100 Lecture Version A Note for multiplechoice questions Choose the closest answer PV of Perpetuity If Alexia receives 1000 per year forever starting nine months from now what is the total PV of all payments Assume a stated annual interest rate of 16 compounded every three months ID: 502398
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Slide1
Quiz 4 solution sketches
1:00 Lecture, Version A
Note for multiple-choice questions: Choose the closest answerSlide2
PV of Perpetuity
If Alexia receives $1,000 per year, forever, starting nine months from now, what is the total PV of all payments? Assume a stated annual interest rate of 16%, compounded every three months.
EAIR = (1.04)
4 – 1 = 16.986%PV = 1,000/.16986 * (1.16986)1/4PV = $6,122.69
She receives payments 3 months sooner than what is in perpetuity formulaSlide3
Balloon Payment
Sunny borrows $5,000 today. She makes monthly payments of $37.50 for 48 months, starting one month from today. She makes one additional payment 60 months from today to completely pay off the loan. How much will this payment be if the stated annual interest rate is 9%, compounded monthly?Slide4
Balloon Payment
Interest-only loan for 48 months:
5000 * (.09/12) = $37.50
Balance after last regular payment in 48 months = $5,000Payment needed 12 months later = 5,000 * (1 + .09/12)12 = $5,469.03Slide5
Profitability Index
Brady invests $500,000 in McKenzie Wealth Management today. He will receive $100,000 per year, forever, starting one year from now. What is the profitability index for this investment if the effective annual interest rate is 25%?
PV of benefits = 100,000/.25 = $400,000
P.I. = 400,000/500,000 = 0.8Slide6
Growing Dividends
Scrubby Dub
Dub
Ghost, Inc. will pay its first dividend three years from today, and will pay annually thereafter forever. The first dividend payment (in 3 years) is $10 per share. Each of the next two dividend payments will be 50% higher than the previous payment. After that, dividend payments will remain the same forever.Slide7
Growing Dividends
What is the PV of this stock if the effective annual interest rate is 10%?
PV = 10/(1.1)
3 + 15/(1.1)4 + 22.50/.1 * 1/(1.1)4
PV = $171.44$22.50 paid every year starting 5 years from nowSlide8
CAPM
KKQJ Products, Inc. currently
has an expected return of 15
%. The risk-free rate of return is 4% and the expected return on the market is 10%. What is the beta for KKQJ Products?Exp. Ret. = Risk-free rate + β*risk premium15% = 4% + β
* (10% - 4%)15% = β * 6%
β = 1.833Slide9
Random Walk
Use the following information for the next two questions:
Deucey
Deuce Dance Productions stock exhibits price changes that are a random walk. In any given day, the value of the stock goes up by $2 with probability 0.4 and goes down by $1 with probability 0.6. The stock’s current value is $50.Slide10
Random Walk
What is the probability that the value of the stock will be the same two days from today?
In 2 days, the stock cannot reach the same value given the problem’s set-up.
Probability = 0Slide11
Random Walk
What is the probability that the value of the stock will be the same three days from today?
Three combinations will achieve the same stock value (with U=up and D=down):
UDD, DUD, DDUEach has the same prob. = (.4)(.6)2 = .144Total probability = 3 * .144 = 43.2%Slide12
Confidence Interval
Over Jan. 1, 1900 to Jan. 1, 2000, the historical average annual rate of return in Greece’s stock market was 12.5%. The annual standard deviation of the rate of return was 25.6%. What is the upper bound of the 95.4% confidence interval for the annual rate of return based on this information?Slide13
Confidence Interval
Hint
: you need to be
within 2 standard errors of the average to find the upper and lower bounds of the 95.4% confidence interval.Upper bound= 12.5% + 2 * 25.6%/(100)1/2= 12.5% + 5.12%
=17.62%Slide14
Confidence Interval
Hint
: you need to be
within 2 standard errors of the average to find the upper and lower bounds of the 95.4% confidence interval.Upper bound= 12.5% + 2 * 25.6%/(100)1/2= 12.5% + 5.12%
=17.62%Slide15
Returns in States of the World
There are 3 states of the world, each with one-third probability of occurring: A, B, and C. When state A occurs, Stock P has a return of 20% and Stock Q has a return of 5
%. When state
B occurs, Stock P has a return of 30% and Stock Q has a return of 10%. When state
C occurs, Stock P has a return of -8% and Stock Q has a return of
18%.Slide16
Returns in States of the World
(a) What is the expected return for each company? (Note: both answers must be correct for credit on this part.)
ER(P) = 1/3 * [.2 + .3 + (-.08)] = .14
ER(Q) = 1/3 * [.05 + .1 + .18] =
.11Slide17
Returns in States of the World
(b) What is the variance of Stock Q’s returns?
Var
(Q) = 1/3 * [(.05-.11)2 + (.1-.11)2 + (.18-.11)2]
Var(Q) = 0.0028667Slide18
Returns in States of the World
What is the covariance of the two stocks’ returns?
Cov
(P,Q) = 1/3 * [(.2-.14)(.05-.11) + (.3-.14)(.1-.11) + (-.08-.14)(.18-.11)]Cov
(P,Q) = 1/3 * (-0.0206)Cov(P,Q) = -0.006867