# 5.3 Review Exercises

### Chapter 5 Review Exercises

- Jeremy is thinking of starting up a candle manufacturing business. The initial outlay for equipment, moulds, and other required production equipment is [latex]\$15,000[/latex]. Working part time on this hobby business, Jeremy estimates that he will lose [latex]\$2,000[/latex] in the first year, break even in the second year, and earn annual profits of [latex]\$5,000[/latex], [latex]\$10,000[/latex], and [latex]\$15,000[/latex] in subsequent years. After the five years, he hopes to sell the business to an investor for [latex]\$17,500[/latex]. If his cost of capital is [latex]8.25\%[/latex] compounded annually, should he pursue this venture? Provide net present value calculations to support your answer.

**Solution**NPV=[latex]\$16,241.50[/latex]; pursue venture

- A company pursues all projects that exceed its [latex]15\%[/latex] cost of capital. Project “Affinity” is available to the company with an initial investment of [latex]\$655,000[/latex]. Forecasted annual profits are expected to be [latex]\$200,000[/latex] for the first three years and [latex]\$160,000[/latex] for the subsequent three years. Based on the [latex]IRR[/latex], should the company pursue Project “Affinity”?

**Solution**IRR=[latex]17.47\%[/latex]; pursue project

- Coca-Cola is considering two new flavours—cherry and vanilla—for expansion of one of its product lines. Based on historical and competitive information, the cherry flavour isn’t quite as popular as the vanilla flavour, but it will endure in the market longer. Both options require an investment of [latex]\$2.25[/latex] million in equipment and modifications. The cherry flavour is expected to have annual profits of [latex]\$750,000[/latex] for the first two years and [latex]\$500,000[/latex] for five more years. The vanilla flavour is expected to initially have annual profits of [latex]\$950,000[/latex] for two years, [latex]\$650,000[/latex] for two years, and [latex]\$250,000[/latex] for the last three years. The cost of capital is [latex]16\%[/latex]. Calculate the [latex]NPV[/latex] for each flavour. Which flavour should Coca-Cola launch?

**Solution**[latex]NVP\;\text{of Cherry}=\$170,590.69[/latex]; [latex]NPV\;\text{of Vanilla}=\$360,483.17[/latex]; launch Vanilla

- A saleswoman informs the head librarian that investing in her new automated library product is a steal at [latex]\$103,000[/latex]. Before purchasing, the head librarian investigates the benefits of the automated product, which is expected to have a useful life of seven years and a [latex]15\%[/latex] cost of capital. Each year, [latex]\$24,000[/latex] in labour savings and reduced book shrinkage is projected. However, the automated products require regular maintenance of [latex]\$1,000[/latex] in the first four years and [latex]\$2,000[/latex] in the last three years. Electricity bills will also rise by [latex]\$1,500[/latex] each year in the first three years and [latex]\$2,100[/latex] each year in the last four years. Calculate the [latex]NPV[/latex] for this product. Is the saleswoman correct? Should the automated system be purchased?

**Solution**[latex]NPV=-\$15,982.73[/latex]; do not pursue automation

- Hershiser has been researching different methods of management leadership that are designed to increase employee motivation and performance. If he pursues a new leadership style, it will require an investment of [latex]\$165,000[/latex] to take the training. A new executive assistant will be hired at a cost of [latex]\$55,000[/latex] annually with expected raises of [latex]5\%[/latex] each year. The techniques and tactics from the style are expected to have an impact on employees for five years before needing to be refreshed and updated with more modern techniques. Increased motivation and performance will produce net profits of [latex]\$100,000[/latex] in the first year, rising by [latex]10\%[/latex] in each subsequent year.
- Calculate the internal rate of return.
- If the cost of capital is [latex]10\%[/latex], should Hershiser take the management leadership course?

**Solution**[latex]IRR=22.36\%[/latex]; take course

- Mariners Inc. in Halifax has the option to purchase only one of two available offshore fishing rights. Both rights are available for purchase on a four-year contract before they have to be renewed.
- Fishing right #1 costs [latex]\$600,000[/latex] to acquire, and [latex]\$64,000[/latex] is needed in new equipment to harvest the fish in the area. For each of the first two years, [latex]\$21,000[/latex] will be spent on equipment maintenance and replacement followed by [latex]\$33,000[/latex] in both of the last two years. Annual profits are expected at [latex]\$300,000[/latex].
- Fishing right #2 costs [latex]\$400,000[/latex] to acquire, and [latex]\$82,000[/latex] is needed in new equipment, which requires annual costs of [latex]\$30,000[/latex] for each of the first two years and [latex]\$41,000[/latex] for both of the last two years. Annual profits are expected to be [latex]\$250,000[/latex].

Calculate the net present value for both projects if the cost of capital is [latex]14\%[/latex]. What decision do you recommend?

**Solution**[latex]NPV\;\text{of #}1=\$133,721.11[/latex]; [latex]NPV\;\text{of #}2=\$145,079.14[/latex]; choose fishing right #2.

- The following projects are available, but only one can be chosen. The cost of capital in all cases is [latex]16\%[/latex].
- Project A requires an initial investment of [latex]\$180,000[/latex] followed by profits of [latex]\$30,000[/latex] in years one to four, [latex]\$40,000[/latex] in years five to seven, and [latex]\$50,000[/latex] in years eight to ten with a residual value of [latex]\$100,000[/latex] in year ten.
- Project B requires an initial investment of [latex]\$335,000[/latex] followed by profits of [latex]\$65,000[/latex] in years one to three, [latex]\$85,000[/latex] in years four to six, and [latex]\$110,000[/latex] in years seven to eight with a residual value of [latex]\$60,000[/latex] in year ten.
- Project C requires an initial investment of [latex]\$372,000[/latex] followed by profits of [latex]\$150,000[/latex] in years four to nine and a residual value of [latex]\$70,000[/latex] in the tenth year.

- If the cost of capital is [latex]16\%[/latex], calculate the net present value for each project. Which project should be selected?
- If the cost of capital is [latex]11\%[/latex], calculate the net present value for each project. What decision should be selected?

**Solution**a. [latex]NPV\;\text{of A}=\$15,962.27[/latex]; [latex]NPV\;\text{of B}=\$19,359.83[/latex]; [latex]NPV\;\text{of C}=-\$2,034[/latex]; choose Project B b. [latex]NPV\;\text{of A}=\$71,533.63[/latex]; [latex]NPV\;\text{of B}=\$97,566.83[/latex]; [latex]NPV\;\text{of C}=\$116,652.84[/latex]; choose Project C

- The Banff Gondola is looking to increase its operational capacity through modifications to its gondola equipment. If it invests [latex]\$2.3[/latex] million it can upgrade the motors, strengthen the necessary supports, and add an additional cable car to its line. The expected life of the project is eight years before the equipment will need to be replaced. Annual increased maintenance costs are [latex]\$50,000[/latex] at the end of every year for four years and then [latex]\$100,000[/latex] at the end of every year during the last four years. Because of construction and down times, Banff Gondola is forecasting a loss of [latex]\$415,000[/latex] in the first year. Afterwards, it projects that the equipment will result in increased profits of [latex]\$850,000[/latex] per year. Calculate the internal rate of return for the project.

**Solution**[latex]IRR=16.07\%[/latex]

#### Attribution

“8.3 Review Exercises” from Business and Financial Mathematics by Valerie Watts is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

“Chapter 15 Summary” from Business Math: A Step-by-Step Handbook (2021B) by J. Olivier and Lyryx Learning Inc. through a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License unless otherwise noted.