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扫描下载二维码Video: Present and Future Value: Calculating the Time Value of Money
Because money can be invested at a given interest rate, it has a time value. Economists recognize that a dollar received today is worth more than a dollar received tomorrow. In this lesson, you'll learn the basics of finance that serve as the foundation for understanding how bonds respond to market interest rates.
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Instructor:
Jon has taught Economics and Finance and has an MBA in Finance
Because money can be invested at a given interest rate, it has a time value. Economists recognize that a dollar received today is worth more than a dollar received tomorrow. In this lesson, you'll learn the basics of finance that serve as the foundation for understanding how bonds respond to market interest rates.
One day in the town of Ceelo, Barbara is on her way back home after a very long day of managing a small clothing store. Business is good, as evidenced by the new designer shades she bought recently. After dinner that night, she turns on the television and accidentally falls asleep. Inside Barbara's dream, an important announcement is taking place on TV. Within a few seconds, they announce the winner of the $50 million lottery. When she looks at her hand, she sees a lottery ticket, and after reviewing the numbers on it, Barbara finds that she has won the lottery! How cool is that! When she calls the phone number on the television screen, a nice young lady by the name of Jane answers the phone and asks her a very important question: Would you rather receive a check for $50 million today or receive payments over the next 20 years totaling $60 million? All of a sudden, Barbara wakes up from her dream and realizes that she was only dreaming, but she does remember the key question that Jane asked her and begins to ponder it carefully. If Barbara chose payments over the next 20 years, she'd get $3 million each year for 20 years in a row, totaling $60 million, which definitely sounds like more than $50 million, doesn't it? Assuming that she could invest $50 million today and earn a 5% interest rate on her money and assuming that there are no taxes, what should Barbara do? As she ponders this important question, she remembers an old saying that she learned as she was growing up - 'A bird in the hand is worth two in the bush.' We'll come back to this later, but I want to direct your attention to another situation taking place right now, as we speak, in the town of Ceelo. Margie the cake baker earns a nice income. Although she spends most of the money she earns, she saves some of it in a savings account at the bank. Suppose her savings account pays 5% interest per year. The question she wants to answer is this: how much would she have to invest today if she wants her account to be worth $100 a year from now? To answer this, Margie needs to know more about the time value of money. If Margie deposited $1 today, a savings account paying 5% interest per year would be worth $1.05 a year from now. The original $1 is what we call the principal that Margie deposited, and the $0.05 is the interest that the bank pays her as a reward for holding the money there. Because the bank is willing to pay Margie interest for holding her savings at their financial institution, money has a time value. In other words, it is worth more today than it is tomorrow. Present Value of Money
Using the formula to find the present value of money
Whenever you hear a situation that involves the choice between a payment later or a payment today, just think of the saying 'A bird in the hand is worth two in the bush.' I know some of you may say that this finance stuff is for the birds, and if so, I can show you that it's real, as we take a little trip through Bird-In-Hand, Pennsylvania, which is the name of a real town, by the way. Here's what the time value of money means. Economists recognize that a dollar today is not the same as a dollar in the future. Why not? Because I can take a dollar today and earn a return on it, it takes more than a dollar in the future to equal a dollar today. For example, if I can invest $1 and earn $0.05 on it over the next year, then that means that my $1 today is worth $1.05 a year from now. It also means that a dollar bill given to me one year from now would be worth less than a dollar today - specifically, about $0.95 - because I could invest this amount and earn interest so that the money I invested plus the interest equals $1 a year from today. If Margie wants her savings account to be worth $100 a year from now, then she needs to know what this future amount is worth today, which is what economists call the present value. Present value is the amount of money today that is equivalent to a single payment or a stream of payments earned in the future, invested at a certain interest rate. The formula for present value takes a future payment, or payments, and discounts them using the interest rate to find the worth of this money today. The higher the interest rate is, the lower the present value is today. The lower the