# Extra Problems

The following is a list of problems for giving the user of this book an extra opportunity to sharpen the application of financial analysis tools.

1-Production equipment is bought at an initial price of \$10,000. The annual operation and maintenance cost is \$100. The salvage value at the end of the 15-year life is \$500.

Using MARR of 10% calculate:

a. the net present worth b. the equivalent uniform annual worth

2-Equipment is bought for an initial cost of \$20,000. Its operation will result in a net income of \$6,000/Yr for the first year, increasing by \$1,000 each year after year one. At the end of the fifth year the equipment is sold for \$5,000. The prevailing interest rate for the next five years is estimated at 10%

a. Draw the cash flow diagram for this project.

b. For this project calculate

1. The NPW

2. The EUAW

### 3. The NFW

c. Another model of the equipment with the same initial price and annual cost brings in an income of \$1,100 per month but has no salvage value. What is the rate of return for this project?

3 -The following two proj ects are recommended for investment:

a. Initial investment \$800K, annual income \$400K

b. Initial investment \$1,500K, annual income \$700K

The lives of both projects are five years. The projects are in a tax-free zone and the inflation is considered to be negligible. The investor has a MARR of 30%. He comes to you for advice and asks you to use the ROR method and make a recommendation. What would you recommend?

4- Mr. ''X", a friend of yours, is asked to invest in the following project: installation and operation of a facility with a life span of five years. The initial investment is \$90M. It will have a net profit of \$25M/Yr the first two years and \$30M/Yr in years 3, 4, and 5. At the end of year 5 it has to be disposed of at a cost of \$10M with no resale value.

a. If he has the money and his opportunity cost of money is 10% (i=10%), would you advise him to invest or not? Yes? No? Why? Explain.

b. If he can only put down \$33M but his bank will extend him a loan for the rest of the initial investment to be used on this project, at 15% in a way that he has to pay it back in equal installments at the end of each of the five years with no collateral, would you advise him to take the loan and invest? Yes? No? Why? Explain.

5-An investment group is considering building a multilevel parking garage in the downtown of a city. They received three proposals. Proposal A is for building a 2-level garage, proposal B is for a 4-level garage, and proposal C is for a 6-level garage. The financial situations estimated for the three proposals are shown below. Their cost of money is 10% annually. Using the NPW method, perform the financial analysis and make your recommendation as to which of the proposals, if any, they should accept.

 Data Proposal A Proposal B Proposal C Initial Cost \$60,000 \$100,000 \$150,000 Annual Revenue \$52,000 \$75,000 \$80,000 Annual Expense \$22,000 \$25,000 \$27,000 Intended Life 3 years 6 years 6 years Estimated Resale \$30,000 \$40,000 \$45,000

6- A Midwestern state is considering building a stretch of 2-lane toll highway between two points. It will cost \$2 million and will bring an annual toll revenue of \$300,000 a year. The cost of operation and maintenance will be \$6,000 annually. If they build a 4-lane divided highway, the cost will be \$3 million but will increase the toll revenue to \$410,000 a year. The cost of maintenance and operation of the 4-lane highway will be \$10,500 a year. They use a 15 year analysis period and 9% MARR. Should they build a 4-lane or a 2-lane or a 2-lane highway? Perform the financial analysis using the rate of return method.

7- An investor in Maryland is offered two investment opportunities. Project A is to invest in a small printing operation consisting of a high-speed printing press. The initial cost of the press including installation is \$60,000. The press costs \$18,000 per year to operate and will bring in an annual income of \$48,000. However, the productive life of this press is only three years and can be sold at \$24,000 at the end of year 3 to a secondhand dealer. Project B is a small taxicab operation involving four cars to be purchased at \$30,000 each. The total operation cost of the four cars is \$40,000 per year and the total annual income is \$72,000. The useful life of the taxicabs is six years each and their salvage value is \$9,000 each. If the MARR of this investor is 10%, which one of the projects if any should he accept? Use the NPW method.

