski

Numerade Educator

01:40

Problem 14

In 2009 , a $$\$ 5$$ silver certificate from 1896 was sold for $$\$ 10,500$$. For this to have been true, what was the annual increase in the value of the certificate?

Lily An

Numerade Educator

01:29

Problem 15

Although appealing to more refined tastes, art as a collectible has not always performed so profitably. During 2003, Sotheby's sold the Edgar Degas bronze sculpture Petite danseuse de quatorze ans at auction for a price of $$\$ 10,311,500$$. Unfortunately for the previous owner, he had purchased it in 1999 at a price of $$\$ 12,377,500$$. What was his annual rate of return on this sculpture?

Carson Merrill

Numerade Educator

Problem 16

Referring to the TMCC security we discussed at the very beginning of the chapter:
a. Based on the $$\$ 24,099$$ price, what rate was TMCC paying to borrow money?
b. Suppose that, on March 28,2016 , this security's price is $$\$ 39,583$$. If an investor had purchased it for $$\$ 24,099$$ at the offering and sold it on this day, what annual rate of return would she have earned?
c. If an investor had purchased the security at market on March 28, 2016, and held it until it matured, what annual rate of return would she have earned?

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01:10

Problem 17

Suppose you are still committed to owning a $$\$ 160,000$$ Ferrari (see Question 9). If you believe your mutual fund can achieve a 10.25 percent annual rate of return, and you want to buy the car in 10 years on the day you turn 30 , how much must you invest today?

Linh Vu

Numerade Educator

Problem 18

You have just made your first $$\$ 5,000$$ contribution to your individual retirement account. Assuming you earn a 10.5 percent rate of return and make no additional contributions, what will your account be worth when you retire in 45 years? What if you wait 10 years before contributing? (Does this suggest an investment strategy?)

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02:48

Problem 19

You are scheduled to receive $$\$ 13,000$$ in two years. When you receive it, you will invest it for six more years at 9 percent per year. How much will you have in eight years?

Charles Carter

Numerade Educator

03:25

Problem 20

You expect to receive $$\$ 25,000$$ at graduation in two years. You plan on investing it at 9 percent until you have $$\$ 160,000$$. How long will you wait from now? (Better than the situation in Question 9, but still no Ferrari.)

Akash M

Numerade Educator

02:04

Problem 21

You have $$\$ 9,000$$ to deposit. Regency Bank offers 12 percent per year compounded monthly ( 1 percent per month), while King Bank offers 12 percent but will only compound annually. How much will your investment be worth in 20 years at each bank?

Tony Ni

Numerade Educator

01:51

Problem 22

An investment offers to quadruple your money in 24 months (don't believe it). What rate per three months are you being offered?

Prashant Bana

Numerade Educator

Problem 23

You can earn 0.35 percent per month at your bank. If you deposit $$\$ 1,800$$, how long must you wait until your account has grown to $$\$ 3,500$$ ?

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Problem 24

You need $$\$ 75,000$$ in 10 years. If you can earn 0.42 percent per month, how much will you have to deposit today?

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03:08

Problem 25

You have decided that you want to be a millionaire when you retire in 45 years. If you can earn an 11 percent annual return, how much do you have to invest today? What if you can earn 5.5 percent?

Ankit Gupta

Numerade Educator

02:24

Problem 26

You have $$\$ 15,000$$ you want to invest for the next 40 years. You are offered an investment plan that will pay you 8 percent per year for the next 20 years and 12 percent per year for the last 20 years. How much will you have at the end of the 40 years? Does it matter if the investment plan pays you 12 percent per year for the first 20 years and 8 percent per year for the next 20 years? Why or why not?

Tony Ni

Numerade Educator