interest rate is, the higher the present value is today. The present value of $100 one year later is going to be worth less than $100 today. Why? Because of the 5% interest. To make things easy, Margie uses the formula for present value: Present Value = FV / (1 + i)^n, where i is the interest rate and n is the number of time periods. Let's use the formula to figure out the present value of a future $100 value, assuming a 5% interest rate and a 1-year time span. FV stands for 'future value.' The future value that Margie wants to grow her account to is $100. i stands for interest rate, which is 5% in this case, and n is the number of periods. Margie has a 1-year time horizon, so, in this case, n = 1. Here's what the calculation looks like that answers Margie's question: $100 / (1 + .05)^1 = $95.24 So, Margie would have to invest $95.24 today when the interest rate is 5% in order to grow it to $100 exactly one year from today. Suppose the interest rate were 3% and the time horizon was 5 years instead. What would the present value of $100 be in 5 years? This is what we'd get: $100 / (1 + .03)^5 = $86.26 Now suppose Margie wants to know how much she'd need to invest today in order to have it grow into $1 million in 20 years, if she assumes that she'll earn a 7% interest rate per year. Here's what this looks like, accounting for the time value of money: $1,000,000 / (1 + .07)^20 Don't even think of trying this in your head. You'd need a calculator, and you can split it up into two calculations. First, enter 1.07^20, which equals 3.. Now divide your future value of $1,000,000 by this discount factor, and you'll get $258,419. What does this mean? If Margie invests $258,419 today into an account earning 7% per year, then this money grows each and every year at 7% until, after 20 years of waiting, she'll have $1 million. Future Value of Money
The formula for finding the future value of money
The time value of money depends on two things - the time interval between now and when you receive it, and the interest rate that money can be invested at in order to earn a return. For example, $100 paid to you in 1 year is worth more than $100 paid to you in 5 years. The longer the time interval, the less that future money is worth to you today and the greater the return you'd expect to earn if you invested money today. Likewise, $1 invested today at a 10% interest rate will pay you more than $1 invested at 5%. The higher the interest rate you earn on your money, the greater the time value of money. Working backwards, $1 paid to you in one year that can earn a 10% return would be worth less than $1 paid to you in 1 year at a 5% interest rate. Now, let's look at this concept from the opposite point of view. $100 invested today at 5% for exactly 1 year will be worth how much? To answer this, let's use the future value. Future value is the future worth of an amount of money invested today, paying a certain interest rate. If Margie invests $100 today in an account earning 5% per year, then 5% of $100 is $5, and in exactly 1 year, her $100 turns into $105. How do we figure that out? By using the formula for future value: Future Value = PV * (1 + i)^n PV stands for present value, which is $100 in this case. i is the interest rate, which we said was 5%, and n is the number of periods - in this case we're talking about years - specifically 1 year - so n = 1. When you plug all this into the future value formula, the future value of Margie's $100 invested at 5% is equal to $100 * (1 + .05)^1 = $105. Calculating the Price of a BondThe formula for present value has a very important application. One of the basic types of investments is called bonds. If you understand the concept of the time value of money, then the idea of a bond is not much of a stretch. A bond is a promise to pay an amount back in the future that is borrowed today. Very simply, it's a debt, or a loan. They call it a bond, which is a type of security, because it can be bought or sold in the free market, but it's really just a loan. When the U.S. government borrows money to fund the operations of the government, it issues bonds and promises to make payments over time to pay back the money it borrows. This is a government bond that can be bought and sold in the free market, and to buy and sell something, you have to have a price. That's where the time value of money comes in. Since bonds pay an ongoing stream of fixed interest payments and market interest rates for new bonds go up and down regularly, the price of an existing bond goes up and down whenever the market interest rates change.
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Here's an important thing to know about bonds and interest rates. Let's say you bought that $1,000 bond paying 5% interest each year. As long as you own it, it's going to keep paying you exactly 5%, no more, no less. But market interest rates go up and down all the time and every year. Suppose new bonds become available, paying whatever the market interest rate is at the time. That means that your old existing bond that's paying you 5% may appear more attractive or less attractive than new bonds that come out.
