Introduction to Valuation: The Time Value of Money

[Pages:10]Chapter 4 ? Introduction to Valuation: The Time Value of Money

A dollar today is worth more than a dollar tomorrow!!! How much more, that is the question.

Future Value

Suppose you have $100 and invest it for 1 year at 10%. How much will you have at the end of the year?

How much will you have in 2 years?

Why isn't it $120? Where did the extra $1 come from?

General Equations

FV = PV(1 + r)t FV = PV(FVIFr,t) You have $20,000 to invest. If you can earn 9% per year, how much will you have in ten years?

The GDP will grow at 2.5% for the next three years. The current GDP is $13,841.3 (billions). What will it be in three years?

Fin 311 Chapter 4 Handout

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You plan to purchase Apple stock for $185.00. You expect the share price to grow at 6% for the next 10 years. What will the price be in 10 years?

You plan to invest $1,500 in a financial asset with a rate of return of 12 percent. What will the vale of the asset be in 35 years?

Present Value

Remember: FV = PV(1 + r)t

1

PV

FV 1 rt

PV = FV(PVIFr,t)

NOTE: The PFIV is just the inverse of the FVIF Suppose you need $110 in 1 year and you can invest at 10%. How much must you invest now?

Suppose you need $121 in 2 years and you can invest at 10%. How much must you invest now?

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Fin 311 Chapter 4 Handout

Suppose you need $20,000 in 10 years. If you can earn 9% per year, how much do you have to invest today?

You will inherit $1.5 million in 40 years. Your bank is the trustee and will allow you to borrow against your inheritance. What is the maximum you can borrow? Assume r = 18%.

Interest Rate

Remember FV = PV(1 + r)t, we can solve for t.

FV 1 r t PV

1

1

FV t 1 r r FV t 1

PV

PV

You purchased one share of Apple stock in 1982 for $2.50. In 2007, (25 years later) it is valued at $185 per share. What is the average growth rate?

Fin 311 Chapter 4 Handout

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The GDP doubled between 1987 and 2007 (20 years). What is the average growth rate of the GDP?

Number of Periods

Remember FV = PV(1 + r)t, we can solve for t.

FV 1 r t ln FV t ln 1 r

PV

PV

ln FV

t

PV

ln 1 r

Suppose you want to buy lawn mower. You currently have $500 and the mower you want costs $1,500. If you can earn 8%, how long will you have to wait to buy the mower?

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Fin 311 Chapter 4 Handout

You want to buy a car. You know your grandparents will give you $10,000 when you graduation. You have researched the car market and decided you will buy a Honda Accord. It will cost $17,500 and you want to pay cash for it. You can invest the $10,000 gift at 12 percent. How long before you can buy the car?

Fin 311 Chapter 4 Handout

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Using the calculator Future Value

You have $20,000 to invest. If you can earn 9% per year, how much will you have in ten years?

FV = $20,000(FVIF9%,10)

N I PV Pmt Cpt FV

The GDP will grow at 2.5% for the next three years. The current GDP is $13,841.3 (billions). What will it be in three years?

FV = $13,841.3(FVIF2.5%,3)

N I PV Pmt Cpt FV

You plan to purchase Apple stock for $185.00. You expect the share price to grow at 6% for the next 10 years. What will the price be in 10 years?

FV = 185(FVIF6%,10)

N I PV Pmt Cpt FV

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Fin 311 Chapter 4 Handout

You plan to invest $1,500 in a financial asset with a rate of return of 12 percent. What will the value of the asset be in 35 years?

FV = $1,500(FVIF12%,35)

N I PV Pmt Cpt FV

Present Value

Suppose you need $110 in 1 year and you can invest at 10%. How much must you invest now?

PV = 110(PVIF10%,1)

N I Cpt PV Pmt FV

Suppose you need $121 in 2 years and you can invest at 10%. How much must you invest now?

PV = 121(PVIF10%,1)

N I Cpt PV Pmt FV

Fin 311 Chapter 4 Handout

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Suppose you need $20,000 in 10 years. If you can earn 9% per year, how much do you have to invest today?

PV = 20,000(PVIF9%,10)

N I Cpt PV Pmt FV

You will inherit $1.5 million in 40 years. Your bank is the trustee and will allow you to borrow against your inheritance. What is the maximum you can borrow? Assume r = 18%.

PV = 1,500,000(PVIF18%,40)

N I Cpt PV Pmt FV

Interest Rate

You purchased one share of Apple stock in 1982 for $2.50. In 2007, (25 years later) it is valued at $185 per share. What is the average growth rate?

2.50 = 185(PVIFr,25) or 185 = 2.50(FVIFr,25)

N Cpt I

PV Pmt FV

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Fin 311 Chapter 4 Handout

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