# Various Investment-Based Problems

1. A saver places $1,000 in a certificate of deposit that matures after 20 years and that each year pays 4 percent interest, which is compounded annually until the certificate matures.

a) How much interest will the saver earn if the interest is left to accumulate?

b) How much interest will the saver earn if the interest is withdrawn each year?

c) Why are the answers to (a) and (b) different?

2. At the end of each year a self-employed person deposits $1,500 in a retirement account that earns 10 percent annually.

a) How much will be in the account when the individual retires at the age of 65 if the contributions start when the person is 45 years old?

b) How much additional money will be in the account if the individual stops making the contribution at the age 65 but defers retirement until age 70?

c) How much additional money will be in the account if the individual continues making the contribution but defers retirement until age 70?

d) Compare the answers to (b) and (c). What is the effect of continuing the contributions? How much is the difference between the two answers?

3. Graduating seniors may earn $45,000 each year. If the annual rate of inflation is 2 percent, what must these graduates earn after 20 years to maintain their current purchasing power? If the rate of inflation rises to 4 percent, will they be maintaining their standard of living if they earn $100,000 after 20 years?

4. You are offered $900 five years from now or $150 at the end of each year for the next five years. If you can earn 6 percent on your funds, which offer will you accept? If you can earn 14 percent on your funds, which offer will you accept? Why are your answers different?

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#### Solution Preview

1.

a) How much interest will the saver earn if the interest is left to accumulate?

Present Value of deposit=PV=$1000

Number of periods=n=20

Rate of interest=r=4%

Future Value of deposit=FV=PV*(1+r)^n=1000*(1+4%)^20=$2191.12

Interest earned=FV-PV=2191.12-1000=$1191.12

b) How much interest will the saver earn if the interest is withdrawn each year?

Interest earned per year=PV*r=1000*4%=$40

Interest earned in 20 years=40*20=$800

c) Why are the answers to (a) and (b) different?

It is because of the fact that interest is reinvested every year and is added to principal amount in the first case. So, earnings are more.

2.

a) How much will be in the account when the ...

#### Solution Summary

There are four investment based problems. Solutions to these problems depict the methodology to calculate present and future values.

Considerations for Investments

139 #1, 5 (under questions sections), pg. 140 #2, 3 (under problems section)

1#. Comment on the following statements:

a. "Because our new expansion project has the same systematic risk as the firm as a whole, we need do no further risk analysis on the project."

b. "Our company should accept the new potash mine project at Moosejaw. The cost of additional loans to fund the project is 12 percent, and our simulations lead us to expect a 14 percent return from the project."

c. "It is difficult to decide whether to spend $10 million to reopen our mine because the price of gold is so uncertain. However, if we assume the price of gold grows at an average of 5 percent a year with a standard deviation of 20 percent a year, simulation indicates the mine has an average NPV of $500,000. Therefore, we should reopen."

5# what is the advantage of using certainty-equivalent cash flows instead of risk-adjusted discount rates to calculate the NPV of an investment project?

#2 In early 1990, Boeing Co. decided to gamble $4 billion to build a new long-distance, 350-seat wide-body airplane called the Boeing 777. The price tag for the 777, scheduled for delivery beginning in 1995, is about $120 million apiece. Assume that Boeing's $4 billion investment is made at the rate of $800 million a year for the years 1990 through 1994 and that the present value of the tax write-off associated with these costs is $750 million. Based on estimated annual fixed costs of $100 million, variable production costs of $90 million apiece, a marginal corporate tax rate of 34 percent and a discount rate of 14 percent, what is the break-even quantity of annual unit sales over the Boeing 777's projected 15-year life? Assume that all cash inflows and outflows occur at the end of the year.

3# The recently opened Grand Hyatt Wailea Resort and Spa on Maui cost $600 million, about $800,000 per room, to build. Daily operating expenses average $135 a room if occupied and $80 a room if unoccupied (much of the labor cost of running a hotel is fixed). At an average room rate of $500 a night, a marginal tax rate of 40 percent, and a cost of capital of 11 percent, what year-round occupancy rate do the Japanese investors who financed the Grand Hyatt Wailea require to break even in economic terms on their investment over its estimated 40-year life? What is the likelihood that this investment will have a positive NPV? Assume that the $450 million expense of building the hotel can be written off straight line over a 30-year period (the other $150 million is for the land which is not depreciable) and that the present value of the hotel's terminal value will be $200 million.

4#

Compare the assumptions underlying Arbitrage Pricing Theory with those underlying the mean-variance Capital Asset Pricing Model. Which set of assumptions seems more realistic to you? Why?