The formula for the present value of an annuity
For example, when the market interest rates go from, say, 5% to 10%, that means new bonds will be issued at 10%. The price (or the present value) of an existing 5% bond adjusts to the new market interest rate by going down. In this case, existing bonds are less attractive than new ones paying a higher interest rate. When interest rates go down, this makes the price of existing bonds, which pay a higher interest rate, go up because they're more attractive than new ones paying a lower rate. The price of existing bonds is inversely correlated with market interest rates. Calculating an AnnuityWe've talked about present value and future value. Now let's go back to the original question I posed in this lesson. When Barbara won the lottery, or at least dreamed that she did, how much would 20 years of payments totaling $60 million be worth today? If you add up $3 million per year * 20, you'd get $60 million. After learning about the time value of money, as well as the price of a bond, I'm sure you can tell now that this stream of payments would be worth less than $60 million today, and how much less? To find out, we use the formula for the present value of an annuity because a stream of lottery payments is considered an annuity. Here's the formula for that one: PV annuity = pmt * ((1 - (1 + i)^-n) / i) As you can see, this formula's a little bit more complicated, but if you know everything to plug in, it's really not as hard as it looks. The annual amount for this lottery payout is $3 million. The number of years is 20, so n = 20. Assuming a reasonable interest rate on an investment that you chose today was 3%, then this stream of equal future payments would only be worth $44,632,425 today. Since Barbara watched this lesson on <, she knows how to make a great financial decision. When she has the choice to receive $50 million today or 20 payments of $3,000,000, she chooses the $50 million today - not because it always works out better to take the lump sum, but because based on the two options she was given and a 3% interest rate, it's better to take the lump sum. Lesson SummaryAlright, let's review. Present value is the amount of money today that is equivalent to a single payment or a stream of payments earned in the future, invested at a certain interest rate. The formula for present value is: Present Value = FV / (1 + i)^n Future value is the future worth of an amount of money invested today, paying a certain interest rate. The formula for future value is: Future Value = PV * (1 + i)^n A bond is a promise to pay an amount back in the future that's borrowed today. Very simply, it's a debt or a loan. When market interest rates go up, new bonds will be issued at a higher rate than existing bonds. That makes old bonds less attractive, so their present value goes down. On the other hand, when market interest rates go down, new bonds will be issued at a lower rate than existing bonds. That makes old, existing bonds more attractive, so their present value adjusts by going up. The price of existing bonds varies inversely with market interest rates. Finally, if you want to calculate the present value of a series of payments received in the future, such as payments received from winning the lottery, for example, use the annuity formula, which is: PV annuity = pmt * ((1 - (1 + i)^-n) / i) Lesson OutcomeAfter seeing this video, you should be able to:
Understand that money has time value
Determine the present value of invested money after a given time period
Solve for future value of invested money
Understand market values of bonds
Figure out the value of annuity payments over time
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Try it free for 5 days!Working mothers: pioneering the way forward | The Japan Times
TOKYO (11 a.m.)
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Working mothers: pioneering the way forward
We talk to five working mothers in an attempt to discover how some women are able to have a career and a family
Special To The Japan Times
Although Japan’s women are on par with their male counterparts in educational achievement, Japan ranks 104th in gender equality out of 142 countries and territories, according to the World Economic Forum’s 2014 Global Gender Gap Report. The country’s Achilles’ heel is its low rate of female participation in the workforce, as society puts pressure on women to marry and become homemakers.
However, the working mothers profiled here are challenging the country’s infamous gender stereotypes and share a resilience and belief that they can work, regardless of their status as parents. Better still, they can be viewed as important role models for Prime Minister Shinzo Abe’s “womenomics” economic growth strategy.
‘It was my task to open the door and break the glass ceiling.’ — Yukiko Imazu
| CHIEKO KATO
Yukiko Imazu
Yukiko Imazu is the first female partner at Anderson Mori & Tomotsune, one of the country’s largest and most prestigious law firms. She’s also the first partner at the firm to have taken maternity leave.
While in elementary school, Imazu’s parents raised her to believe that her generation of women should work outside of the home — that the idea of being a housewife would become “old-fashioned.”
“You have to have some skills so that you can work for a lifetime,” her father had warned her.
After graduating from Keio University and gaining the proper training and certifications to become a lawyer, Imazu joined Anderson & Mori in 1996. Within two years, she married and had a child. Her firm had no policy regarding maternity leave.
“I was very nervous,” Imazu recalls. “I had to leave the office by 7 p.m. to pick up my daughter from day care at 8 p.m. The first day I returned to work I sent an email to the partners and explained that I wanted to work but I also had to pick up my daughter at a fixed time so I couldn’t be flexible (with my schedule). I received no response.”
Sometimes she would leave meetings early, apologizing for “sneaking out.” Imazu could only stay late on the occasions her husband was able to pick their daughter up.
Fortunately, the day care center near her home looked after her daughter until 8 p.m. and fed her dinner — a rarity as most require a pre-dinner pick-up by 6 p.m. The forward-thinking manager of this day care center believed that working mothers should be better supported.
Imazu’s family has also been instrumental in helping her continue her career. When her daughter started preschool, Imazu’s mother or grandmother would pick her child up at midday, take her to her afternoon classes and look after her until Imazu picked her up in the evening. Now a teenager, Imazu’s daughter continues to go to her grandmother’s house after school.
