Chapter 4 Introduction to Valuation: The Time Value of Money

Transcription

1 Chaper 4 nroducion o Valuaion: The Time Value of Money A dollar oday is worh more han a dollar omorrow!!! How much more, ha is he quesion. Fuure Value Suppose you have $00 and inves i for year a 0%. How much will you have a he end of he year? How much will you have in 2 years? Why isn i $20? Where did he exra $ come from? General Equaions = ( + r) = (F r, ) You have $20,000 o inves. f you can earn 9% per year, how much will you have in en years? The GDP will grow a 2.5% for he nex hree years. The curren GDP is $3,84.3 (billions). Wha will i be in hree years? Fin 3 Chaper 4 Handou Page

2 You plan o purchase Apple sock for $ You expec he share price o grow a 6% for he nex 0 years. Wha will he price be in 0 years? You plan o inves $,500 in a financial asse wih a rae of reurn of 2 percen. Wha will he vale of he asse be in 35 years? Presen Value Remember: = ( + r) r = (F r, ) OTE: The PFV is jus he inverse of he F Suppose you need $0 in year and you can inves a 0%. How much mus you inves now? Suppose you need $2 in 2 years and you can inves a 0%. How much mus you inves now? Page 2 Fin 3 Chaper 4 Handou

3 Suppose you need $20,000 in 0 years. f you can earn 9% per year, how much do you have o inves oday? You will inheri $.5 million in 40 years. Your bank is he rusee and will allow you o borrow agains your inheriance. Wha is he maximum you can borrow? Assume r = 8%. neres Rae Remember = ( + r), we can solve for. r r r You purchased one share of Apple sock in 982 for $2.50. n 2007, (25 years laer) i is valued a $85 per share. Wha is he average growh rae? Fin 3 Chaper 4 Handou Page 3

4 The GDP doubled beween 987 and 2007 (20 years). Wha is he average growh rae of he GDP? umber of Periods Remember = ( + r), we can solve for. r ln ln r ln ln r Suppose you wan o buy lawn mower. You currenly have $500 and he mower you wan coss $,500. f you can earn 8%, how long will you have o wai o buy he mower? Page 4 Fin 3 Chaper 4 Handou

5 You wan o buy a car. You know your grandparens will give you $0,000 when you graduaion. You have researched he car marke and decided you will buy a Honda Accord. will cos $7,500 and you wan o pay cash for i. You can inves he $0,000 gif a 2 percen. How long before you can buy he car? Fin 3 Chaper 4 Handou Page 5

6 Using he calculaor Fuure Value You have $20,000 o inves. f you can earn 9% per year, how much will you have in en years? = $20,000(F 9%,0 ) Cp The GDP will grow a 2.5% for he nex hree years. The curren GDP is $3,84.3 (billions). Wha will i be in hree years? = $3,84.3(F 2.5%,3 ) Cp You plan o purchase Apple sock for $ You expec he share price o grow a 6% for he nex 0 years. Wha will he price be in 0 years? = 85(F 6%,0 ) Cp Page 6 Fin 3 Chaper 4 Handou

7 You plan o inves $,500 in a financial asse wih a rae of reurn of 2 percen. Wha will he value of he asse be in 35 years? = $,500(F 2%,35 ) Cp Presen Value Suppose you need $0 in year and you can inves a 0%. How much mus you inves now? = 0(F 0%, ) Cp Suppose you need $2 in 2 years and you can inves a 0%. How much mus you inves now? = 2(F 0%, ) Cp Fin 3 Chaper 4 Handou Page 7

8 Suppose you need $20,000 in 0 years. f you can earn 9% per year, how much do you have o inves oday? = 20,000(F 9%,0 ) Cp You will inheri $.5 million in 40 years. Your bank is he rusee and will allow you o borrow agains your inheriance. Wha is he maximum you can borrow? Assume r = 8%. =,500,000(F 8%,40 ) Cp neres Rae You purchased one share of Apple sock in 982 for $2.50. n 2007, (25 years laer) i is valued a $85 per share. Wha is he average growh rae? 2.50 = 85(F r,25 ) or 85 = 2.50(F r,25 ) Cp Page 8 Fin 3 Chaper 4 Handou

9 The GDP doubled beween 987 and 2007 (20 years). Wha is he average growh rae of he GDP? = 2(F r,20 ) or 2 = (F r,20 ) Cp Eigh years ago, you invesed $0,000 in an accoun ha is now worh $22,000. Wha ineres rae per year did you earn? 0,000 = 22,000(F r,8 ) or 22,000 = 0,000(F r,8 ) Cp An avid ar collecor bough a famous paining for $8.5 million. Unforunaely, when he sold he paining 7 years laer, he only received $6.4 million. Wha was his rae of reurn on his invesmen? 8.5 = 6.4(F r,7 ) or 6.4 = 8.5(F r,7 ) Cp Fin 3 Chaper 4 Handou Page 9

10 umber of Periods Suppose you wan o buy lawn mower. You currenly have $500 and he mower you wan coss $,500. f you can earn 8%, how long will you have o wai o buy he mower? 500 =,500(F 8%, ) or,500 = 500(F 8%, ) Cp You wan o buy a car. You know your grandparens will give you $0,000 when you graduaion. You have researched he car marke and decided you will buy a Honda Accord. will cos $7,500 and you wan o pay cash for i. You can inves he $0,000 gif a 2 percen. How long before you can buy he car? 0,000 = 7,500(F 2%, ) or 7,500 = 0,000(F 2%, ) Cp You jus won he loery and received $25,000. You wan o inves he money unil you have enough o buy a $0,000 car. f you can earn percen per year, how long do you have o wai unil you buy he car? 25,000 = 0,000(F %, ) or 0,000 = 25,000(F %, ) Cp Page 0 Fin 3 Chaper 4 Handou