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# Applying the Time Value of Money

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Applying Time Value. You can buy property today for \$3 million and sell it in 5 years for \$4 million. (You earn no rental income on the property).
a. If the interest rate is 8 percent, what is the present value of the sales price?
b. Is the property investment attractive to you? Why or why not?
c. Would your answer to (b) change if you also could earn \$200,000 per year rent on the property?

Applying Time Value. You invest \$1000 today and expect to sell your investment for \$2000 in 10 years.
a. Is this a good deal if the discount rate is 6 percent?
b. What if the discount rate is 10 percent?

Retirement Savings. You believe you will spend \$40,000 a year for 20 years once you retire in 40 years. If the interest rate is 6 percent per year, how much must you save each year until retirement to meet your retirement goal?

Retirement planning. A couple thinking about retirement decide to put aside \$3000 each year in a savings plan that earns 8 percent interest. In 5 years they will receive a gift of \$10,000 that also can be invested.
a. How much money will they have accumulated 30 years from now?
b. If their goal is to retire with \$800,000 of savings, how much extra do they need to save every year?

#### Solution Preview

Applying Time Value. You can buy property today for \$3 million and sell it in 5 years for \$4 million. (You earn no rental income on the property).
a. If the interest rate is 8 percent, what is the present value of the sales price?

You need to discount the future value to arrive at the PV. Use the PVIF table to get the factor. For 5 years and 8% it is 0.681. The PV is 4,000,000X0.681=2,724,000.

b. Is the property investment attractive to you? Why or why not?

It is not an attractive investment. Since the PV at 8% is lower than the cost price, it would imply that the rate of return on the property is lower than 8%. Therefore I am better off investing the money at 8% than investing in the property.

c. Would your answer to (b) change if you also could earn \$200,000 per year rent on the property?

We need to find the PV of the rental income. This is an annuity, we use the PVIFA table to get the factor. For 5 years and 8% it is ...

#### Solution Summary

The solution has various time value of money problems dealing with retirement planning, present value and discount rates.

\$2.19