In 2005, Anderson & Mori merged with Tomotsune & Kimura to become today’s Anderson Mori & Tomotsune. Fortuitously, founding female partner Akiko Kimura paved the way for Imazu to be promoted as a partner that year.
“It was my task to open the door and break the glass ceiling,” Imazu recalls.
Imazu questions Abe’s three-year child care leave proposal. “If I took a year off, I wouldn’t want to come back,” she says. “So three years is out of the question.”
Employees, she says, should “work more efficiently and not be evaluated by their length of stay at the workplace. Also, men should spend more time outside of work to look after their families.”
Imazu is grateful for the support she has received to date. “Mothers,” she says, “tsuneni mawari ni kansha (cannot work without the help of others).”
Miho Sakai
‘Women are born to multitask and they can use that experience at work.’ — Miho Sakai
| CHIEKO KATO
Miho Sakai, a Sendai native and mother of 9-year-old twins, is a marketing manager at the Tokyo office of Brightcove, a digital marketing and media company headquartered in Boston. Sakai’s commitment to her career has been shaped by her experiences abroad. “Maybe it’s because I’ve been to the States and have learned to do things myself or maybe it’s just my personality,” Sakai says.
As a young adult, Sakai went to the U.S. to study English and then went on to attend a college in San Francisco, where she remained for five years to work at Sega Corp. Upon returning to Japan, Sakai married, had children, successfully secured spaces for her children in an oversubscribed day care system, and continued to work in the technology industry. Her husband was transferred to a post in the U.S. for five years, during which time she was a full-time homemaker.
When they returned to Japan, Sakai began work at her present position. She works with the Asia-Pacific and North American teams of her company, allowing her to utilize her language skills and bicultural understanding. Although she typically works nine hours a day and is home by 6:30 p.m. when her children return, she continues to work after they go to sleep and usually wakes up early to complete work.
She says her manager is not a traditional salaryman and is therefore not concerned about in-office work hours as long as the work is completed. She says he has a more Western way of thinking, having graduated with a master’s degree in business administration from the Tuck School of Business of Dartmouth College, an Ivy League school in the United States. She also attributes the acceptance of her situation to the firm being multinational.
With no relatives nearby, Sakai’s husband is her greatest supporter.
“Although he’s really busy, he supports me mentally,” she says. “If the house gets a little messy, he starts tidying things up without me saying anything.”
Her closest friends also frequently help out. They, too, are working mothers and understand one another.
Ultimately, Sakai feels women are integral to the success of any given company.
“Women are born to multitask and they can use that experience at work,” she says.
Not all women should feel they have to work while raising children, Sakai says, “but if they feel like they are better for it, they should go back to it.”
She believes it’s essential for working women to have support from their husbands. “You don’t want to create any problems within the household,” she says. “Hmmm … I think I should spend some more time with my husband.”
Megumi Uchida
‘(Existing policies to support working mothers) are putting the entire burden on women and do not help create an environment for women to work.’ — Megumi Uchida
| CHIEKO KATO
Megumi Uchida is a real-estate consultant running a company that offers clients a full suite of business solutions with their investments. She is also a single mother who has a 5-year-old daughter. For Uchida, not working is not an option.
A day care center takes care of her daughter from 7:30 a.m. until 6 p.m. every day, but when Uchida has to meet clients in the evenings, she must pick up her daughter, take her to her older sister’s house and then return to work. “I think I waste one to two hours a day, going back and forth on trains, picking her up from the day care center and taking her to someone who looks after her,” Uchida says. “It also costs a lot of money for taxis.”
Uchida started her own company by necessity. The only way she could increase her earnings at her previous place of employment was to increase her overtime, which was not possible because she needed to take care of her daughter.
“Those I was supervising were much better paid,” she says. “I challenged the company and said I could finish the same workload within office hours. I could get it done by the end of each working day. They replied that the company does not think in such a way.”
However, when Uchida fell ill — most likely from stress — she had to reduce her workload, which made her ineligible to continue with her daughter’s day care, as she could not fulfill the minimum hours of employment required for mothers to receive public child care benefits.
“I need my daughter to cooperate with me to keep things working,” she says. “It may be too much for a 4-year-old to handle, but I explained to her that I cannot always do what other families are able to. I am a single mom and we are a family of two. I will work hard to do what I can for her, including paying for her ballet lessons. I wonder if she thinks this is a heavy burden, and I feel guilty about it.”
At the same time, Uchida feels she had little emotional support.
“My parents were opposed to having children outside marriage,” she recalls. “I had to cut ties with them and have my baby without any assistance.”