8- Thrift Transportation Company wants to bid for a new business involving transporting passengers in a new line between two cities. The company is studying the size of the bus needed for purchase for this new route. The company has three choices:

a. Purchase a 20-passenger bus with a price of \$49,500 that has an operating cost of \$40,000 per year, an estimated life of three years, and a salvage value of \$10,000.

b. Purchase a 40-passenger bus with a price of \$107,000 that has an operating cost of \$75,000 per year, an estimated life of five years, and a salvage value equal to the cost of its removal.

c. Purchase a 50-passenger bus with a price of \$151,000 that has an operating cost of \$95,000 per year, an estimated life of six years, and a salvage value equal to the cost of its removal.

Assume that the bus in all the cases will operate with a full load and that the passenger seat annual income is \$3,000 (i.e., each passenger capacity will bring an income of \$3,000 per year). If the transportation company has MARR of 15%, which of the buses if any should the company buy? Use the ROR method.

9- An investor is being asked to invest in a project with an initial investment of \$3,000 with first year income of \$400 increasing by \$100 every year for five years. His MARR is 5%. If he phones you with this problem when you have no access to anything other than paper and pen, what would be your recommendation to him? Should he accept this proposal or not? Explain your answer.

10- An investor is offered the opportunity of investing \$100,000 in a six year project that will have a net income of \$25,000 per year.

a. If inflation is a constant 4% per year and his after inflation MARR is 10%, should he invest in this project?

b. If he is looking to invest his \$100,000 where he can get an inflation adjusted (i.e., net, after inflation is taken into account) of 12%, what minimum rate of interest he should shop for?

11- Hosbol Corporation purchased a system for \$ 1 million. The net income from operating this system is \$300,000 per year. Assuming a life of five years and no salvage value, what is the Net Present Worth (NPW) of this system? Hosbol uses the double declining balance (DDB) depreciation method, its cost of money is 12%, and its tax rate is 33.33%.

12- The initial cost of equipment is \$1,000,000. Assuming a life of five years and a resale value of

\$200,000, a. Calculate the depreciation and the book value of this equipment for the next seven years. Use both straight-line and DDB depreciation methods.

b. If the equipment is sold at year 4 for \$400,000, what is the capital gain or loss using both of the above mentioned methods of depreciation.

13- An Idaho farmer buys farm equipment for \$120,000. He is using DDB depreciation. The intended life of the equipment is four years and the estimated resale value is \$20,000. If he sells the equipment at the end of the third year for \$15,000, what is the capital gain or loss?

14- Tacoma Shipbuilding Company (TSC) in Tacoma, Washington, is purchasing a machine at \$165,000 for a plate-forming project. Transportation and installation will add \$15,000 to the initial cost. The total initial cost is to be depreciated using a five year life DDB method with an assumed resale or salvage value of \$40,000. The yearly income from this project for the first year is \$60,000 with an associated expense of \$35,000. In the second year, the income increases to \$70,000 with the same expense as the first year. In year 3 income is \$80,000, and increases by \$5,000 each year thereafter. Associated expenses remain at \$40,000 after year two. The operation is terminated at the end of year 5, and the equipment is sold for \$35,000. If TSC has a tax rate of 35% and MARR of 12%, what is the NPW of this operation? Assume as we always do, that the TSC has other profitable operations.

15- ABC manufacturing has a project involving the purchase of equipment for \$35,000 that will increase sales of ABC by \$14,500 per year. The annual operation costs of this equipment for the first three years are \$1,000, \$2,000, \$4,000, respectively. The costs will increase by \$3,500 every year from then on. The equipment is sold for \$5,000 at the end of year 5. The MARR for the owner of this equipment is 10%, their tax rate is 20%, and they use straight-line depreciation assuming a four-year life and a \$10,000 resale value. Determine the after-tax cash flow of this project. What is the after-tax NPW of this project? ABC has other projects going and is very profitable.

LIFETIME WORTH (LTW) ESTIMATION AND CALCULATION