Share
Explore BrainMass

Time Value Money, Rate of return

1. U have been tracking a non-dividend paying share that you purchased. Its price since you purchased it (t = 0) until today (t = 3) has been P0 = $27.50, P1 = $17.50, P2 = $31.50 and P3 = $26.50.

a) Compute the periodic rates of return.

b) Compute the arithmetic and geometric rate of return for this stock over the past three years. Which is the most appropriate measure?

2. With an 8% annual interest rate, how long does it take a sum of money to double given
a) annual compounding,
b) semi-annual compounding and
c) daily compounding?

3. You are considering selling for $6,250 a Volvo which you purchased five years ago for $4,670. What would be your annualized rate of return on the Volvo investment?

4. Some day, you will buy an Acura NSX, drive it for 10 years and sell it for more than you paid for it. If you pay $89,000 for it and your expected rate of return is 6%, how much must you sell it for?

Solution Preview

1. U have been tracking a non-dividend paying share that you purchased. Its price since you purchased it (t = 0) until today (t = 3) has been P0 = $27.50, P1 = $17.50, P2 = $31.50 and P3 = $26.50.

a) Compute the periodic rates of return.

Time period Price Return=
0 P0= $27.50
1 P1= $17.50 -36.36% =(17.5-27.5)/27.5
2 P2= $31.50 80.00% =(31.5-17.5)/17.5
3 P3= $26.50 -15.87% =(26.5-31.5)/31.5

Answer:
Time period Return
1 -36.36%
2 80.00%
3 -15.87%

b) Compute the arithmetic and geometric rate of return for this stock over the past three years. Which is the most appropriate measure?

Arithemetic rate of return= 9.26% ={(-36.36%)+(80.%)+(-15.87%)}/3

Time period Price Current price/ Previous period price
0 P0= $27.50
1 P1= $17.50 0.6364 =17.5/27.5
2 P2= $31.50 1.8 =31.5/17.5
3 P3= $26.50 0.8413 =26.5/31.5

Geometric rate of return= -1.22% ={(0.6364)*(1.8)*(0.8413)}^(1/3) ...

Solution Summary

Answers questions on Time Value Money, Rate of return.

$2.19