Today, however, they have since reconciled. “I want to move from where I am to be closer to my family, but there is no opening at a day care center near them,” she says. “It’s easier for me to wait for another year or two until she goes to elementary school.”
“(Existing policies to support working mothers) are putting the entire burden on women and do not help create an environment for women to work,” she says. “It doesn’t seem as if any politicians understand this. I am concerned about what the future will be like when my child’s generation grows up.”
Yuki Honda
‘Children grow healthier when people other than the mother — namely, the father and adults outside of the family — are involved in the process of raising them.’ — Yuki Honda
| CHIEKO KATO
Yuki Honda is a professor of social science in education at the University of Tokyo and the mother of two teenagers. She is an outspoken advocate of gender equality and has authored or edited more than 15 books and countless academic papers on family and education.
“When I was very young, my maternal grandmother used to tell me to work,” Honda recalls. “She raised my mother and my aunt (on her own) after her husband died young. It must have been hard for her to make a living. My mother also worked, so I was raised by this grandmother. I loved her, and she inspired me.”
The life of a professor offers Honda a fairly flexible schedule.
While she must be on campus to teach classes, she says, “I decide how I work, how long I work, and when I work.”
The drawback to this, however, is that she usually works after dinner and late into the night. With her daughter now in high school and involved in club activities that take place before and after school, Honda wakes up at 5:40 a.m. to prepare a lunch box. “I am always sleep-deprived and groggy,” she says, sipping on a Red Bull.
Honda and her partner, who is also a professor with a similarly flexible schedule, maintain a weekly calendar to ensure the household responsibilities are shared.
With no relatives in Tokyo, they have needed to rely on the public support of day care centers and after-school care.
Honda says that Japanese women may need to rethink their beliefs toward who bears responsibility for raising their children. “Children grow healthier when people other than the mother — namely, the father and adults outside of the family — are involved in the process of raising them,” she says.
What’s more, Honda would like to dispel the myth that children should be raised by their mothers until they turn 3 years old. “It is crucial to start building vocabulary when children first learn to speak,” she says. “If children only spend time with their mothers until they are 3, it can inadvertently hurt them.”
“I notice that Japanese mothers typically feel really guilty about working, thinking it inconveniences the family,” she says. “I would like to tell them that they don’t have to feel guilty, and there are lots of good things that come from moms working.”
As for Japan’s traditional gender roles, Honda is concerned that both men and women are disadvantaged in the event of divorce. “Both the husband and wife are disadvantaged because each of them can play just one role. And, women, in particular, face financial hardship,” she says. “Statistics show that single mothers earn very little money and are quite vulnerable. I think it is important for women to become financially independent.”
Rieko Kaneko
‘For now, raising my children is my first priority. I will think about my own future when they are older.’ — Rieko Kaneko
| CHIEKO KATO
Rieko Kaneko is an industrial physician, and is employed in a large company that is required to have a full-time doctor on the premises. She has a 5-year-old child and a 1-year-old toddler.
Kaneko’s parents raised her to believe that women should work and hold a qualification. Interested in biology, medical school seemed like the natural next step. However, her career is second to her family.
“I am not interested in getting promoted or attaining great career achievements,” Kaneko says. “For now, raising my children is my first priority. I will think about my own future when they are older.”
Kaneko is solely responsible for the schedules of her children as her husband’s work hours are extensive. Her children’s day care center and kindergarten are close to one another, so the morning drop-off is manageable. However, after she leaves work at 5 p.m., she picks up her older child who has already been taken from the kindergarten in the early afternoon to afternoon day care. She then has to pick up her younger child from a different day care center. In emergencies, she calls on her in-laws to come to Tokyo.
“I would like to relax my work schedule for my children,” she says. “If I did, however, my children may become ineligible to attend day care.”
Kaneko says day care centers should be encouraged to look after children of part-time working mothers. What’s more, she says, the government should create programs that support babysitting and employ the elderly for child care.
At present, any reduction in her working hours would require her to send her children to private child care. “That can be quite expensive,” she says. “You might end up spending all of your earnings on it.”
Kaneko is also concerned the government is not addressing how the critical years in one’s career path often coincide with a woman’s peak period of healthy reproduction. “This issue must be addressed, especially as the country’s falling birthrate and the aging of the Japanese population become serious concerns,” she says.
Kaneko hopes her children will view working mothers as the norm. “They will think it is natural for women to continue working after they marry,” she says.
This is the final installment of a two-part series on working women. Read the first part:
