Part 3: Comparing funds at different times

equation 1: F=P(1+i)^n

F is future value P is present value i is the interest rate per period

n is the number per periods

equation 2: P=A( ((1+i)^n-1)/ (i(1+i)^n) )

equation 3: F=A( ((1+i)^n-1)/ (i) )

At times, we need to compare projects, or make choices between multiple options. However, we cant directly compare the costs because the amounts are at different times. In cases like this, we must first find the equivalent values of the options at the same time, then we can make a direct comparison.

The time that we choose is not important, as long as all values are set to the same time.

12. Suppose you need to choose between two investments:

Project A will return 2000 in 10 years Project B will return 1500 in 7 years

If you value your capital at 12% per year, which is the more attractive investment?

Since you have two amounts of money at different times (year 7 and to compare them at the same time. Here are some possible methods:

(a) Compare at time 0: Find the values of project A, and project right now). Choose the larger project.

(b) Compare at time 10: Find the value of project B in 10 years. since there is 3 years between years 7 and 10. Choose the larger

(c) Compare at time 7: Find the value of project A at 7 years. $1423) Choose the larger project.

13. Consider the following career paths:

After your bachelors degree (in year 2020), you get a job right $70,000 per year. If you plan to work from now until retirement, you work for 45 years.

Alternatively, you spend 6 years getting a Masters and Phd, and you get a job that pays $100,000 per year starting from 2026. Since you had to spend an extra 6 years in school, if you still want to retire at the same time, your career is 39 years.

Ignoring the cost of tuition, if you value your capital at 5% per year, should you go to grad school or not?

In this example, if you choose to use equation 2, you still cant compare the costs directly, because the present value of the graduate salary is still 6 years in the future from the bachelors salary.