Time Value of Money Practice Problems: A Comprehensive Guide to Financial Concepts, Study notes of Business Finance

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FIN

EXAM 1 PRACTICE PROBLEMS

• CAPITAL MARKETS
• TIME VALUE OF MONEY
• DISCOUNTED CASH FLOWS APPLICATIONS
• STATISTICS

CAPITAL MARKET

PRACTICE

QUESTIONS

QUESTION 2: TYPES OF TRADES Match each of the following trades with the appropriate sentiment: Trade Sentiment Buy a call option Optimistic about a stock Buy a put option Pessimistic about a stock Buy a stock on margin Short sell a stock Answer: Buy call option → Optimistic about a stock Buy a put option → Pessimistic about a stock Buy a stock on margin → Optimistic about a stock Short sell stock → Pessimistic about a stock

QUESTION 3: ANNUAL RETURN Consider an investment that produces a return of 3.5% in the first year, - 2% for the next year, and 5% for the last two years.

1. If you invested $1,000 in this investment, what would it be worth at the end of the four years?
2. What is the annual return on this investment? Answer: Value in four years=$1,000 1+0.035 1 −0.02 (1+0.05)(1+0.05) = $1,118. Annual return = 4 1+0.035 1 −0.02 (1+0.05)(1+0.05) − 1 = 2.834% Check your work: $1,000 (1+ 0.02834) 4 = $1,118.

QUESTION 5: ANNUAL RETURN Consider a stock that had a $20 per share price on January 1 st

. At the end of three months, the stock had a price of $21 per share. What is the effective annual return for this stock? Answer: Return over three months = $21 − 20 $ = 0. 05 Annualized return = (1 + 0.05) 4

• 1 = 21.55%

QUESTION 6:YIELDS ON MONEY MARKET SECURITIES A US Treasury security has a price of 99.75, and 31 days to maturity. What is this security’s discount yield and investment yield? Answer: Discount yield = 100 − 99. 75 100

×

360 31

Investment yield = 100 − 99. 75

99. 750

×

365 31

QUESTION 1: GEOMETRIC MEAN RETURN Suppose that you invest $10,000 in an investment that will grow in value 6% the first year, 7% the second year, and 8% the third year. What is the average annual rate of return on this investment? Answer: Future value = $10,000 (1+ 0.06)(1+0.07)(1+0.08) = $12,249. Return = (^3) $12, 249. 36 $10, 000. 00

Alternatively: 3

1. 06 × 1. 07 × 1. 08 − 1 = 6 .997%

QUESTION 2: INTEREST-ON-INTEREST Suppose you deposit $1 million in an account that pays 5% interest, compounded daily. What is the interest-on-interest that you earn over a six-year period? Answer: Interest-on-interest = FVcompounding – FVsimple interest Future value with compound interest = $1 1 +

1. 05 365 365 × 6 = $1. 34983 million Future value with simple interest = $1 + $1 × 0. 05 × 6 = $1. 3 million Interest-on-interest = $1.34983 million – 1.3 million = $0.04983 million

QUESTION 4: DEFERRED ANNUITY An investment promised $1,000 per year, at the end of each of five years, but the cash flows do not begin until four years from today. If the discount rate is 5%, what is the value of this investment today? Answer: PV three years from today = $1, 000 1 − 1

1. 05 5
2. 05 = $1, 000 4. 32947667 = $4, 329. 47667 PV today = $4, 329. 47667 ( 1 + 0. 05 )^3 = $3,739. Why discount 3 periods instead of 4? Because if the first cash flow is 4 periods from today, the PV of this ordinary annuity is at the end of period 3 (PV of ordinary annuity is always one period before first cash flow).

QUESTION 5: EFFECTIVE ANNUAL RATE What is the effective annual rate of interest if the nominal rate is 6% and interest is compounded weekly? Answer: Effective rate = 1 +

1. 06 52 52 − 1 = 𝟔. 𝟏𝟕𝟗𝟗𝟖% TI-83/84: Eff(6,52) Excel: =EFFECT(.06,52)

QUESTION 7: COMPOUNDING Suppose you invest $10,000 in a security that grows 5% the first year and 6% the second year. What is the value of this investment at the end of the second period? 16 Answer: PV = $10, r 1 = 5% r 2 = 6% FV = PV (1 + r 1 )(1+r 2 ) = $10,000 (1.05) (1.06) = $11,

QUESTION 8: DISCOUNTING Suppose you expect $10,000 in three years. The appropriate discount rate in the first year is 4%, the second is 5%, and the third is 6%. What is the present value of this cash flow today? Answer: FV = $10, r 1 = 4% r 2 = 5% r 3 = 6% PV = $10, 000 ( 1. 04 )( 1. 05 )( 1. 06 ) = $𝟖, 𝟔𝟑𝟗. 𝟏𝟔

QUESTION 10: DISCOUNTING WITH CONTINUOUS COMPOUNDED RATES Suppose you expect $1,000 in three years. If the discount rate is 8%, continuously compounded, what is the present value of this future cash flow? Answer: FV = $1, I = 8% PV = $1, 000 𝑒

1. 08 × 3 = $1, 000 𝑒
2. 24 = $𝟕𝟖𝟔. 𝟔𝟑

QUESTION 11:VALUATION WITH A GROWING PERPETUITY Suppose a stock pays annual dividends, and that today’s dividend is $2 per share. If dividends are expected to grow at a rate of 5% per year, and the required rate of return on this stock is 8%, what is the value of this stock today? 20 Answer: D 0 = $ g = 5% r = 8% PV = 𝐷 0 ( 1 +𝑔) 𝑟 −𝑔

$2 ( 1 + 0. 05 )

1. 08 − 0. 05