F301 Advanced Practice Problems on Time Value of Money. 1. What is ...
Solution: When cash flows occur at different points in time, their value is affected
by the.
F301 Advanced Practice Problems on Time Value of Money 1. What is the present value of $2,000 to be received two years from now, and another $3,000 to be received three years from now, at a rate of return of 7.6% per year? Solution: When cash flows occur at different points in time, their value is affected by the passage of time. Cash flows at different points in time cannot be added. When cash flows occur at the same point in time, however, they can be added. In this problem, convert both cash flows to present value and sum the PVs.
2. The number of periods does not have to be measured in years. The periods can be anything: months, weeks, quarters, etc. Just make sure the rate is given for the same type of period. In other words, if “t” is measured in weeks, then the rate must be a rate per week. If “t” is measured in quarters, then the rate must be a rate per quarter. So what is the future value of $5,000 at the end of six months, if the rate of return is one-half percent per month? Solution: First convert the rate as a percent to the 1+r format: Divide by 100 and add 1 = 1.005.
3. The quarterly returns on my investment account over the past year have been as follows: First Quarter Second Quarter Third Quarter Fourth Quarter
5% 2% –7% –1.5%
If I had $12,000 in the account at the beginning of the year, what is the value in the account at the end of the fourth quarter? Solution: This is simply a series of percent changes, where the percent change is different in each period. To solve for the future value, you must multiply by (1 + r) for each period, and the “r” changes each time. So first convert each percent (Big R) to the (1 + r) format: Divide by 100 and add 1. First Quarter Second Quarter Third Quarter Fourth Quarter
(1 + r) = 1.05 (1 + r) = 1.02 (1 + r) = 0.93 (1 + r) = 0.985
FV = 12,000 x 1.05 x 1.02 x 0.93 x 0.985 = $11,773.07
4. Suppose the value of a $1,000 investment went up 15% in its first year, and down 3% in its second year. What was the average rate of return over the two-year period? Solution: You cannot simply average the two rates. The answer is not 6%. This is because of the effect of compounding: In the second year, the interest from the first year is also earning that 3% decline. You can solve for the average rate in two steps: First find the future value, then use the yx key to find the constant rate for two years which will produce that same future value. The steps are shown below.
Just as a check, try solving for the future value with the TVM keys on your calculator, using a rate per year of 5.6172%. The correct future value does, indeed, result. N
I/Y
PV
FV
2
5.6172
-1,000
CPT $1,115.50
5. Solving for the number of periods is easiest to do using the TVM keys on your calculator. For example, suppose an investor places $950 in an investment which earns interest at the rate of 12% per year. Later, the investment has grown to a value of $1,494.50. How many years did that take? Solution: Solve for N with your calculator. It took four years. N
I/Y
PV
FV
CPT
12
-950
1,494.50
4.00
