quiz 4 solution sketches 1:00 lecture, version a note for multiple-choice questions: choose the...

Quiz 4 solution sketches

1:00 Lecture, Version A

Note for multiple-choice questions: Choose the closest

answer

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)1/4

PV = $6,122.69She receives payments 3 months sooner than what is in perpetuity formula

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?

Balloon Payment

Interest-only loan for 48 months: 5000 * (.09/12) = $37.50

Balance after last regular payment in 48 months = $5,000

Payment needed 12 months later = 5,000 * (1 + .09/12)12 = $5,469.03

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 = 0.8

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.

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 now

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

premium 15% = 4% + β * (10% - 4%) 15% = β * 6% β = 1.833

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.

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 = 0

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, DDU Each has the same prob. = (.4)(.6)2

= .144 Total probability = 3 * .144 = 43.2%

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?

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%

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%.


(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] = .11


(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) = 0.0028667


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

quiz 4 solution sketches 1:00 lecture, version a note for multiple-choice questions: choose the...

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