Money Value of Time (12 problems)

A company invests $10,000. It will be repaid in a single sum at the end of 10 years. During the first five years the investment grows by 15% (nominal), compounded monthly. During the second 5 years the rate is 18% growth (nominal) compounded quarterly.

a) How much is the investment worth at the end of 10 years.

b) Calculate the internal rate of return for the entire 10-year period.

Organization A owns a facility that requires $750,000 in renovation and upgrade costs. You take out a 15-year loan with payments at 9% interest. You have just made the 6th annual payment. How much principal do you still have?

Sanders Enterprises, Inc. has been considering the purchase of a new manufacturing facility for $120,000. The facility is to be fully depreciated on a straight-line basis over seven years. It is expected to be in operations for seven years, and that it will have no resale value after the seven years. Operating revenues from the facility are expected to be $50,000 at the end of the first year, and are expected to increase at the rate of 5 percent per year. Production costs at the end of the first year will be $20,000, and they are expected to increase at 7 percent per year. The discount rate is 14 percent. The corporate tax rate is 34 percent. Sanders has other ongoing, profitable operations. Should the company accept the project?

The Big Burrito is planning to purchase a touch screen order system for its drive-thru window that would allow customers to select their order as soon as they arrive. This would reduce customer wait time and increase order accuracy. The touch screen and software would cost the Big Burrito $150,000 and would last five years. There would also be an annual maintenance cost of $5,000. In addition to improved customer service, the Big Burrito would gain two benefits. First, they could totally eliminate the full-time worker who used to accept and enter these orders. His annual salary plus benefits total $30,000 per year. Second, they expect drive-thru sales to increase by $15,000 a year due to improved customer perception and increased through-put. Cost of goods sold is 25 percent of the incremental sales. If the appropriate discount rate is 15 percent and you ignore taxes, should the Big Burrito go ahead with this investment?

Your firm has an opportunity to make an investment of $50,000. Its cost of capital is 12 percent. It expects after-tax cash flows (including the tax shield from depreciation) for the next 5 years to be as follows:

A hazardous waste site will cost your company far into the future. One-time construction costs are $70 million in year 0 and $30 million in year 5. Containment tanks must be replaced every 20 years at a cost of $5 million. O&M costs are $1 million per year. The interest rate is I=10%. What single sum of money must be set aside in year 0 to cover all costs far into the future?

Publix is considering some upgrades to its Distribution Center in Lakeland. Evaluate the proposal below using the Internal Rate of Return approach. Publix’s MARR is 15%.

Should Publix approve this project? Hint: Try 30%.

Conveyor Improvements

Initial cost $150,000

Annual O&M 10,000

Salvage value 45,000

Estimated useful life 20 years

Estimated annual savings 55,000

Sony International has an investment opportunity to produce a new stereo color TV. The required investment on January 1 of this year is $32 million. The firm will depreciate the investment to zero using the straight-line method over four years. The investment has no resale value after completion of the project. The firm is in the 34 percent tax bracket. The price of the product will be $400 per unit, and will not change over the life of the project. Labor costs for Year 1 will be $15.30 per hour and will increase at 2 percent per year. Energy costs for Year 1 will be $5.15 per physical unit and will increase at 3 percent per year. Revenues are received and costs are paid at year-end. Refer to the table below for the production schedule.

The discount rate for Sony is 8 percent. Calculate the NPV of this project.

It is early January 2005. Your company is currently operating a machine you purchased 4 years ago for $1.2m. The machine, which is subject to a 6-year straight line depreciation schedule, has been operating for the past 4 years and will operate for another 6, including the current year. This machine will have a salvage value of $400k. The machine requires periodic maintenance. You still have a service contract with the supplier at the annual cost of $10k; this contract expires at the end of next year, after which you expect to pay an annual cost of $50k for servicing. You are considering the purchase of a new machine to be put in use immediately. It costs $600k, it has the same production capacity as the old one, and it has useful life of 6 years total (including the current year). The new machine is subject to a 4-year straight-line depreciation schedule. At the end of its life it will have no salvage value. The cost of servicing the new machine is 30k per year. The new machine is more efficient and allows you to save $20k a year in production costs. The current resale value of the old machine is $500k. The corporate tax rate is 40%, there is no inflation, and the appropriate discount rate is 14%. Should you replace the machine?

Consider the following two investment alternatives, for which MARR is 10%.

a) If repeatability is assumed, determine the best alternative.

b) If cotermination is assumed and the study period is 9 years, what market value of B at the EOY 9 would make the two alternatives equally attractive?

You start a wind tower manufacturing company. You will sell 65 towers per year. Each tower sells for $300.000.The first cost for investment is $2 million. Annual manufacturing costs are $2600 per ton. Each tower weighs 110 tons.

a) find the NPV to determine if you made a good investment. The MARR is 20% and the study period is five years.

b) what is the simple payback period for this investment>

c) What is the payback period with discounted cash flow for this investment.

Using future worth analysis, which of the following alternatives is the best choice for a hospital project intended to reduce the cost of the sterilization of equipment? Assume a MARR of 15%.

Option A Option B

Initial cost $503,000 $456,000

Installation cost 30,000 25,000

Annual maintenance cost 25,000 18,000

Annual operating cost 100,000 120,000

Salvage value 28,000 20,000

Estimated life 15 years 10 years

Estimated annual savings 350,000 245,000