Question

1. Brockman Corporation's earnings per share were $3.50 last year, and its growth rate during the prior 5 years was 8.4% per year. If that growth rate were maintained, how many years would it take for Brockman's EPS to triple?

Select the correct answer.

a. 10.62

b. 13.62

c. 15.12

d. 16.62

e. 12.12 2. Your friend offers to pay you an annuity of $2,000 at the end of each year for 3 years in return for cash today. You could earn 5.5% on your money in other investments with equal risk. What is the most you should pay for the annuity? Select the correct answer. a. $5,371.87 b. $5,389.87 c. $5,395.87 d. $5,383.87 e. $5,377.87 3. A new investment opportunity for you is an annuity that pays $3,950 at the beginning of each year for 3 years. You could earn 5.5% on your money in other investments with equal risk. What is the most you should pay for the annuity? Select the correct answer. a. $11,295.16 b. $11,260.36 c. $11,242.96 d. $11,225.56 e. $11,277.76 4. Suppose you earned a $565,000 bonus this year and invested it at 8.25% per year. How much could you withdraw at the end of each of the next 20 years? Select the correct answer. a. $58,621.22 b. $58,612.62 c. $58,604.02 d. $58,638.42 e. $58,629.82 5. What's the present value of $5,000 discounted back 5 years if the appropriate interest rate is 4.5%, compounded semiannually? Select the correct answer. a. $3,219.64 b. $3,229.34 c. $3,209.94 d. $3,239.04 e. $3,200.24

Answer 1

Answer to Question 1:

Last Year EPS = $3.50
Growth Rate = 8.40%

Desired EPS = 3 * $3.50
Desired EPS = $10.50

Let it will take n years to earn desired EPS

Last Year EPS * (1 + Growth Rate)^Period = Desired EPS
$3.50 * 1.0840^n = $10.50
1.0840^n = 3
n * ln(1.0840) = ln(3.00)
n = 13.62

Time Period = 13.62 years

Answer to Question 2:

Annual Payment = $2,000
Number of Payments = 3
Interest Rate = 5.50%

Present Value = $2,000/1.055 + $2,000/1.055^2 + $2,000/1.055^3
Present Value = $2,000 * (1 - (1/1.055)^3) / 0.055
Present Value = $2,000 * 2.69793
Present Value = $5,395.87

Answer to Question 3:

Annual Payment = $3,950
Number of Payments = 3
Interest Rate = 5.50%

Present Value = $3,950 + $3,950/1.055 + $3,950/1.055^2
Present Value = $3,950 * 1.055 * (1 - (1/1.055)^3) / 0.055
Present Value = $3,950 * 2.84632
Present Value = $11,242.96

Answer to Question 4:

Amount Deposited = $565,000
Interest Rate = 8.25%
Time Period = 20 years

Let annual withdrawal be $x

$565,000 = $x/1.0825 + $x/1.0825^2 + … + $x/1.0825^19 + $x/1.0825^20
$565,000 = $x * (1 - (1/1.0825)^20) / 0.0825
$565,000 = $x * 9.63815
$x = $58,621.21

Annual Withdrawals = $58,621.22